a wavelet transform based application for seismic waves. analysis of the performance
TRANSCRIPT
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A Wavelet Transform based
application for seismic waves.
Analysis of the performance.
Telecommunication EngineeringThesis
Author: Pedro Cerón Colás
Fraunhofer IIS, Erlangen December 9th 2013
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General outline of the presentation
Introduction
Method and Process
Simulation of the algorithm
Conclusions
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Overview of the problem
Geophysicsfield
ComplexContinuous
Wavelet Transform
Design of Matlabalgorithms
But… Where can we apply the
Wavelet Transform?
Bio
Sound
Proccesing
_QRS Complex, “Biomedical Signal
Processing”, Sorno & Laguna.
_Circular buffer 3rd FIR filter. “Sound digital
processing”, Rocchesso.
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Some geophysical issues• 3 components:
EW, NS, Z (transverse)
• Body Waves (P and S
waves) and Surphase
Waves (Rayleigh and
Love).
• Seismic Spectrum:
0.001-10hz [1].
• Frequency
characterization:
Spectrum overlaping of
Body and Surphase
Waves .
Image taken from Dr. José Ignacio Badal Nicolás (Faculty
of Geologics, Zaragoza University). Shared resource.
[1] “Fundamentals of Geophysics” Agustín Udías & Julio
Mezcua. Chap.13
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General Outline of the
presentation
Introduction
Method and Process
Simulation of the algorithm
Conclusions
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Method and process
Conversionof the
signals
Preprocessing: Correction
Multiresolutionfilter (WT)
Processingstep:
Filtering
SurphaseWavesBody Waves
Polarization
analysis
• Data format? SAC or Mseed
• Compressed Info?
STEIM1, STEIM2
• Not compressed Info?
ASCII, float, integer…
Onsetdetection
Matlab
.mat
D
A
T
A
B
A
S
E
S
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Seismic formats: SAC and MiniSEED
Word Type NAMES o o o o
0 F DELTA DEPMIN DEPMAX SCALE ODELTA
5 F B E O AINTERNAL
10 F T0 T1 T2 T3 T4
15 F T5 T6 T7 T8 T9
20 F F RESP0 RESP1 RESP2 RESP3
25 F RESP4 RESP5 RESP6 RESP7 RESP8
30 F RESP9 STLA STLO STEL STDP
35 F EVLA EVLO EVEL EVDP MAG
40 F USER0 USER1 USER2 USER3 USER4
45 F USER5 USER6 USER7 USER8 USER9
50 F DIST AZ BAZ GCARCINTERNAL
55 FINTERNAL
DEPMEN
CMPAZ CMPINCXMINIMUM
60 FXMAXIMUM
YMINIMUM
YMAXIMUM
UNUSED UNUSED
65 F UNUSED UNUSED UNUSED UNUSED UNUSED
70 I NZYEAR NZJDAY NZHOUR NZMIN NZSEC
75 I NZMSEC NVHDR NORID NEVID NPTS
80 IINTERNAL
NWFID NXSIZE NYSIZE UNUSED
85 I IFTYPE IDEP IZTYPE UNUSED IINST
90 I ISTREG IEVREG IEVTYP IQUAL ISYNTH
95 IIMAGTYP
IMAGSRC
UNUSED UNUSED UNUSED
100 I UNUSED UNUSED UNUSED UNUSED UNUSED
105 L LEVEN LPSPOL LOVROK LCALDA UNUSED
110 K KSTNM KEVNM*
116 K KHOLE KO KA
122 K KT0 KT1 KT2
128 K KT3 KT4 KT5
134 K KT6 KT7 KT8
140 K KT9 KF KUSER0
146 K KUSER1 KUSER2KCMPNM
152 K KNETWK KDATRD KINST
Algorithms to decode the
information.
Tables taken from:
http://www.iris.edu/software/sac/manual/file_format.html, november 2013.
SEED manual v.2.4, B appendix.
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Compressional techniques: STEIM 1 and
STEIM 2
STEIM 2:More number of
possibilities (8) with dnib.
Algorithms to decompress the
information.
Tables taken from:
SEED reference manual (version 2.4). B appendix. November 2013.
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Response for channel correction
•
.PAZ
.RESPONSE
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Multiresolution filtering using the Wavelet
Transform
Mathematical toolAmplitude
Phase
Inst. Freq.
Multiresolution filter: www.sciencedirect.com, nov.
2013.Plot of a .cwt matrix in Matlab.
Freq?
Input
(Div.)
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Prepocessing stage: Filtering
• Band pass filtering.
• Once we have seen in the .cwt plot where we can locate
the parts of the signal with higher energetic
contributions, we can remove the unnecesary bands
(coefficients).
• Remove DC level and high frequency seismic noise.
Computations are done directly to
the .cwt matrixHow?
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Onset detector (body waves)
What’s the concept?Body Waves tend to be at higher frequencies in the
octaves (higher divisions) than Surface waves.
Energetic Criteria:
Mk1
Mk2
Variability Criteria:
Fineradjustment
Lowfrequencyenvelope
High Frequencyenvelope
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Onset detector (surphase waves)
What’s the
concept?
Surphase Waves tend to be at lower
frequencies every octaves
Derivative
Derivative + envolope
We can roughly locate
where it’s located the
onset of the Surphase
waves.
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Surphase wave: Dispersion
What is the distinctive element that define
the Surphase Waves?Dispersion
How can be use the wavelet coefficients to
analyse this phenomenon?
.cwt
matrix
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Polarization analysisA
rriv
altim
es
P wave onset
S wave onset
Surphase wave onset
Transformation of 3
axis into 2:
• Polarization of P, S, Love
and Rayleigh waves?
http://www.motionscript.com/mastering-expressions/random-
sphere.html, november 2013
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General Outline of the
presentation
Introduction
Method and Process
Simulation of the algorithm
Conclusions
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Time errors: First onsetInner
structure
problem
0
0.5
1
1.5
2
2.5
3
3.5
1 2 3 4 5 6 7 8 9 10 11 12
Low SNR
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Time errors: Second onsetInner
structure
problem
0
0.5
1
1.5
2
2.5
3
3.5
4
1 2 3 4 5 6 7 8 9 10 11 12
Low SNR
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General Outline of the
presentation
Introduction
Method and Process
Simulation of the algorithm
Conclusions
![Page 20: A wavelet transform based application for seismic waves. Analysis of the performance](https://reader033.vdocument.in/reader033/viewer/2022042701/559cfc5f1a28abd4298b4862/html5/thumbnails/20.jpg)
Conclusions
• Algoritms easy to apply (engineering principles: energy, variability, derivatives…)
• Very satisfactory results.
• Automatic algorithm: Input (signal).
• Outputs are specially interesting in terms of the signal processingand geophysic field: Time-Frequency analysis, onsets, analysis of the dispersion phenomena, polarization.
• Formats (SAC and Miniseed) and compressional techniques.
• The multiresolution analysis is specially appropiate for the non-stationary signals where we don’t know (in advance) where are the frequency bands of interest.
FIR of how many coefficients and what are the frequenciesof the design?