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Bulletin of the Seismological Society of America
Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequencesusing coda-based methods
--Manuscript Draft--
Manuscript Number: BSSA-D-20-00132R1
Article Type: Article
Section/Category: Observations, Mechanisms and Hazards of Induced Seismicity
Full Title: Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequencesusing coda-based methods
Corresponding Author: Junkee Rhie, Ph.D.Seoul National UniversitySeoul, KOREA, REPUBLIC OF
Corresponding Author's Institution: Seoul National University
Corresponding Author E-Mail: [email protected]
Order of Authors: Gyeongdon Chai, M.S.
Seung-Hoon Yoo, Ph.D.
Junkee Rhie, Ph.D.
Tae-Seob Kang, Ph.D.
Abstract: Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016and November 2017, causing damage near the epicentral areas. We analyze thestress drop scaling of these two earthquake sequences using coda-based methodsand Bayesian inversion. The 2016 Gyeongju earthquake sequence is a typicalearthquake sequence generated by tectonic processes. In contrast, the 2017 Pohangearthquake sequence is believed to be related to fluid injections conducted fordevelopment of enhanced geothermal systems. As the two sequences occurred in thesame tectonic regime, our study provides a good opportunity to compare stress dropscaling between a tectonic earthquake sequence and an earthquake sequenceinfluenced by fluid injections. We found that the stress drops of events in the Pohangsequences are lower than those of the Gyeongju sequence with similar magnitude.Although it is likely that this difference results from focal depth variations, a reduction ofstress drop due to fluid injections cannot be ruled out.
Author Comments:
Suggested Reviewers: Rengin GökLawrence Livermore National [email protected]
William Scott PhillipsLos Alamos National [email protected]
William WalterLawrence Livermore National [email protected]
Adrian OthEuropean Center for Geodynamics and [email protected]
Opposed Reviewers:
Response to Reviewers:
Additional Information:
Question Response
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<b>Key Point #1: </b><br><i>Three keypoints will be printed at the front of yourmanuscript so readers can get a quickoverview. Please provide threeCOMPLETE sentences addressing thefollowing: 1) state the problem you areaddressing in a FULL sentence; 2) stateyour main conclusion(s) in a FULLsentence; and 3) state the broaderimplications of your findings in a FULLsentence. Each point must be 110characters or less (including spaces).
Tectonic (Gyeongju) and possible anthropogenic (Pohang) earthquakes occurred inthe same tectonic regime.
Key Point #2: The stress drop of the Pohang sequence is lower than that of the Gyeongju sequence.
Key Point #3: Low stress drop may be attributed to the fluid injection.
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Dear Editor:
I am submitting the revised research article for publication in the Bulletin of the Seismological
Society of America, titled “Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake
sequences using coda-based methods” by Gyeongdon Chai, Seung-Hoon Yoo, Junkee Rhie, and
Tae-Seob Kang (Manuscript # BSSA-D-20-00132_R1).
Following all of comments by the editor and anonymous reviewers, we revised figures and text for
improving our original manuscript. And we used a professional English editing service to check
the English of the revised manuscript. We hope our revised manuscript concur in the standard of
the Bulletin of the Seismological Society of America.
Thank you for your consideration.
Sincerely,
Junkee Rhie
Seoul National University
1 Gwanak-ro, Gwanak-gu, Seoul, Republic of Korea (08826)
+82 2 880 8172
+82 2 871 3269
Letter to Editor Click here to access/download;Letter toEditor;cover_letter_GC02.docx
Thank you for your manuscript submission to the Bulletin. Please note that I have now received
the two external reviews which I requested. Based on these reviews and my own reading of
your manuscript, I find that it presents very well a detailed and careful analysis, on a topic of
interest for our readership. This being said, the reviewers raised a number of questions and
made several comments which I think that you need to study and address. Consequently, I
recommend that you undertake a careful revision, for the benefit of your work.
Since I appreciate that their reviews are clear and to the point, I don’t believe that it is necessary
to summarize them here. Instead, allow me to add a few remarks of my own:
(a) Based on the referenced information, I am not convinced that Pohang earthquake was
induced, and so its classification as such is rather speculative. The differences in stress behavior
between the two earthquake sequences don’t have to be justified by fluid induced changes. A
depth dependent tectonic stress, supported by the significant depth difference between the two
sequences, can explain your results very well.
We have revised the discussion and conclusion sections after considering your comments.
(b) The presentation flows nicely and it is easy to follow, but I appreciate that the conclusions
and discussion read a little too much like speculation rather than objective material, based on
the results obtained in the analysis. I suggest that you look to remedy this on the one hand by
changing the narrative to remove some of the speculative part, and on the other hand by adding
perhaps some information (results) based on discussions suggested by the reviewers.
We have revised the discussion and conclusion sections after considering your comments.
(c) Table 2 lists location parameters and magnitudes with two decimals, while corner
frequencies and stress drops with four decimals. There is no error information presented for
the location parameters and magnitudes to allow the reader to estimate whether listing the
respective values with decimals is relevant (although I doubt it for the magnitudes). However,
errors are given for the remaining parameters, and listing the values with four decimals is
unnecessary. Note that magnitude is given with two decimals throughout the manuscript, while
stress drops are presented elsewhere with only two decimals. You may want to look into this,
ensuring both relevance and consistency.
We have revised Table 2 to show the precision of the parameters used in this study to two
decimals places. However, we have not changed the presentation of the location parameters
because they were adopted in their original form from other studies.
(d) For text and figures: you are often using “main” and “fore” as they would be nouns, which
they are not. I suggest that you use “main shock” and “foreshock”.
We appreciate your comment and have revised the manuscript accordingly.
(e) Figures are generally well done, but I suggest that you check the following:
Fig 2: indicate what colours represent;
Fig 4: use only symbols for source parameters, without add their full names;
Fig 6a,b: I don’t see why colours are needed here, but if you insist to have them, let the reader
know in the caption;
Fig 7b: indicate the legends that you indicated in 7a.
We have modified these figures to include your suggestions.
Reviewer #1: Review of BSSA-D-20-00132
Response to Reviews
"Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake sequences using coda-
based methods" by Chai et al.
This is a well written paper comparing and contrasting the spectral and inferred stress drop
characteristics of two moderate earthquake sequences in South Korea. Given the sequences
have different average depths and mechanisms, and one of these sequences is related to
geothermal fluid injection, this study will be of high interest to the seismological community
and BSSA readers. I recommend this paper be published after addressing the relatively minor
comments below.
The paper uses coda envelopes to estimate source spectra (e.g. Mayeda et al 2003). This has
advantages in getting good azimuthally averaged source spectra, which is helpful given the
network is mostly west of the events. The authors might wish to mention this when discussing
how the coda measures are more stable.
We appreciate your kind suggestion and have added the following sentence in the revised
manuscript (Lines 195-198) to incorporate this information.
Because the excitations of the coda waves are nearly insensitive to the radiation pattern
(Mayeda et al., 2003), we were able to obtain azimuthally averaged source spectra, even
though the stations were mainly located westward of the events.
A challenge with using coda is its amplitude dependence on depth, particularly for shallow
events with depths less than say 3-5 km (e.g. Mayeda and Walter, JGR 1996; Walter et al GRL
2017). The authors need to provide some more details on if they are using the same envelope
shapes for the both earthquake sequences (which may be fine if they don't show much
variation).
Of greater importance is the authors should be using or testing different site and excitation
corrections for the different earthquake sequences. See the comments at lines 74-101 below.
We used the same coda envelopes for both sequences because there were no significant
differences in the coda envelope shapes between the two sequences (Please refer to Figure R1).
However, we separately derived the site and source excitation terms for the Gyeongju and
Pohang sequences.
Figure R1. Coda envelopes recorded at BUS2 station for GJ main shock (Mw 5.58), GJ
foreshock (Mw 5.13), and PH main shock (Mw 5.44).
There are other ways to get at stress differences between events than the two methods used
here. For example, methods by Peter Shearers and colleagues and methods looking at spectral
ratio levels the second author here Seung-Hoon Yoo has been involved in previously. Given
the highest frequency studied here is 14 Hz perhaps it is not high enough to look at spectral
ratio levels? This area could use a little more discussion in the paper.
We agree that 14 Hz may be too low to constrain fc for very small events; however, in our
study, we did not analyze very small events that have fc higher than 14 Hz. From Table 2, it is
seen that the highest fc estimated in our study is ~6 Hz. Therefore, we believe that 14 Hz is
sufficiently high for our study.
Finally, the differences in stress behavior between the two sequences is quite interesting. Given
the different mechanisms for sequences close in space it implies either depth dependent
tectonic stress or fluid induced changes in tectonic stress. Perhaps this is a topic better covered
in other papers, but it could use some more discussion here.
Strike slip and thrust earthquakes coexist in the study area, leading us to believe that the
different faulting types are due to depth-dependent tectonic stress and fault geometry (strike
and dip).
Detailed comments:
Line 32 - which event is this ML 5.8, "the largest instrumentally recorded earthquake in this
region"? Should give at least a date here.
We have rephrased the sentence as follows in the revised manuscript (Lines 32-33):
However, the largest earthquake recorded in this region with instruments is the ML 5.8
Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration;
KMA).
Lines 41 - Would be helpful to put labels on inset boxes in Figure 2 if possible, like a "GJ" and
"PH". In Figure 2 caption note that ISOLA is software and give references (Sokos and
Zahradnik, 2008; Vackář et al., 2017) there.
We have modified Figure 2 and its caption as suggested.
Line 51-53 - accuracy in the determination of the depths of these earthquakes is important.
How good is the depth determination? Are there seismic stations within a focal depth of the
events to really constrain the depth well?
We agree that the accuracy of the determined focal depth is important in our study. For the GJ
main shock, there was no observation at close distance. However, the focal depths of the
aftershocks are very well constrained using the data from the dense aftershock monitoring
networks deployed in the epicentral area. Because the focal depths of the main shock and
aftershocks are similar, we are confident that the depth estimate of the main shock has an
acceptable degree of accuracy. For the PH main shock, many stations in the epicentral area
were in operation at the time of the event. In addition, the estimates of the focal depths reported
by different researchers, including the one cited by us, are more or less consistent.
Lines 61 - It is asserted that both earthquake sequences occurred in the same tectonic regime,
but the mechanisms are different - GJ being strike-slip and PH being more thrust. Authors may
need to discuss more. Is this because the largest tectonic stresses are similar and horizontal and
vertical so both strike-slip and thrust mechanisms are common? Or if the fluid injection
changed the local stress regime and caused the change from tectonic strike-slip mechanism to
thrust mechanisms for the PH sequence.
We do not believe that the fluid injection changed the local stress regime in the Pohang area.
In general, the direction of SHmax (sigma 1) in the Korean Peninsula is spatially homogeneous
and nearly parallel to the E-W direction. Therefore, events with strike slip and thrust
mechanisms are commonly observed in both regions (GJ and PH). We have clarified in the text
that both these mechanisms are popular in the study area.
Strike slip and thrust mechanisms are both popular mechanisms in our study area (Lines
54-55)
Lines 74-101 - Are the authors using the same envelopes for both sequences or did they develop
one set for the PH and a different set of the GJ? If so need to state this explicitly. If not, why
not? Given the different average depths of the sequences and the strong dependence of coda
excitation on depth, this seems important to do to get the right answer.
Earthquakes causing the two seismic sequences depicted in Figure R1 have enough similarities
in the shapes and decay rates of their coda envelopes to enable measurement of the coda
amplitudes using the same envelope function. Therefore, we have used the same coda
envelopes for both sequences. However, we derived site correction terms separately for the two
sequences to account for the different coda excitations due to the different source depths. We
have revised the manuscript to clearly indicate our use of the coda envelope shape.
Because the coda envelope shapes for both sequences are similar, we used the same set of
reference coda envelopes for both sequences (Lines 84-85).
Line 116 - I would argue only applicable to events with similar Hypocenters (not epicenters)
and significant differences in magnitude. The depths cannot be very different due to the depth
dependence of coda for shallow events.
We appreciate your comment and have changed “epicenters” to “hypocenters” accordingly
(Line 120).
Lines 198-204 - So what is going on here? Why the discrepancy between the ratio and spectral
results? Are the new corner frequencies within the error bounds in the ratios and they just could
not be determined very well? The Figure 6 caption needs to better explain what figure 6c is,
it's the spectra determined use the ratio corner frequencies.
To clarify our analysis, we have added some details and modified the caption of Figure 6.
First, we determined the Brune spectra, which fit the corrected NDCA for each event,
and then recalculated the site correction terms by averaging the differences between the
Brune spectra and the NDCAs for the three events (Lines 211-214).
(c) Yellow dashed lines indicate the Brune spectra calculated using the fc values from
the spectral ratios. Symbols (open triangles, squares, and circles) show the NDCAs for
stations after revision using the recalculated site correction terms. [Caption of Figure
6]
Lines 211-212 - What is highest resolved frequency here? Based on Table 1 its 14 Hz. Is this
20 Hz Nyquist frequency but then limited to 14 Hz analysis? Need to provide these details. If
you cannot sample high enough in frequency, then may not be able to get accurate corner
frequency for small events. Or is the Signal-to-noise ratio poor at high frequencies? Paper
would benefit form some more details.
We agree that higher frequency envelopes are required to constrain the fc values of very small
events. However, this does not affect our study because we are not interested in very small
events. The minimum magnitude of interest in this work is around 3, and its corner frequency
is much lower than 14 Hz (~ 6 Hz), as shown in Table 2.
Line 217-221 - So the PH sequence might follow a different stress drop versus magnitude trend
than the GJ sequence in addition to the PH sequence having systematically lower stress drops
because of its shallower depth. Not all earthquake sequences follow a pattern of increase
between 4.5 and 5.5 - see for example the Parkfield sequence which shows little change in
stress drop.
Thank you for your comment. We have added a new sentence to note that there was a study
reporting a non-increasing trend in a given magnitude range.
No significant increase in the stress drop for the specific magnitude range was reported for
the Parkfield sequence (Lines 232-233)
Lines 264-267 - I don't understand this comment. If depth rather than fluid injection is the main
cause of the lower stress drop of the PH sequence, then all the events should be low stress
regardless of if they are directly or indirectly related to fluid injection.
Our comment was intended to convey that the difference in focal depth may not fully explain
the variation in stress drop for the PH sequence. We found that the stress drop of the PH
sequence was lower than that of the GJ sequence. Furthermore, two events in the PH sequence
had much lower stress drops, and they were more likely to be affected by the fluid injection:
the main shock and an event that occurred during the injection period. With the exception of
these two events, all the other events were aftershocks. However, we are not sure whether the
change due to fluid injection necessarily explains the lower stress drops for these two events.
Line 507 - very happy to see this full table of events and their parameters included.
Thank you for the encouraging comment!
Reviewer #2: Nice study, definitely recommend for publication. I have few comments about
the flow and clarification of the paper.
1) Coda envelope ratio method provides ground truth events (mainly the stress drop) to feed
into the NDCA Mw and (sigma,fc) calculation for the site term improvement. What is
presented here is to sort of feeding values in between two methods and correcting. You may
want to state this or rephrase it at the beginning.
We have added a sentence in the revised manuscript to address this concern.
We used the information obtained from the ratio of the NDCAs to define the site correction
terms, and then applied these terms to study the source spectra of the events. (Lines 123-
124)
2) Ratio method may also be suffering from trade off (smaller event Mw inaccuracy may affect
fc)
We agree that the fc values determined from the ratio method can be inaccurate for smaller
events. For this reason, we only used the fc values of large events for further analyses.
3)The paragraph around L151-153 needs further clarification. What is "final values for only
large events"?
The final fc values estimated for large events are better constrained than those for small events
because of their large SNRs. Therefore, we only used the fc values of large events to define the
correction terms. To clarify this, we have rephrased the first sentence as follows.
Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their
large signal-to-noise ratios, we only used the fc values of large events for further analyses
(Lines 157-159)
4) L200-203 Figure 6 b,c: How was the recalculation estimated? Spectral ratio fitting or
NDCA? There is no information about it.
The detailed process of recalculation is as follows: 1) Correct the NDCAs for the three events
using the site terms determined by the spectral ratios. 2) Find the best fitting Brune spectra for
the three events. 3) Recalculate the site terms by measuring the differences between the
observed NDCAs and the best fitting Brune spectra. We have added the following sentence to
clarify this in our revised manuscript and have also changed the caption of Figure 6.
First, we determined the Brune spectra, which fit the corrected NDCA for each event,
and then recalculated the site correction terms by averaging the differences between the
Brune spectra and the NDCAs for the three events (Lines 211-214).
(c) Yellow dashed lines indicate the Brune spectra calculated using the fc values from
the spectral ratios. The symbols (open triangles, squares, and circles) show the NDCAs
for stations after revision using the recalculated site correction terms. [Caption of
Figure 6]
We appreciate your comments!
1
Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake 1
sequences using coda-based methods 2
3
Gyeongdon Chai1, Seung-Hoon Yoo2, Junkee Rhie1*, and Tae-Seob Kang3 4
5 1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, South 6
Korea 7
2Applied Research Associates, Inc., Arlington, VA 22203, USA 8
3Division of Earth Environmental System Science, Pukyong National University, Busan 9
48513, South Korea 10
11
Abstract 12
Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016 and 13
November 2017, causing damage near the epicentral areas. We analyze the stress drop 14
scaling of these two earthquake sequences using coda-based methods and Bayesian inversion. 15
The 2016 Gyeongju earthquake sequence is a typical earthquake sequence generated by 16
tectonic processes. In contrast, the 2017 Pohang earthquake sequence is believed to be related 17
to fluid injections conducted for development of enhanced geothermal systems. As the two 18
sequences occurred in the same tectonic regime, our study provides a good opportunity to 19
compare the stress drop scaling between a tectonic earthquake sequence and an earthquake 20
sequence influenced by fluid injections. We found that the stress drops of events in the 21
Pohang sequences are lower than those of the Gyeongju sequence with similar magnitude. 22
Although it is likely that this difference results from focal depth variations, a reduction of 23
stress drop due to fluid injections cannot be ruled out. 24
25
Annotated Manuscript Click here to access/download;AnnotatedManuscript;ChaiGD.BSSA.R01_GC08_JR01_annotated.docx
2
Introduction 26
A study of the scaling relationship between magnitude and stress drop for earthquakes 27
occurring in a given region is important not only for understanding the fundamentals of the 28
earthquake rupture process but also for mitigating earthquake damage by precisely predicting 29
the ground motions of possible future earthquakes. There are many historical documents on 30
the occurrence of large earthquakes (M >6) in the southeastern part of the Korean Peninsula. 31
However, the largest earthquake recorded in this region with instruments is the ML 5.8 32
Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration; KMA). 33
This region is susceptible to large earthquakes. Efforts toward mitigating the seismic risk in 34
this region are very important because this region has valuable infrastructure, including 35
nuclear power plants and cities with dense populations. In this study, we analyze the stress 36
drop scaling of two moderate earthquake sequences that occurred in the southeastern Korean 37
Peninsula using the analysis of coda waves, which is known to be more stable than the 38
analysis of direct waves (Mayeda et al., 2007; Yoo et al., 2010). 39
The two earthquake sequences considered in this study are the 2016 Mw 5.6 Gyeongju (GJ) 40
earthquake and the 2017 Mw 5.5 Pohang (PH) earthquake sequences (Figures 1 and 2). The 41
distance between the epicenters of the GJ and PH main shocks is approximately 43 km, and 42
both earthquakes occurred in the Gyeongsang Basin. The Gyeongsang Basin is a tectonic unit 43
classified based on the tectonic evolution in the Korean Peninsula. Although the Pohang 44
Basin, where the PH sequence occurred, had been tectonically active until recently compared 45
to the epicentral region of the GJ sequence, the current tectonic environment for generating 46
earthquakes in both regions should be similar because they belong to the same tectonic unit 47
(Park et al., 2007; Soh et al., 2018). We can also expect that tectonic stresses in both regions 48
are similar because they are spatially close to each other. However, the reported source 49
characteristic of the two sequences, especially the main shocks, are quite different. The focal 50
3
depths of the GJ and PH main shocks are 14.5 km (Woo et al., 2019a) and 4.27 km (Lee et al., 51
2019; Woo et al., 2019b), respectively. The focal mechanism for the GJ main shock 52
determined by moment tensor inversion is strike slip. The faulting style of the PH main shock 53
is strike slip with a significant thrust component. Strike slip and thrust mechanisms are both 54
popular mechanisms in our study area (Rhie and Kim, 2010). The most important difference 55
between the two earthquakes is whether fluid injection affected the occurrence of earthquake. 56
The GJ main shock is a natural earthquake generated because of tectonic stress, whereas the 57
PH main shock is a “runaway” earthquake triggered by stress perturbation caused by 58
injecting fluids for the development of enhanced geothermal systems (EGS) (Ellsworth et al., 59
2019). The objective of this study is to show that different mechanisms between tectonic and 60
“runaway” earthquakes can be revealed by comparing source parameters of the GJ and PH 61
earthquake sequences, which occurred in the same tectonic region. 62
63
Data and Methods 64
Data used in this study are seismic waveforms recorded at broadband stations operated by the 65
Korea Meteorological Administration (KMA) and the Korea Institute of Geoscience and 66
Mineral Resources (KIGAM) (Figure 1), and they were divided into two sets for different 67
research purposes. The first data set was used to define a reference coda envelope, which is 68
necessary for calculating the source spectrum. For the lower frequency range (0.05–8.0 Hz), 69
we used waveforms from earthquakes with magnitudes greater than 4.0 that occurred in and 70
around the Korean Peninsula between 2006 and 2012. The sampling rate of this data set is 20 71
Hz. For the higher frequency range (8.0–14.0 Hz), we used waveforms from earthquakes in 72
the 2016 Gyeongju sequence with magnitudes greater than 3.0; their sampling rate is 100 Hz. 73
The second data set was used for analysis of source spectra for the GJ and PH sequences. 74
4
To determine a reference coda envelope, we defined its theoretical functional form following 75
a previous study (Mayeda et al., 2003) to be 76
𝐸(𝑡, 𝑓, 𝑟) = 𝐻 (𝑡 −𝑟
𝑣(𝑓,𝑟)) (𝑡 −
𝑟
𝑣(𝑓,𝑟))
−𝛾(𝑓,𝑟)
× exp [𝑏(𝑓, 𝑟) (𝑡 −𝑟
𝑣(𝑓,𝑟))], (1) 77
where r, f, and t indicate distance in km, frequency in Hz, and the time elapsed from the event 78
origin time in s, respectively; H is the Heaviside step function; and 𝑣(𝑓, 𝑟) is the velocity of 79
the peak arrival in km/s. Two functions, 𝑏(𝑓, 𝑟) and 𝛾(𝑓, 𝑟), control the shape of the coda 80
envelope. To define the reference coda envelope, we determined 𝑣(𝑓, 𝑟), 𝑏(𝑓, 𝑟), and 81
𝛾(𝑓, 𝑟) from the observed data by following the procedures presented in Yoo et al. (2011). 82
We defined reference coda envelopes for 14 consecutive narrow frequency bands (Table 1, 83
Figure 3). Because the coda envelope shapes for both sequences are similar, we used the 84
same set of reference coda envelopes for both sequences. 85
The relation between the observed and reference coda envelopes can be represented as 86
follows: 87
𝐴𝐶(𝑡, 𝑓, 𝑟) = 𝑊0(𝑓)𝑆(𝑓)𝑃(𝑓, 𝑟)𝐸(𝑡, 𝑓, 𝑟), (2) 88
where 𝐴𝐶(𝑡, 𝑓, 𝑟) , 𝑆(𝑓) , 𝑃(𝑓, 𝑟) , and 𝑊0(𝑓) are the observed coda envelope, site 89
correction, path correction, and S-wave source amplitude, respectively. 90
To measure 𝐴𝐶(𝑡, 𝑓, 𝑟), we removed the instrument response of two horizontal component 91
waveforms to velocity seismograms. A four-pole two-pass Butterworth filter, for which 92
corner frequencies correspond to 14 consecutive narrow frequency bands was applied, and 93
then an envelope for each frequency was calculated using 94
𝐸obs = √𝑣(𝑡)2 + ℎ(𝑡)2, (3) 95
where 𝑣(𝑡) and ℎ(𝑡) are the band-pass-filtered horizontal velocity seismogram and its 96
Hilbert transform, respectively. To distinguish the observed and reference envelopes, we use 97
𝐸obs for the observed envelope. The final observed envelope was calculated by taking the 98
5
logarithm base 10 of two horizontal envelopes and then averaging them. By doing this, we 99
measured 𝐴𝐶(𝑡, 𝑓, 𝑟) for each frequency and epicentral distance. We can see in Eq. (2) that 100
changes in 𝐴𝐶(𝑡, 𝑓, 𝑟) with time for a given frequency and distance should be the same as 101
the changes in 𝐸(𝑡, 𝑓, 𝑟). The difference between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟) is called non-102
dimensional coda amplitude (NDCA), and it can be measured by finding the optimum DC 103
shift, which minimizes the L1 norm between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟). We then compared 104
the reference and observed coda envelopes at each frequency band. 105
Two methods are widely used to study seismic sources using measured NDCA. The first 106
method involves directly estimating 𝑊0(𝑓) by correcting 𝑃(𝑓, 𝑟) and 𝑆(𝑓) from NDCA. 107
The advantage of this method is that it can be used to estimate source spectra of all events in 108
a given region once models for 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are defined. Because source spectra are 109
available, we can estimate M0 and fc, the seismic moment in Newton meters and the corner 110
frequency in Hertz, which are two representative source parameters, but we can also estimate 111
radiated energy. However, unless 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are precise enough, the reliability of 112
estimated source spectra can be low. The second method is to estimate fc only, or fc and M0 113
together, from the ratio of NDCA between two events without calculating the individual 114
source spectrum of each event (Mayeda et al., 2007). This method is based on the assumption 115
that if NDCAs are measured at the identical station and two earthquakes occurred at close 116
locations, 𝑃(𝑓, 𝑟) and 𝑆(𝑓) for both events should be identical and the ratio of NDCA is 117
the same as the ratio of the source spectra. In this case, we do not need to determine 𝑃(𝑓, 𝑟) 118
and 𝑆(𝑓) to apply the method. However, this method is only applicable to event pairs with 119
similar hypocenters but large differences in magnitude. In this study, we are interested in 120
examining the source characteristics of two earthquake sequences, where the earthquakes in 121
each sequence are spatially clustered. Therefore, a combined procedure of the two methods 122
can be applied. We used the information obtained from the ratio of the NDCAs to define the 123
6
site correction terms, and then applied these terms to study the source spectra of the events. 124
The detailed procedure is as follows. First, we selected event pairs with a magnitude 125
difference larger than 1 in each sequence. Total numbers of selected events and 126
corresponding event pairs for the GJ sequence are 9 and 15, respectively, and 6 and 7 for the 127
PH sequence. The maximum distance between epicenters among event pairs is 7 km. Mw for 128
each event was independently calculated using ISOLA (Sokos and Zahradnik, 2008; Vackář 129
et al., 2017) software based on the waveform inversion method (Figure 2). We considered 66 130
stations for our analysis, but the actual number of data points used for each process was not 131
consistent (Figure 1). To estimate fc of both events from the spectral ratio for a given event 132
pair, we used the Bayesian inversion method. A hierarchical scheme was applied to account 133
for data error in the inversion (Bodin et al., 2012; Kim et al., 2016). We assumed that prior 134
probability of Δσ is uniform in the range 10−3 − 103 MPa. Once we selected Δσ, we 135
calculated fc by using the following equation, because M0 of the event is pre-defined: 136
𝑓𝑐 =2.34𝛽
2𝜋 ( 7
16∙𝑀0∆𝜎
)
13
. (4) 137
Equation (4) was derived from the following two equations based on the circular fault model 138
(Eshelby, 1957). Shear wave velocity (𝛽) was set to be 3.5 km/s. 139
Δσ =7
16
𝑀0
𝑟3 (5) 140
𝑟 =2.34β
2π𝑓𝑐. (6) 141
Using fc and M0 of both events, we can define a spectral ratio between two events based on 142
Brune’s source model as follows (Aki, 1967; Brune, 1970; 1971): 143
𝑅(𝑓) =𝑀01[1+(𝑓/𝑓𝑐2)2]
𝑀02[1+(𝑓/𝑓𝑐1)2]. (7) 144
The misfit between the synthetic and observed spectral ratio was measured using the L1 norm, 145
and the likelihood function was defined as 146
7
𝐿 =1
2𝜎× exp [∑
|𝑅syn(𝑓𝑖)−𝑅obs(𝑓𝑖)|
𝜎
𝑛𝑖=1 ], (8) 147
where 𝑅syn and 𝑅obs indicate the synthetic and observed spectral ratio, respectively, and 𝑓𝑖 148
represents the center frequency of a given frequency band. To consider the data error in the 149
inversion, we assumed that 𝜎 has a positive uniform prior probability. We updated model 150
parameters (two stress drops and 𝜎) 200,000 times using the Metropolis-Hastings sampling 151
(MHS) method (Metropolis et al., 1953; Hastings, 1970). After the first half of the 152
calculations, which is considered a burn-in period, we selected 1 sample per every 100 153
calculations to estimate the posterior probability density (PPD) of two values of stress drop 154
(or fc) and 𝜎. For each event pair, we selected the fc with highest PPD. The final fc value for 155
each event was calculated by averaging selected fc values for all event pairs. 156
Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their 157
large signal-to-noise ratios, we only used the fc values of only large events for further 158
analyses. The number of final fc values was three for each of the PH and GJ sequences. Once 159
we determined fc and M0, the theoretical Brune’s source spectrum can be calculated using the 160
following equation: 161
𝑀(𝑓) =𝑀0
(1+(𝑓
𝑓𝑐)
2). (9) 162
For each station, a site correction term can be determined by measuring the difference 163
between the theoretical Brune’s source spectrum and the corresponding NDCA. We note that 164
a site correction term contains 𝑃(𝑓, 𝑟) and 𝑆(𝑓) in Eq. (1). Because we define the site 165
correction terms of individual stations separately for PH and GJ sequences, we can ignore 166
variation in the site correction term with distance. We calculated the difference between the 167
theoretical Brune’s spectrum and the NDCA for each event and then averaged them for each 168
sequence to determine the final site correction term as a function of frequency. Once a site 169
correction term was defined, we calculated the source spectrum for each event by correcting 170
8
NDCA. By averaging the estimated source spectra of each event for all available stations, we 171
calculated the final source spectrum for each event. To estimate the PPD of stress drop (or fc) 172
and Mw from the final source spectrum, we used Bayesian inversion, which is similar to the 173
method previously applied for spectral ratio. We assumed that the stress drop and M0 have 174
uniform prior probability in the ranges between 10–3 and 103 MPa and between –2 and 2 in 175
logarithmic scale about the maximum value of the corrected NDCA, respectively. The 176
parameter fc was determined from a given stress drop and M0. To consider data error, we 177
adopted two parameters, 𝜎𝑓rms and 𝜎𝑓
SD. Here, 𝜎𝑓rms indicates an envelope fitting error 178
when measuring coda amplitudes of observed envelopes at a given frequency and 𝜎𝑓SD is 179
defined as one standard deviation of the site-correction term at the given frequency. The 180
likelihood function is defined as 181
𝐿 =1
2× exp [∑
|𝑀syn(𝑓𝑖)−𝑀obs(𝑓𝑖)|
𝜎𝑓rms+𝜎𝑓
SD𝑛𝑖=1 ]. (10) 182
The same sampling procedure of Bayesian inversion using the MHS method that was used for 183
the spectral ratio method was applied to estimate the PPD of Mw and fc. The PPD of stress 184
drop was also determined from Eqs. (5) and (6). We can technically estimate source 185
parameters of all events with measured NDCA. However, low signal-to-noise ratio of small 186
events can distort the results. Therefore, we used 9 and 6 events with Mw larger than 3.0 for 187
the GJ and PH sequences, respectively. We calculated Brune’s source spectrum using M0 and 188
fc estimated by Bayesian inversion and used this spectrum to calculate a site correction term. 189
190
Results and Discussion 191
We applied coda-based methods and Bayesian inversion to the GJ and PH earthquake 192
sequences. We calculated the reference coda envelopes and compared them with the observed 193
coda envelopes. Figure 3 depicts an example of the comparison between the reference and 194
observed coda envelopes at selected frequency bands. Because the excitations of the coda 195
9
waves are nearly insensitive to the radiation pattern (Mayeda et al., 2003), we were able to 196
obtain azimuthally averaged source spectra, even though the stations were mainly located 197
westward of the events. The final fc value was calculated for each event using the MHS 198
method and the PPD was estimated; for each event pair, we selected the fc with the highest 199
PPD. Figure 4 shows examples of spectral ratios determined for selected events. The 200
calculated difference between the theoretical Brune’s spectrum and the NDCA for each event 201
was averaged for each sequence to determine the final site correction term as a function of 202
frequency, as shown in Figure 5 for three events in the GJ sequence. 203
If the site correction term is well-defined, we can expect the estimated source spectra of the 204
events involved in determining the site correction terms to be consistent with the site-205
corrected NDCA for the same event. In the case of the GJ sequence, we can see that the two 206
values are well-matched, as expected (Figure 6(a)). However, there are significant 207
discrepancies in the PH sequence (Figure 6(c)). The reason for these discrepancies appears to 208
be that the original estimates of fc obtained from the spectral ratio method for the PH 209
sequence are not accurate because the number of applicable earthquakes is insufficient. To 210
overcome this problem, we recalculated the site correction term for the PH sequence. First, 211
we determined the Brune spectra, which fit the corrected NDCA for each event, and then 212
recalculated the site correction terms by averaging the differences between the Brune spectra 213
and the NDCAs for the three events. The corrected NDCA using the recalculated site 214
correction term demonstrates a significantly improved fit to the theoretical Brune’s spectrum 215
(Figure 6(b)). 216
Using coda-based methods and Bayesian inversion, we estimated the PPD of Mw, fc, and 217
stress drop for 12 and 7 earthquakes in the GJ and PH sequences, respectively (Table 2). The 218
stress drop scaling for both the GJ and PH sequences show that stress drop increases with 219
increasing magnitude on the overall scale (Figure 7). The observed trends in stress drop 220
10
scaling cannot be explained by the self-similar model with a constant stress drop (Aki, 1967). 221
The estimates of the stress drop appear to be considerably scattered for smaller earthquakes 222
(Mw < ~3.5) in both sequences. This may indicate that estimates of stress drop for smaller 223
events are not stable because of the low signal-to-noise ratio. The stress drop of the smallest 224
PH event (PH01 in Table 2) is much smaller than that of other events with similar magnitudes. 225
For relatively larger events (Mw >= 4.0) in the GJ sequence, it is likely that the stress drop 226
increases with increasing Mw in a range between Mw 4.5 and 5.5. This observation is 227
consistent with other previous studies using similar coda-based methods (Mayeda and 228
Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; Yoo and Mayeda, 2013). For the 229
PH sequence, we do not observe an increasing trend in the given magnitude range because 230
the stress drop of the PH main shock (PH02) is smaller than those of the shocks of similar 231
magnitude in the GJ sequence. No significant increase in the stress drop for the specific 232
magnitude range was reported for the Parkfield sequence (Allman and Shearer, 2007). 233
Additionally, the stress drops of two other PH events (PH04 and PH07) with Mw larger than 234
4.0 are also smaller than the stress drops of similar-sized GJ events. 235
To summarize the characteristics of stress drop scaling for the two sequences, the stress drops 236
of the PH sequence appear to be smaller than those of the GJ sequence, and two PH events 237
(PH01 and PH02) have much smaller stress drops in comparison with those of events with 238
similar magnitudes in the GJ sequence. The stress drop of PH01 (Mw 3.3) is smaller than that 239
of GJ13 (Mw 3.3) by a factor of approximately 4. The stress drop of PH02 (Mw 5.5) is smaller 240
than that of GJ03 (Mw 5.6) and GJ01 (Mw 5.1) by a factor of 4.3 and 2.5, respectively. 241
Estimates of the stress drops for the GJ and PH main shocks reported by other studies show 242
similar results. Son et al. (2018) reported that the stress drop of GJ03 is 11.2 MPa based on 243
the analysis of the S-wave source spectrum. The mean stress drop of the same event derived 244
from finite fault inversion using the empirical Green’s function method is 23 MPa (Uchide 245
11
and Song, 2018). These values are somewhat larger than our estimate (8.29 MPa). For PH02, 246
Song and Lee (2019) estimated the mean stress drop of PH02 to be approximately 2 MPa 247
from finite fault inversion using InSAR data, and this value is consistent with our result (1.92 248
MPa). We note that PH02 and PH01 are considered anthropogenic earthquakes (Kim et al., 249
2018; Grigoli et al., 2018; Lee et al., 2019; Ellsworth et al., 2019; Woo et al., 2019b). PH01 250
was an induced earthquake, which occurred during a period when fluid injections for EGS 251
development were conducted. PH02 (the PH main shock) is considered a “runaway” 252
earthquake, which implies that its occurrence is affected by fluid injections even though it 253
releases strain energy accumulated through natural tectonic processes (Ellsworth et al., 2019). 254
Therefore, a question arises as to whether the low stress drops of PH02 and PH01 result from 255
the influence of fluid injections. There have been several studies reporting that stress drops of 256
induced earthquakes are smaller than those of tectonic earthquakes (Sumy et al., 2017; Boyd 257
et al., 2017; Hough, 2014). Hough (2014) argued that the stress drops of induced earthquakes 258
are smaller than those of tectonic earthquakes by a factor of 2–10 based on differences in 259
intensity between tectonic and induced earthquakes measured by a “Did You Feel It?” system. 260
Although the difference in the stress drop between the PH and GJ main shocks derived in this 261
study lies within the range proposed by Hough (2014), it is not sufficient to conclude that the 262
low stress drops observed in the PH sequence, especially for PH02 and PH01, are caused by 263
fluid injections. It is well known that the stress drop is controlled by many other factors, such 264
as focal depth, faulting type, and heat flow. Therefore, it is possible that the discrepancy in 265
the stress drop can be attributed to other factors. The PH and GJ main shocks differ in several 266
ways besides fluid injection. First, the focal depth of the PH main shock (4.27 km; Lee et al., 267
2019) is much shallower than that of the GJ main shock (14.5 km; Woo et al., 2019a). 268
Second, while the faulting type of the GJ main shock is nearly pure strike-slip, that of the PH 269
main shock is strike slip with considerable thrust-faulting components. 270
12
Although several studies have found that there is no clear depth dependence of stress drop 271
(Wu et al., 2018; Allmann and Shearer, 2009), most previous studies support the theory that 272
shallow earthquakes have lower stress drops than deep earthquakes (Huang et al., 2017; Oth, 273
2013). Huang et al. (2017) reported that induced earthquakes with deep focal depths (<5 km) 274
show similar stress drops as those of tectonic earthquakes in the central United States and 275
concluded that induced and tectonic earthquakes are not distinguishable based only on 276
differences in stress drop. Therefore, it is possible that the lower stress drop of the PH main 277
shock compared to the GJ main shock is caused only by the difference in focal depth. The 278
difference in focal depth can explain why the stress drops of the PH events are relatively 279
lower than those of the GJ events. Regarding the faulting style of earthquakes, the relations 280
between faulting style and stress drop reported by previous studies are not consistent. In 281
general, it is well-accepted that reverse-faulting earthquakes have higher stress drops (e.g., 282
McGarr, 1984; McGarr and Fletcher, 2002). However, Allmann and Shearer (2009) 283
suggested that the stress drop of strike-slip is higher than that of other faulting types. Our 284
observation shows that the stress drop of the GJ main shock, which has pure strike-slip 285
mechanism, is higher than that of the PH main shock, which has considerable reverse-faulting 286
components; this is consistent with the result presented by Allmann and Shearer (2009). Oth 287
(2013) suggested that stress drop variations are strongly correlated with heat flow variations 288
in crustal earthquakes in Japan. Therefore, heat flows can be another factor that affects stress 289
drop; however, we do not have sufficient information on whether there is a considerable 290
difference in heat flow between the epicentral regions of the GJ and PH sequences. 291
292
Conclusions 293
We analyzed the stress drop scaling of two moderate earthquake sequences that occurred in 294
the same tectonic regime. The stress drop seems to increase with an increasing magnitude in 295
13
both sequences. The observed magnitude dependence in stress drop scaling cannot be 296
explained by a self-similar model with a constant stress drop (Aki, 1967). The scaling of the 297
GJ sequence is similar to the results of other earthquake sequences studied using similar 298
coda-based methods (Mayeda and Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; 299
Yoo and Mayeda, 2013). The characteristic feature is that stress drop rapidly increases with 300
Mw in the range between Mw 4.5 and 5.5. This rapid increase in stress drop is not found in the 301
PH sequence. On average, stress drops of the PH sequence are lower than those of the GJ 302
sequence. Stress drops of PH02 and PH01 are much smaller than the events with similar 303
magnitudes in the GJ sequence. Considering previous studies on factors controlling the stress 304
drop, it is likely that differences in focal depth between the two sequences cause differences 305
in the stress drop. Although the focal depths of all PH events are similar, the stress drops for 306
the two PH events (PH01 and PH02) are particularly lower than those of the other PH events. 307
In addition, these two events are likely to be influenced by fluid injections. It may be inferred 308
that the much lower stress drops for the two events are caused by fluid injection. However, it 309
is not conclusive that the effect of fluid injection is adequate to explain the lower stress drops 310
based on only the observations in our study. 311
312
Data and Resources 313
Waveform data were acquired from seismograph networks and data centers in the region, 314
including those of the Korea Institute of Geology and Mineral Resources (KIGAM) and the 315
Korea Meteorological Administration (KMA) (the event catalog and data are available from 316
authors upon request). Geotectonic lines were obtained from KIGAM 317
(https://mgeo.kigam.re.kr, last accessed March 2017). The figures in this article were 318
generated using generic mapping tools (GMT; https://www.soest.hawaii.edu/gmt/, last 319
accessed March 2017). 320
14
321
Acknowledgments 322
We thank Vanessa Napoli (Applied Research Associates, Inc.) whose comments/suggestions 323
helped improve and clarify the original manuscript. This work was supported by the Nuclear 324
Safety Research Program through the Korea Foundation of Nuclear Safety (KoFONS) using 325
the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the 326
Republic of Korea (No. 1705010). Seung-Hoon Yoo received support under the Air Force 327
Research Laboratory contract FA9453-16-C-0022. And we appreciate to Cezar I. Trifu, 328
associate editor of Bulletin of the Seismological Society of America, and anonymous 329
reviewers for the revision comments/suggestions. 330
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Full mailing address of each author 496 497
498
Gyeongdon Chai1; [email protected] 499
Seung-Hoon Yoo2; [email protected] 500
Junkee Rhie1* ; [email protected] 501
Tae-Seob Kang3; [email protected] 502
503
504
505
506
507
508
509
510
511
21
Table 1. Consecutive 14 frequency bands used for making coda envelopes. 512
513
No. Frequency (Hz)
FREQ01 0.05 ~ 0.1
FREQ02 0.1 ~ 0.2
FREQ03 0.2 ~ 0.3
FREQ04 0.3 ~ 0.5
FREQ05 0.5 ~ 0.7
FREQ06 0.7 ~ 1.0
FREQ07 1.0 ~ 1.5
FREQ08 1.5 ~ 2.0
FREQ09 2.0 ~ 3.0
FREQ10 3.0 ~ 4.0
FREQ11 4.0 ~ 6.0
FREQ12 6.0 ~ 8.0
FREQ13 8.0 ~ 11.0
FREQ14 11.0 ~ 14.0
514
515
516
517
518
519
520
521
522
523
524
525
526
527
22
Table 2. Source parameters of the 2016 Gyeongju and 2017 Pohang earthquake sequences. 528
Seq. Event (No.) Lat Lon Dep Mw(1) Mw(2) fc(1) (Hz) fc(2) (Hz) Δσ(1) (MPa) Δσ(2) (MPa)
2016.256.104432 (GJ01) 35.77 129.20 14.96 5.14 5.13 0.71 ± (0.03) 0.73 ± (0.00) 4.73 ± (0.08) 4.75 ± (0.01)
2016.256.111050 (GJ02) 35.76 129.19 15.83
3.19
3.23 ± (0.01)
0.51 ± (0.03)
2016.256.113254 (GJ03) 35.75 129.19 14.46 5.57 5.58 0.57 ± (0.02) 0.52 ± (0.00) 10.55 ± (0.06) 8.27 ± (0.01)
2016.256.141827 (GJ04) 35.78 129.20 13.83 3.07 3.14 2.79 ± (0.03) 2.91 ± (0.01) 0.26 ± (0.08) 0.32 ± (0.02)
2016.256.145230 (GJ05) 35.76 129.19 13.52 3.21 3.26 3.73 ± (0.04) 2.55 ± (0.04) 0.98 ± (0.12) 0.32 ± (0.08)
2016.256.153710 (GJ06) 35.78 129.21 13.53
3.07
4.71 ± (0.01)
1.05 ± (0.03)
Gyeongju 2016.256.232447 (GJ07) 35.76 129.18 13.00 3.23 3.25 4.34 ± (0.03) 3.93 ± (0.01) 1.65 ± (0.09) 1.15 ± (0.03)
2016.257.053142 (GJ08) 35.76 129.19 13.96
3.03
3.81 ± (0.01)
0.47 ± (0.03)
2016.263.113358 (GJ09) 35.75 129.18 15.80 4.46 4.49 1.15 ± (0.03) 1.22 ± (0.01) 1.94 ± (0.09) 2.47 ± (0.02)
2016.265.025354 (GJ10) 35.76 129.19 13.79 3.43 3.42 4.84 ± (0.03) 4.45 ± (0.01) 4.38 ± (0.09) 2.95 ± (0.03)
2016.272.073430 (GJ11) 35.76 129.19 12.96
3.14
3.63 ± (0.02)
0.60 ± (0.03)
2016.276.115307 (GJ12) 35.75 129.20 15.42 2.98 2.94 6.41 ± (0.03) 5.41 ± (0.01) 2.14 ± (0.10) 1.01 ± (0.03)
2016.284.135910 (GJ13) 35.75 129.19 14.40 3.3 3.31 3.10 ± (0.03) 2.89 ± (0.01) 0.97 ± (0.10) 0.55 ± (0.03)
2017.105.023113 (PH01) 36.11 129.36 5.0 3.33 3.34 2.75 ± (0.05) 1.80 ± (0.03) 0.73 ± (0.16) 0.14 ± (0.05)
2017.319.052931 (PH02) 36.11 129.37 5.0 5.48 5.44 0.34 ± (0.03) 0.38 ± (0.01) 1.73 ± (0.08) 1.92 ± (0.01)
2017.319.060949 (PH03) 36.09 129.34 8.0(KMA) 3.45 3.10 ± (0.05) 0.89 ± (0.09)
Pohang 2017.319.074930 (PH04) 36.12 129.36 6.6 4.31 4.3 1.04 ± (0.02) 1.31 ± (0.01) 0.81 ± (0.07) 1.66 ± (0.01)
2017.323.144547 (PH05) 36.12 129.36 4.2 3.53 3.54 3.66 ± (0.04) 2.61 ± (0.02) 2.78 ± (0.13) 0.90 ± (0.04)
2017.323.210515 (PH06) 36.14 129.36 4.0 3.59 3.62 2.95 ± (0.03) 2.17 ± (0.02) 1.86 ± (0.08) 0.63 ± (0.03)
2018.041.200303 (PH07) 36.08 129.33 8.0 4.61 4.6 1.22 ± (0.04) 0.77 ± (0.01) 3.86 ± (0.11) 1.08 ± (0.01)
529
*hypoDD relocation data from Woo et al. (2019b) were used for Gyeongju, and Pohang 530
sequence location data were obtained from the KMA catalog; focal depths were computed by 531
ISOLA. (1) and (2) denote the results of coda spectral ratio and source calibration methods, 532
respectively. 533
534
535
536
23
List of Figure Captions 537
1) Map showing the seismic stations used in this study to create synthetic coda envelope 538
models and perform the coda-based spectral ratio and source calibration study. The white and 539
black triangles indicate the station networks operated by Korea Meteorological 540
Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 541
respectively. The area in the dashed square is shown in Figure 2. 542
2) Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 543
earthquake sequences occurred. The focal mechanisms determined by ISOLA software 544
(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 545
Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 546
aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 547
Pohang sequence has reverse and strike-slip faulting events. 548
3) Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, showing 549
the frequency-dependent decaying trends. The synthetic coda envelope models fit well with 550
the observed data envelopes (grey lines). 551
4) Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) main shock 552
and largest aftershock with the same EGF events in sequence. The focal mechanisms and 553
Pohang event depth information were determined using ISOLA, and the Gyeongju event 554
depth information was obtained from Woo et al. (2019b). Dashed lines (yellow) indicate the 555
use of posterior distribution to determine the corner frequency by full-Bayesian MCMC. The 556
black and white colors of triangles indicate the corner frequencies of the target and EGF 557
events. 558
5) To correct the site effect, we prepared the site-term with the GJ main shock (Mw 5.58), 559
foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). In 560
addition, we created the synthetic Brune model (the lines overlaying the squares) for the 561
events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 562
we determined the correction-term (grey dotted lines) for each event. The site-term (black 563
line) of this station was obtained by averaging all the correction-terms. The site-term of the 564
station was applied to obtain the site-corrected amplitudes for every recorded event. 565
6) Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) Pohang. 566
The symbols represent the mean values of the site-corrected amplitude data with one standard 567
deviation. Synthetic Brune curves (black lines) are the results of the source calibration. The 568
stars denote the corner frequencies on the Brune curve with posterior distributions (yellow 569
lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, MHS; Metropolis-570
Hastings Sampling method). The same colors as in Figure 2 are used here for the 571
corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using the 572
fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show the 573
NDCAs for stations after revision using the recalculated site correction terms. Blue lines are 574
the same as the black lines in (b). 575
7) Scaling relations of corner frequency and stress drop versus seismic moment for two 576
earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented by 577
grey dotted lines. Black vertical and horizontal lines with the symbols represent one standard 578
24
deviation. The source scaling trend of the Gyeongju sequence is consistent with the 579
previously reported trend (thick dotted lines) of coda-based source studies. Both source 580
scaling trends cannot be explained by a constant stress drop model. 581
25
582
Figure 1. Map showing the seismic stations used in this study to create synthetic coda 583
envelope models and perform the coda-based spectral ratio and source calibration study. The 584
white and black triangles indicate the station networks operated by Korea Meteorological 585
Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 586
respectively. The area in the dashed square is shown in Figure 2. 587
26
588 589
Figure 2. Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 590
earthquake sequences occurred. The focal mechanisms determined by ISOLA software 591
(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 592
Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 593
aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 594
Pohang sequence has reverse and strike-slip faulting events. 595
596
597
27
598
Figure 3. Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, 599
showing the frequency-dependent decaying trends. The synthetic coda envelope models fit 600
well with the observed data envelopes (grey lines). 601
602
603
604
605
28
606
Figure 4. Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) 607
main shock and largest aftershock with the same EGF events in sequence. The focal 608
mechanisms and Pohang event depth information were determined using ISOLA, and the 609
Gyeongju event depth information was obtained from Woo et al. (2019b). Dashed lines 610
(yellow) indicate the use of posterior distribution to determine corner frequency by full-611
Bayesian MCMC. The black and white colors of triangles indicate the corner frequencies of 612
the target and EGF events. 613
29
614
Figure 5. To correct the site effect, we prepared the site-term with the GJ main shock (Mw 615
5.58), foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). 616
In addition, we created the synthetic Brune model (the lines overlaying the squares) for the 617
events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 618
we determined the correction-term (grey dotted lines) for each event. The site-term (black 619
line) of this station was obtained by averaging all the correction-terms. The site-term of the 620
station was applied to obtain the site-corrected amplitudes for every recorded event. 621
30
622
623 624
625
626
31
Figure 6. Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) 627
Pohang. The symbols represent the mean values of the site-corrected amplitude data with one 628
standard deviation. Synthetic Brune curves (black lines) are the results of the source 629
calibration. The stars denote the corner frequencies on the Brune curve with posterior 630
distributions (yellow lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, 631
MHS; Metropolis-Hastings Sampling method). The same colors as in Figure 2 are used for 632
the corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using 633
the fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show 634
the NDCAs for stations after revision using the recalculated site correction terms. Blue lines 635
are the same as the black lines in (b). 636
32
637
Figure 7. Scaling relations of corner frequency and stress drop versus seismic moment for 638
two earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented 639
by grey dotted lines. Black vertical and horizontal lines with the symbols represent one 640
standard deviation. The source scaling trend of the Gyeongju sequence is consistent with the 641
previously reported trend (thick dotted lines) of coda-based source studies. Both source 642
scaling trends cannot be explained by a constant stress drop model. 643
1
Stress drop scaling of the 2016 Gyeongju and 2017 Pohang earthquake 1
sequences using coda-based methods 2
3
Gyeongdon Chai1, Seung-Hoon Yoo2, Junkee Rhie1*, and Tae-Seob Kang3 4
5 1School of Earth and Environmental Sciences, Seoul National University, Seoul 08826, South 6
Korea 7
2Applied Research Associates, Inc., Arlington, VA 22203, USA 8
3Division of Earth Environmental System Science, Pukyong National University, Busan 9
48513, South Korea 10
11
Abstract 12
Two M5 earthquakes struck the southeastern Korean Peninsula in September 2016 and 13
November 2017, causing damage near the epicentral areas. We analyze the stress drop 14
scaling of these two earthquake sequences using coda-based methods and Bayesian inversion. 15
The 2016 Gyeongju earthquake sequence is a typical earthquake sequence generated by 16
tectonic processes. In contrast, the 2017 Pohang earthquake sequence is believed to be related 17
to fluid injections conducted for development of enhanced geothermal systems. As the two 18
sequences occurred in the same tectonic regime, our study provides a good opportunity to 19
compare the stress drop scaling between a tectonic earthquake sequence and an earthquake 20
sequence influenced by fluid injections. We found that the stress drops of events in the 21
Pohang sequences are lower than those of the Gyeongju sequence with similar magnitude. 22
Although it is likely that this difference results from focal depth variations, a reduction of 23
stress drop due to fluid injections cannot be ruled out. 24
25
Manuscript Click here toaccess/download;Manuscript;ChaiGD.BSSA.R01_GC08_JR01
2
Introduction 26
A study of the scaling relationship between magnitude and stress drop for earthquakes 27
occurring in a given region is important not only for understanding the fundamentals of the 28
earthquake rupture process but also for mitigating earthquake damage by precisely predicting 29
the ground motions of possible future earthquakes. There are many historical documents on 30
the occurrence of large earthquakes (M >6) in the southeastern part of the Korean Peninsula. 31
However, the largest earthquake recorded in this region with instruments is the ML 5.8 32
Gyeongju earthquake of 12 September, 2016 (Korean Meteorological Administration; KMA). 33
This region is susceptible to large earthquakes. Efforts toward mitigating the seismic risk in 34
this region are very important because this region has valuable infrastructure, including 35
nuclear power plants and cities with dense populations. In this study, we analyze the stress 36
drop scaling of two moderate earthquake sequences that occurred in the southeastern Korean 37
Peninsula using the analysis of coda waves, which is known to be more stable than the 38
analysis of direct waves (Mayeda et al., 2007; Yoo et al., 2010). 39
The two earthquake sequences considered in this study are the 2016 Mw 5.6 Gyeongju (GJ) 40
earthquake and the 2017 Mw 5.5 Pohang (PH) earthquake sequences (Figures 1 and 2). The 41
distance between the epicenters of the GJ and PH main shocks is approximately 43 km, and 42
both earthquakes occurred in the Gyeongsang Basin. The Gyeongsang Basin is a tectonic unit 43
classified based on the tectonic evolution in the Korean Peninsula. Although the Pohang 44
Basin, where the PH sequence occurred, had been tectonically active until recently compared 45
to the epicentral region of the GJ sequence, the current tectonic environment for generating 46
earthquakes in both regions should be similar because they belong to the same tectonic unit 47
(Park et al., 2007; Soh et al., 2018). We can also expect that tectonic stresses in both regions 48
are similar because they are spatially close to each other. However, the reported source 49
characteristic of the two sequences, especially the main shocks, are quite different. The focal 50
3
depths of the GJ and PH main shocks are 14.5 km (Woo et al., 2019a) and 4.27 km (Lee et al., 51
2019; Woo et al., 2019b), respectively. The focal mechanism for the GJ main shock 52
determined by moment tensor inversion is strike slip. The faulting style of the PH main shock 53
is strike slip with a significant thrust component. Strike slip and thrust mechanisms are both 54
popular mechanisms in our study area (Rhie and Kim, 2010). The most important difference 55
between the two earthquakes is whether fluid injection affected the occurrence of earthquake. 56
The GJ main shock is a natural earthquake generated because of tectonic stress, whereas the 57
PH main shock is a “runaway” earthquake triggered by stress perturbation caused by 58
injecting fluids for the development of enhanced geothermal systems (EGS) (Ellsworth et al., 59
2019). The objective of this study is to show that different mechanisms between tectonic and 60
“runaway” earthquakes can be revealed by comparing source parameters of the GJ and PH 61
earthquake sequences, which occurred in the same tectonic region. 62
63
Data and Methods 64
Data used in this study are seismic waveforms recorded at broadband stations operated by the 65
Korea Meteorological Administration (KMA) and the Korea Institute of Geoscience and 66
Mineral Resources (KIGAM) (Figure 1), and they were divided into two sets for different 67
research purposes. The first data set was used to define a reference coda envelope, which is 68
necessary for calculating the source spectrum. For the lower frequency range (0.05–8.0 Hz), 69
we used waveforms from earthquakes with magnitudes greater than 4.0 that occurred in and 70
around the Korean Peninsula between 2006 and 2012. The sampling rate of this data set is 20 71
Hz. For the higher frequency range (8.0–14.0 Hz), we used waveforms from earthquakes in 72
the 2016 Gyeongju sequence with magnitudes greater than 3.0; their sampling rate is 100 Hz. 73
The second data set was used for analysis of source spectra for the GJ and PH sequences. 74
4
To determine a reference coda envelope, we defined its theoretical functional form following 75
a previous study (Mayeda et al., 2003) to be 76
𝐸(𝑡, 𝑓, 𝑟) = 𝐻 (𝑡 −𝑟
𝑣(𝑓,𝑟)) (𝑡 −
𝑟
𝑣(𝑓,𝑟))
−𝛾(𝑓,𝑟)
× exp [𝑏(𝑓, 𝑟) (𝑡 −𝑟
𝑣(𝑓,𝑟))], (1) 77
where r, f, and t indicate distance in km, frequency in Hz, and the time elapsed from the event 78
origin time in s, respectively; H is the Heaviside step function; and 𝑣(𝑓, 𝑟) is the velocity of 79
the peak arrival in km/s. Two functions, 𝑏(𝑓, 𝑟) and 𝛾(𝑓, 𝑟), control the shape of the coda 80
envelope. To define the reference coda envelope, we determined 𝑣(𝑓, 𝑟), 𝑏(𝑓, 𝑟), and 81
𝛾(𝑓, 𝑟) from the observed data by following the procedures presented in Yoo et al. (2011). 82
We defined reference coda envelopes for 14 consecutive narrow frequency bands (Table 1, 83
Figure 3). Because the coda envelope shapes for both sequences are similar, we used the 84
same set of reference coda envelopes for both sequences. 85
The relation between the observed and reference coda envelopes can be represented as 86
follows: 87
𝐴𝐶(𝑡, 𝑓, 𝑟) = 𝑊0(𝑓)𝑆(𝑓)𝑃(𝑓, 𝑟)𝐸(𝑡, 𝑓, 𝑟), (2) 88
where 𝐴𝐶(𝑡, 𝑓, 𝑟) , 𝑆(𝑓) , 𝑃(𝑓, 𝑟) , and 𝑊0(𝑓) are the observed coda envelope, site 89
correction, path correction, and S-wave source amplitude, respectively. 90
To measure 𝐴𝐶(𝑡, 𝑓, 𝑟), we removed the instrument response of two horizontal component 91
waveforms to velocity seismograms. A four-pole two-pass Butterworth filter, for which 92
corner frequencies correspond to 14 consecutive narrow frequency bands was applied, and 93
then an envelope for each frequency was calculated using 94
𝐸obs = √𝑣(𝑡)2 + ℎ(𝑡)2, (3) 95
where 𝑣(𝑡) and ℎ(𝑡) are the band-pass-filtered horizontal velocity seismogram and its 96
Hilbert transform, respectively. To distinguish the observed and reference envelopes, we use 97
𝐸obs for the observed envelope. The final observed envelope was calculated by taking the 98
5
logarithm base 10 of two horizontal envelopes and then averaging them. By doing this, we 99
measured 𝐴𝐶(𝑡, 𝑓, 𝑟) for each frequency and epicentral distance. We can see in Eq. (2) that 100
changes in 𝐴𝐶(𝑡, 𝑓, 𝑟) with time for a given frequency and distance should be the same as 101
the changes in 𝐸(𝑡, 𝑓, 𝑟). The difference between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟) is called non-102
dimensional coda amplitude (NDCA), and it can be measured by finding the optimum DC 103
shift, which minimizes the L1 norm between 𝐴𝐶(𝑡, 𝑓, 𝑟) and 𝐸(𝑡, 𝑓, 𝑟). We then compared 104
the reference and observed coda envelopes at each frequency band. 105
Two methods are widely used to study seismic sources using measured NDCA. The first 106
method involves directly estimating 𝑊0(𝑓) by correcting 𝑃(𝑓, 𝑟) and 𝑆(𝑓) from NDCA. 107
The advantage of this method is that it can be used to estimate source spectra of all events in 108
a given region once models for 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are defined. Because source spectra are 109
available, we can estimate M0 and fc, the seismic moment in Newton meters and the corner 110
frequency in Hertz, which are two representative source parameters, but we can also estimate 111
radiated energy. However, unless 𝑃(𝑓, 𝑟) and 𝑆(𝑓) are precise enough, the reliability of 112
estimated source spectra can be low. The second method is to estimate fc only, or fc and M0 113
together, from the ratio of NDCA between two events without calculating the individual 114
source spectrum of each event (Mayeda et al., 2007). This method is based on the assumption 115
that if NDCAs are measured at the identical station and two earthquakes occurred at close 116
locations, 𝑃(𝑓, 𝑟) and 𝑆(𝑓) for both events should be identical and the ratio of NDCA is 117
the same as the ratio of the source spectra. In this case, we do not need to determine 𝑃(𝑓, 𝑟) 118
and 𝑆(𝑓) to apply the method. However, this method is only applicable to event pairs with 119
similar hypocenters but large differences in magnitude. In this study, we are interested in 120
examining the source characteristics of two earthquake sequences, where the earthquakes in 121
each sequence are spatially clustered. Therefore, a combined procedure of the two methods 122
can be applied. We used the information obtained from the ratio of the NDCAs to define the 123
6
site correction terms, and then applied these terms to study the source spectra of the events. 124
The detailed procedure is as follows. First, we selected event pairs with a magnitude 125
difference larger than 1 in each sequence. Total numbers of selected events and 126
corresponding event pairs for the GJ sequence are 9 and 15, respectively, and 6 and 7 for the 127
PH sequence. The maximum distance between epicenters among event pairs is 7 km. Mw for 128
each event was independently calculated using ISOLA (Sokos and Zahradnik, 2008; Vackář 129
et al., 2017) software based on the waveform inversion method (Figure 2). We considered 66 130
stations for our analysis, but the actual number of data points used for each process was not 131
consistent (Figure 1). To estimate fc of both events from the spectral ratio for a given event 132
pair, we used the Bayesian inversion method. A hierarchical scheme was applied to account 133
for data error in the inversion (Bodin et al., 2012; Kim et al., 2016). We assumed that prior 134
probability of Δσ is uniform in the range 10−3 − 103 MPa. Once we selected Δσ, we 135
calculated fc by using the following equation, because M0 of the event is pre-defined: 136
𝑓𝑐 =2.34𝛽
2𝜋 ( 7
16∙𝑀0∆𝜎
)
13
. (4) 137
Equation (4) was derived from the following two equations based on the circular fault model 138
(Eshelby, 1957). Shear wave velocity (𝛽) was set to be 3.5 km/s. 139
Δσ =7
16
𝑀0
𝑟3 (5) 140
𝑟 =2.34β
2π𝑓𝑐. (6) 141
Using fc and M0 of both events, we can define a spectral ratio between two events based on 142
Brune’s source model as follows (Aki, 1967; Brune, 1970; 1971): 143
𝑅(𝑓) =𝑀01[1+(𝑓/𝑓𝑐2)2]
𝑀02[1+(𝑓/𝑓𝑐1)2]. (7) 144
The misfit between the synthetic and observed spectral ratio was measured using the L1 norm, 145
and the likelihood function was defined as 146
7
𝐿 =1
2𝜎× exp [∑
|𝑅syn(𝑓𝑖)−𝑅obs(𝑓𝑖)|
𝜎
𝑛𝑖=1 ], (8) 147
where 𝑅syn and 𝑅obs indicate the synthetic and observed spectral ratio, respectively, and 𝑓𝑖 148
represents the center frequency of a given frequency band. To consider the data error in the 149
inversion, we assumed that 𝜎 has a positive uniform prior probability. We updated model 150
parameters (two stress drops and 𝜎) 200,000 times using the Metropolis-Hastings sampling 151
(MHS) method (Metropolis et al., 1953; Hastings, 1970). After the first half of the 152
calculations, which is considered a burn-in period, we selected 1 sample per every 100 153
calculations to estimate the posterior probability density (PPD) of two values of stress drop 154
(or fc) and 𝜎. For each event pair, we selected the fc with highest PPD. The final fc value for 155
each event was calculated by averaging selected fc values for all event pairs. 156
Because the final fc values for large events (Mw >= 4.0) are more accurate owing to their 157
large signal-to-noise ratios, we only used the fc values of only large events for further 158
analyses. The number of final fc values was three for each of the PH and GJ sequences. Once 159
we determined fc and M0, the theoretical Brune’s source spectrum can be calculated using the 160
following equation: 161
𝑀(𝑓) =𝑀0
(1+(𝑓
𝑓𝑐)
2). (9) 162
For each station, a site correction term can be determined by measuring the difference 163
between the theoretical Brune’s source spectrum and the corresponding NDCA. We note that 164
a site correction term contains 𝑃(𝑓, 𝑟) and 𝑆(𝑓) in Eq. (1). Because we define the site 165
correction terms of individual stations separately for PH and GJ sequences, we can ignore 166
variation in the site correction term with distance. We calculated the difference between the 167
theoretical Brune’s spectrum and the NDCA for each event and then averaged them for each 168
sequence to determine the final site correction term as a function of frequency. Once a site 169
correction term was defined, we calculated the source spectrum for each event by correcting 170
8
NDCA. By averaging the estimated source spectra of each event for all available stations, we 171
calculated the final source spectrum for each event. To estimate the PPD of stress drop (or fc) 172
and Mw from the final source spectrum, we used Bayesian inversion, which is similar to the 173
method previously applied for spectral ratio. We assumed that the stress drop and M0 have 174
uniform prior probability in the ranges between 10–3 and 103 MPa and between –2 and 2 in 175
logarithmic scale about the maximum value of the corrected NDCA, respectively. The 176
parameter fc was determined from a given stress drop and M0. To consider data error, we 177
adopted two parameters, 𝜎𝑓rms and 𝜎𝑓
SD. Here, 𝜎𝑓rms indicates an envelope fitting error 178
when measuring coda amplitudes of observed envelopes at a given frequency and 𝜎𝑓SD is 179
defined as one standard deviation of the site-correction term at the given frequency. The 180
likelihood function is defined as 181
𝐿 =1
2× exp [∑
|𝑀syn(𝑓𝑖)−𝑀obs(𝑓𝑖)|
𝜎𝑓rms+𝜎𝑓
SD𝑛𝑖=1 ]. (10) 182
The same sampling procedure of Bayesian inversion using the MHS method that was used for 183
the spectral ratio method was applied to estimate the PPD of Mw and fc. The PPD of stress 184
drop was also determined from Eqs. (5) and (6). We can technically estimate source 185
parameters of all events with measured NDCA. However, low signal-to-noise ratio of small 186
events can distort the results. Therefore, we used 9 and 6 events with Mw larger than 3.0 for 187
the GJ and PH sequences, respectively. We calculated Brune’s source spectrum using M0 and 188
fc estimated by Bayesian inversion and used this spectrum to calculate a site correction term. 189
190
Results and Discussion 191
We applied coda-based methods and Bayesian inversion to the GJ and PH earthquake 192
sequences. We calculated the reference coda envelopes and compared them with the observed 193
coda envelopes. Figure 3 depicts an example of the comparison between the reference and 194
observed coda envelopes at selected frequency bands. Because the excitations of the coda 195
9
waves are nearly insensitive to the radiation pattern (Mayeda et al., 2003), we were able to 196
obtain azimuthally averaged source spectra, even though the stations were mainly located 197
westward of the events. The final fc value was calculated for each event using the MHS 198
method and the PPD was estimated; for each event pair, we selected the fc with the highest 199
PPD. Figure 4 shows examples of spectral ratios determined for selected events. The 200
calculated difference between the theoretical Brune’s spectrum and the NDCA for each event 201
was averaged for each sequence to determine the final site correction term as a function of 202
frequency, as shown in Figure 5 for three events in the GJ sequence. 203
If the site correction term is well-defined, we can expect the estimated source spectra of the 204
events involved in determining the site correction terms to be consistent with the site-205
corrected NDCA for the same event. In the case of the GJ sequence, we can see that the two 206
values are well-matched, as expected (Figure 6(a)). However, there are significant 207
discrepancies in the PH sequence (Figure 6(c)). The reason for these discrepancies appears to 208
be that the original estimates of fc obtained from the spectral ratio method for the PH 209
sequence are not accurate because the number of applicable earthquakes is insufficient. To 210
overcome this problem, we recalculated the site correction term for the PH sequence. First, 211
we determined the Brune spectra, which fit the corrected NDCA for each event, and then 212
recalculated the site correction terms by averaging the differences between the Brune spectra 213
and the NDCAs for the three events. The corrected NDCA using the recalculated site 214
correction term demonstrates a significantly improved fit to the theoretical Brune’s spectrum 215
(Figure 6(b)). 216
Using coda-based methods and Bayesian inversion, we estimated the PPD of Mw, fc, and 217
stress drop for 12 and 7 earthquakes in the GJ and PH sequences, respectively (Table 2). The 218
stress drop scaling for both the GJ and PH sequences show that stress drop increases with 219
increasing magnitude on the overall scale (Figure 7). The observed trends in stress drop 220
10
scaling cannot be explained by the self-similar model with a constant stress drop (Aki, 1967). 221
The estimates of the stress drop appear to be considerably scattered for smaller earthquakes 222
(Mw < ~3.5) in both sequences. This may indicate that estimates of stress drop for smaller 223
events are not stable because of the low signal-to-noise ratio. The stress drop of the smallest 224
PH event (PH01 in Table 2) is much smaller than that of other events with similar magnitudes. 225
For relatively larger events (Mw >= 4.0) in the GJ sequence, it is likely that the stress drop 226
increases with increasing Mw in a range between Mw 4.5 and 5.5. This observation is 227
consistent with other previous studies using similar coda-based methods (Mayeda and 228
Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; Yoo and Mayeda, 2013). For the 229
PH sequence, we do not observe an increasing trend in the given magnitude range because 230
the stress drop of the PH main shock (PH02) is smaller than those of the shocks of similar 231
magnitude in the GJ sequence. No significant increase in the stress drop for the specific 232
magnitude range was reported for the Parkfield sequence (Allman and Shearer, 2007). 233
Additionally, the stress drops of two other PH events (PH04 and PH07) with Mw larger than 234
4.0 are also smaller than the stress drops of similar-sized GJ events. 235
To summarize the characteristics of stress drop scaling for the two sequences, the stress drops 236
of the PH sequence appear to be smaller than those of the GJ sequence, and two PH events 237
(PH01 and PH02) have much smaller stress drops in comparison with those of events with 238
similar magnitudes in the GJ sequence. The stress drop of PH01 (Mw 3.3) is smaller than that 239
of GJ13 (Mw 3.3) by a factor of approximately 4. The stress drop of PH02 (Mw 5.5) is smaller 240
than that of GJ03 (Mw 5.6) and GJ01 (Mw 5.1) by a factor of 4.3 and 2.5, respectively. 241
Estimates of the stress drops for the GJ and PH main shocks reported by other studies show 242
similar results. Son et al. (2018) reported that the stress drop of GJ03 is 11.2 MPa based on 243
the analysis of the S-wave source spectrum. The mean stress drop of the same event derived 244
from finite fault inversion using the empirical Green’s function method is 23 MPa (Uchide 245
11
and Song, 2018). These values are somewhat larger than our estimate (8.29 MPa). For PH02, 246
Song and Lee (2019) estimated the mean stress drop of PH02 to be approximately 2 MPa 247
from finite fault inversion using InSAR data, and this value is consistent with our result (1.92 248
MPa). We note that PH02 and PH01 are considered anthropogenic earthquakes (Kim et al., 249
2018; Grigoli et al., 2018; Lee et al., 2019; Ellsworth et al., 2019; Woo et al., 2019b). PH01 250
was an induced earthquake, which occurred during a period when fluid injections for EGS 251
development were conducted. PH02 (the PH main shock) is considered a “runaway” 252
earthquake, which implies that its occurrence is affected by fluid injections even though it 253
releases strain energy accumulated through natural tectonic processes (Ellsworth et al., 2019). 254
Therefore, a question arises as to whether the low stress drops of PH02 and PH01 result from 255
the influence of fluid injections. There have been several studies reporting that stress drops of 256
induced earthquakes are smaller than those of tectonic earthquakes (Sumy et al., 2017; Boyd 257
et al., 2017; Hough, 2014). Hough (2014) argued that the stress drops of induced earthquakes 258
are smaller than those of tectonic earthquakes by a factor of 2–10 based on differences in 259
intensity between tectonic and induced earthquakes measured by a “Did You Feel It?” system. 260
Although the difference in the stress drop between the PH and GJ main shocks derived in this 261
study lies within the range proposed by Hough (2014), it is not sufficient to conclude that the 262
low stress drops observed in the PH sequence, especially for PH02 and PH01, are caused by 263
fluid injections. It is well known that the stress drop is controlled by many other factors, such 264
as focal depth, faulting type, and heat flow. Therefore, it is possible that the discrepancy in 265
the stress drop can be attributed to other factors. The PH and GJ main shocks differ in several 266
ways besides fluid injection. First, the focal depth of the PH main shock (4.27 km; Lee et al., 267
2019) is much shallower than that of the GJ main shock (14.5 km; Woo et al., 2019a). 268
Second, while the faulting type of the GJ main shock is nearly pure strike-slip, that of the PH 269
main shock is strike slip with considerable thrust-faulting components. 270
12
Although several studies have found that there is no clear depth dependence of stress drop 271
(Wu et al., 2018; Allmann and Shearer, 2009), most previous studies support the theory that 272
shallow earthquakes have lower stress drops than deep earthquakes (Huang et al., 2017; Oth, 273
2013). Huang et al. (2017) reported that induced earthquakes with deep focal depths (<5 km) 274
show similar stress drops as those of tectonic earthquakes in the central United States and 275
concluded that induced and tectonic earthquakes are not distinguishable based only on 276
differences in stress drop. Therefore, it is possible that the lower stress drop of the PH main 277
shock compared to the GJ main shock is caused only by the difference in focal depth. The 278
difference in focal depth can explain why the stress drops of the PH events are relatively 279
lower than those of the GJ events. Regarding the faulting style of earthquakes, the relations 280
between faulting style and stress drop reported by previous studies are not consistent. In 281
general, it is well-accepted that reverse-faulting earthquakes have higher stress drops (e.g., 282
McGarr, 1984; McGarr and Fletcher, 2002). However, Allmann and Shearer (2009) 283
suggested that the stress drop of strike-slip is higher than that of other faulting types. Our 284
observation shows that the stress drop of the GJ main shock, which has pure strike-slip 285
mechanism, is higher than that of the PH main shock, which has considerable reverse-faulting 286
components; this is consistent with the result presented by Allmann and Shearer (2009). Oth 287
(2013) suggested that stress drop variations are strongly correlated with heat flow variations 288
in crustal earthquakes in Japan. Therefore, heat flows can be another factor that affects stress 289
drop; however, we do not have sufficient information on whether there is a considerable 290
difference in heat flow between the epicentral regions of the GJ and PH sequences. 291
292
Conclusions 293
We analyzed the stress drop scaling of two moderate earthquake sequences that occurred in 294
the same tectonic regime. The stress drop seems to increase with an increasing magnitude in 295
13
both sequences. The observed magnitude dependence in stress drop scaling cannot be 296
explained by a self-similar model with a constant stress drop (Aki, 1967). The scaling of the 297
GJ sequence is similar to the results of other earthquake sequences studied using similar 298
coda-based methods (Mayeda and Malagnini, 2009; Malagnini et al., 2010; Yoo et al., 2010; 299
Yoo and Mayeda, 2013). The characteristic feature is that stress drop rapidly increases with 300
Mw in the range between Mw 4.5 and 5.5. This rapid increase in stress drop is not found in the 301
PH sequence. On average, stress drops of the PH sequence are lower than those of the GJ 302
sequence. Stress drops of PH02 and PH01 are much smaller than the events with similar 303
magnitudes in the GJ sequence. Considering previous studies on factors controlling the stress 304
drop, it is likely that differences in focal depth between the two sequences cause differences 305
in the stress drop. Although the focal depths of all PH events are similar, the stress drops for 306
the two PH events (PH01 and PH02) are particularly lower than those of the other PH events. 307
In addition, these two events are likely to be influenced by fluid injections. It may be inferred 308
that the much lower stress drops for the two events are caused by fluid injection. However, it 309
is not conclusive that the effect of fluid injection is adequate to explain the lower stress drops 310
based on only the observations in our study. 311
312
Data and Resources 313
Waveform data were acquired from seismograph networks and data centers in the region, 314
including those of the Korea Institute of Geology and Mineral Resources (KIGAM) and the 315
Korea Meteorological Administration (KMA) (the event catalog and data are available from 316
authors upon request). Geotectonic lines were obtained from KIGAM 317
(https://mgeo.kigam.re.kr, last accessed March 2017). The figures in this article were 318
generated using generic mapping tools (GMT; https://www.soest.hawaii.edu/gmt/, last 319
accessed March 2017). 320
14
321
Acknowledgments 322
We thank Vanessa Napoli (Applied Research Associates, Inc.) whose comments/suggestions 323
helped improve and clarify the original manuscript. This work was supported by the Nuclear 324
Safety Research Program through the Korea Foundation of Nuclear Safety (KoFONS) using 325
the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the 326
Republic of Korea (No. 1705010). Seung-Hoon Yoo received support under the Air Force 327
Research Laboratory contract FA9453-16-C-0022. And we appreciate to Cezar I. Trifu, 328
associate editor of Bulletin of the Seismological Society of America, and anonymous 329
reviewers for the revision comments/suggestions. 330
331
332
333
334
335
336
337
338
339
340
341
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343
344
345
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494
495
Full mailing address of each author 496 497
498
Gyeongdon Chai1; [email protected] 499
Seung-Hoon Yoo2; [email protected] 500
Junkee Rhie1* ; [email protected] 501
Tae-Seob Kang3; [email protected] 502
503
504
505
506
507
508
509
510
511
21
Table 1. Consecutive 14 frequency bands used for making coda envelopes. 512
513
No. Frequency (Hz)
FREQ01 0.05 ~ 0.1
FREQ02 0.1 ~ 0.2
FREQ03 0.2 ~ 0.3
FREQ04 0.3 ~ 0.5
FREQ05 0.5 ~ 0.7
FREQ06 0.7 ~ 1.0
FREQ07 1.0 ~ 1.5
FREQ08 1.5 ~ 2.0
FREQ09 2.0 ~ 3.0
FREQ10 3.0 ~ 4.0
FREQ11 4.0 ~ 6.0
FREQ12 6.0 ~ 8.0
FREQ13 8.0 ~ 11.0
FREQ14 11.0 ~ 14.0
514
515
516
517
518
519
520
521
522
523
524
525
526
527
22
Table 2. Source parameters of the 2016 Gyeongju and 2017 Pohang earthquake sequences. 528
Seq. Event (No.) Lat Lon Dep Mw(1) Mw(2) fc(1) (Hz) fc(2) (Hz) Δσ(1) (MPa) Δσ(2) (MPa)
2016.256.104432 (GJ01) 35.77 129.20 14.96 5.14 5.13 0.71 ± (0.03) 0.73 ± (0.00) 4.73 ± (0.08) 4.75 ± (0.01)
2016.256.111050 (GJ02) 35.76 129.19 15.83
3.19
3.23 ± (0.01)
0.51 ± (0.03)
2016.256.113254 (GJ03) 35.75 129.19 14.46 5.57 5.58 0.57 ± (0.02) 0.52 ± (0.00) 10.55 ± (0.06) 8.27 ± (0.01)
2016.256.141827 (GJ04) 35.78 129.20 13.83 3.07 3.14 2.79 ± (0.03) 2.91 ± (0.01) 0.26 ± (0.08) 0.32 ± (0.02)
2016.256.145230 (GJ05) 35.76 129.19 13.52 3.21 3.26 3.73 ± (0.04) 2.55 ± (0.04) 0.98 ± (0.12) 0.32 ± (0.08)
2016.256.153710 (GJ06) 35.78 129.21 13.53
3.07
4.71 ± (0.01)
1.05 ± (0.03)
Gyeongju 2016.256.232447 (GJ07) 35.76 129.18 13.00 3.23 3.25 4.34 ± (0.03) 3.93 ± (0.01) 1.65 ± (0.09) 1.15 ± (0.03)
2016.257.053142 (GJ08) 35.76 129.19 13.96
3.03
3.81 ± (0.01)
0.47 ± (0.03)
2016.263.113358 (GJ09) 35.75 129.18 15.80 4.46 4.49 1.15 ± (0.03) 1.22 ± (0.01) 1.94 ± (0.09) 2.47 ± (0.02)
2016.265.025354 (GJ10) 35.76 129.19 13.79 3.43 3.42 4.84 ± (0.03) 4.45 ± (0.01) 4.38 ± (0.09) 2.95 ± (0.03)
2016.272.073430 (GJ11) 35.76 129.19 12.96
3.14
3.63 ± (0.02)
0.60 ± (0.03)
2016.276.115307 (GJ12) 35.75 129.20 15.42 2.98 2.94 6.41 ± (0.03) 5.41 ± (0.01) 2.14 ± (0.10) 1.01 ± (0.03)
2016.284.135910 (GJ13) 35.75 129.19 14.40 3.3 3.31 3.10 ± (0.03) 2.89 ± (0.01) 0.97 ± (0.10) 0.55 ± (0.03)
2017.105.023113 (PH01) 36.11 129.36 5.0 3.33 3.34 2.75 ± (0.05) 1.80 ± (0.03) 0.73 ± (0.16) 0.14 ± (0.05)
2017.319.052931 (PH02) 36.11 129.37 5.0 5.48 5.44 0.34 ± (0.03) 0.38 ± (0.01) 1.73 ± (0.08) 1.92 ± (0.01)
2017.319.060949 (PH03) 36.09 129.34 8.0(KMA) 3.45 3.10 ± (0.05) 0.89 ± (0.09)
Pohang 2017.319.074930 (PH04) 36.12 129.36 6.6 4.31 4.3 1.04 ± (0.02) 1.31 ± (0.01) 0.81 ± (0.07) 1.66 ± (0.01)
2017.323.144547 (PH05) 36.12 129.36 4.2 3.53 3.54 3.66 ± (0.04) 2.61 ± (0.02) 2.78 ± (0.13) 0.90 ± (0.04)
2017.323.210515 (PH06) 36.14 129.36 4.0 3.59 3.62 2.95 ± (0.03) 2.17 ± (0.02) 1.86 ± (0.08) 0.63 ± (0.03)
2018.041.200303 (PH07) 36.08 129.33 8.0 4.61 4.6 1.22 ± (0.04) 0.77 ± (0.01) 3.86 ± (0.11) 1.08 ± (0.01)
529
*hypoDD relocation data from Woo et al. (2019b) were used for Gyeongju, and Pohang 530
sequence location data were obtained from the KMA catalog; focal depths were computed by 531
ISOLA. (1) and (2) denote the results of coda spectral ratio and source calibration methods, 532
respectively. 533
534
535
536
23
List of Figure Captions 537
1) Map showing the seismic stations used in this study to create synthetic coda envelope 538
models and perform the coda-based spectral ratio and source calibration study. The white and 539
black triangles indicate the station networks operated by Korea Meteorological 540
Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 541
respectively. The area in the dashed square is shown in Figure 2. 542
2) Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 543
earthquake sequences occurred. The focal mechanisms determined by ISOLA software 544
(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 545
Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 546
aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 547
Pohang sequence has reverse and strike-slip faulting events. 548
3) Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, showing 549
the frequency-dependent decaying trends. The synthetic coda envelope models fit well with 550
the observed data envelopes (grey lines). 551
4) Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) main shock 552
and largest aftershock with the same EGF events in sequence. The focal mechanisms and 553
Pohang event depth information were determined using ISOLA, and the Gyeongju event 554
depth information was obtained from Woo et al. (2019b). Dashed lines (yellow) indicate the 555
use of posterior distribution to determine the corner frequency by full-Bayesian MCMC. The 556
black and white colors of triangles indicate the corner frequencies of the target and EGF 557
events. 558
5) To correct the site effect, we prepared the site-term with the GJ main shock (Mw 5.58), 559
foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). In 560
addition, we created the synthetic Brune model (the lines overlaying the squares) for the 561
events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 562
we determined the correction-term (grey dotted lines) for each event. The site-term (black 563
line) of this station was obtained by averaging all the correction-terms. The site-term of the 564
station was applied to obtain the site-corrected amplitudes for every recorded event. 565
6) Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) Pohang. 566
The symbols represent the mean values of the site-corrected amplitude data with one standard 567
deviation. Synthetic Brune curves (black lines) are the results of the source calibration. The 568
stars denote the corner frequencies on the Brune curve with posterior distributions (yellow 569
lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, MHS; Metropolis-570
Hastings Sampling method). The same colors as in Figure 2 are used here for the 571
corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using the 572
fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show the 573
NDCAs for stations after revision using the recalculated site correction terms. Blue lines are 574
the same as the black lines in (b). 575
7) Scaling relations of corner frequency and stress drop versus seismic moment for two 576
earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented by 577
grey dotted lines. Black vertical and horizontal lines with the symbols represent one standard 578
24
deviation. The source scaling trend of the Gyeongju sequence is consistent with the 579
previously reported trend (thick dotted lines) of coda-based source studies. Both source 580
scaling trends cannot be explained by a constant stress drop model. 581
25
582
Figure 1. Map showing the seismic stations used in this study to create synthetic coda 583
envelope models and perform the coda-based spectral ratio and source calibration study. The 584
white and black triangles indicate the station networks operated by Korea Meteorological 585
Administration (KMA) and Korea Institute of Geoscience and Mineral Resource (KIGAM), 586
respectively. The area in the dashed square is shown in Figure 2. 587
26
588 589
Figure 2. Study areas where the Gyeongju (right lower inset) and Pohang (right upper inset) 590
earthquake sequences occurred. The focal mechanisms determined by ISOLA software 591
(Sokos and Zahradnik, 2008; Vackář et al., 2017) are plotted in the inset of each study area. 592
Symbols in red, blue, and green colors indicate the main shock, foreshock, and largest 593
aftershock, respectively. The Gyeongju sequence has only strike-slip faulting events, but the 594
Pohang sequence has reverse and strike-slip faulting events. 595
596
597
27
598
Figure 3. Narrow-band coda envelope of the Pohang main shock recorded at DAG2 station, 599
showing the frequency-dependent decaying trends. The synthetic coda envelope models fit 600
well with the observed data envelopes (grey lines). 601
602
603
604
605
28
606
Figure 4. Spectral ratio of Gyeongju (red) main shock and foreshocks and Pohang (blue) 607
main shock and largest aftershock with the same EGF events in sequence. The focal 608
mechanisms and Pohang event depth information were determined using ISOLA, and the 609
Gyeongju event depth information was obtained from Woo et al. (2019b). Dashed lines 610
(yellow) indicate the use of posterior distribution to determine corner frequency by full-611
Bayesian MCMC. The black and white colors of triangles indicate the corner frequencies of 612
the target and EGF events. 613
29
614
Figure 5. To correct the site effect, we prepared the site-term with the GJ main shock (Mw 615
5.58), foreshock (Mw 5.13), and largest aftershock (Mw 4.49) records at the station (DAG2). 616
In addition, we created the synthetic Brune model (the lines overlaying the squares) for the 617
events. By subtracting the observed amplitude (black dotted lines) from the synthetic model, 618
we determined the correction-term (grey dotted lines) for each event. The site-term (black 619
line) of this station was obtained by averaging all the correction-terms. The site-term of the 620
station was applied to obtain the site-corrected amplitudes for every recorded event. 621
30
622
623 624
625
626
31
Figure 6. Source calibration results of two earthquake sequences, (a) Gyeongju and (b-c) 627
Pohang. The symbols represent the mean values of the site-corrected amplitude data with one 628
standard deviation. Synthetic Brune curves (black lines) are the results of the source 629
calibration. The stars denote the corner frequencies on the Brune curve with posterior 630
distributions (yellow lines) as a result of full Bayesian MCMC (Markov Chain Monte Carlo, 631
MHS; Metropolis-Hastings Sampling method). The same colors as in Figure 2 are used for 632
the corresponding events. (c) Yellow dashed lines indicate the Brune spectra calculated using 633
the fc values from the spectral ratios. The symbols (open triangles, squares, and circles) show 634
the NDCAs for stations after revision using the recalculated site correction terms. Blue lines 635
are the same as the black lines in (b). 636
32
637
Figure 7. Scaling relations of corner frequency and stress drop versus seismic moment for 638
two earthquake sequences. (a) Constant Brune (1970; 1971) stress drop trends are represented 639
by grey dotted lines. Black vertical and horizontal lines with the symbols represent one 640
standard deviation. The source scaling trend of the Gyeongju sequence is consistent with the 641
previously reported trend (thick dotted lines) of coda-based source studies. Both source 642
scaling trends cannot be explained by a constant stress drop model. 643