Moment-tensor inversion of Very Long Period explosion events recorded on the Ubinas volcano, Peru

*V. Monteiller1, J.-P. Métaxian2, O. Macedo3, G. S. O’Brien4 I. Lokmer4 and E. Taipe3

1

Dynamique Terrestre et Planétaire, CNRS UMR 5562, Observatoire Midi Pyrénées, 31400 Toulouse, France 2 LGIT, Université de Savoie, 73376 Le Bourget du lac cedex, France (metaxian@univ-savoie.fr)

3 Instituto Geofisico del Peru, Arequipa, Peru (omacedo@geo.igp.gob.pe)

4 School of Geological Sciences, University College Dublin, Ireland (gareth.obrien@ucd.ie)

* Corresponding author: (vadim.monteiller@dtp.obs-mip.fr)

Abstract

Vulcanian explosions at Ubinas volcano, Peru, produce Very Long Period (VLP)

events. About 30 explosions were recorded by an array of 7 broadband stations that were

installed for a 3 month period. The recorded VLP events have similar waveforms,

suggesting a common source location and mechanism. We performed several moment

tensor inversions on a stacked VLP signal. We first left all inversion parameters free in

order to fix the more probable source position, which was found under the southern part of

the caldera, 10 m below the crater. We then inverted the moment tensor assuming specific

source geometries. Results suggest a crack geometry with a normal vector oriented

N15°E in the horizontal plane and 40° from the vertical axis.

Introduction

Ubinas stratovolcano (5,672 m above sea level) is located 60 km east from

Arequipa city in Peru and is historically the most active volcano in Peru. During the last

450 years Ubinas erupted 23 times with a maximum Volcanic Explosivity Index of 3

(Simkin and Siebert, 1994; Rivera, 1998; Thouret et al., 2005). No permanent seismic

station operated before the last eruption, which began on March 25th 2006. However,

‘screw’ type events were recorded during a temporary seismic experiment in 1996 (Taipe,

2008). A temporary broadband station was installed at the end of April, equipped with a

short period vertical sensor and a radio telemetry system; the first permanent seismic

station began to recording at the end of May. The present monitoring system, which has

been in operation since October 2007, includes 4 seismic stations. One of these stations is

equipped with a broadband sensor and 2 tiltmeters. A temporary experiment was

performed on Ubinas from May to July 2006 with 6 additional broadband stations (Figure

1).

Figure 1. (a) Ubinas topography. Red triangles: stations. Black dots: 3-D grid inside the volcanic cone where the Green's functions were computed. (b) Misfit function map at different elevations. Two areas have a low misfit value with the most likely position for source location under the crater.

Recent activity has been dominated by almost permanent ash emissions covering

an area of several kilometers around the volcano. The most common eruptive activity

involves exhalations rising a few hundred meters above the crater rim, to larger plumes

produced by explosions that may reach up to 3 kilometers. The seismic activity is

characterized by high rates of long period (LP) event production, accompanying eruptive

activity and very long period (VLP) events. A main characteristic of this activity is the

occurrence of LP swarms preceding most of the VLP events. Figure 2 shows a

characteristic explosive sequence. In this case, the LP swarm begins 2 hours before the

explosion. LP events, initially separated by several minutes, merge into tremor half an hour

before the explosion. Swarms of LP, LP merging into tremor and VLP events, have been

observed on several andesitic volcanoes (Montserrat, Neuberg et al., 1998, 2000; Merapi,

Hidayat et al., 2002; Popocatépetl, Chouet et al., 2005; Mount St Helens, Waite et al.,

2008), where they are related to dome growth and, in some cases, to dome collapse or

dome explosions. Source processes of LP and VLP signals using full-waveform inversion

have been investigated by many authors (Legrand et al., 2000; Kumagai et al., 2002;

Nakano et al., 2005; Lokmer et al., 2007). A better understanding of the source processes

generating VLP events is essential for any hazard evaluation. In this paper, we present the

quantitative inversion of VLP events recorded by the temporary broadband network at

Ubinas volcano between May and July 2006. The Green’s functions are calculated for a

homogeneous velocity model. We begin by describing the broadband network and the

data recorded during the experiment. We then discuss the inversion and present our

conclusions.

Figure 2. An example of an explosion sequence preceding a LP swarm merging into tremor.

Data

The data used in this work were recorded by the network of 7 broadband

seismometers (Figure 1). The stations were distributed between 3,900 m and 4,700 m

above sea level. Data were recorded by 6 Agecodagis Titan recorders and 1 RefTek

recorder, operating in continuous mode at 125 samples/s and 100 samples/s per channel,

respectively. VLP events have a spectral content dominated by frequencies between 0.3-

0.9 Hz. The signal is filtered between 0.1 and 1 Hz. All VLP events exhibit similar

waveforms with a very high coherency ranging from 0.82 to 0.97 between different

stations. Given this coherency we have assumed that a single source mechanism and

location is responsible for generating the VLP events. Filtered traces were then stacked for

each component to obtain a unique waveform, which is then used for the waveform

inversion.

Method

The displacement field generated by a seismic source is described by the

representation theorem (Aki and Richard, 1980). For a point source, the theorem may be

written in the frequency domain as:

us

n ω( )= Gnp,q

s ω( ).M pq ω( )+Gnp

s .Fp ω( ),n, p,q = x, y, z (1)

where ω is the frequency us

n is the nth-component of seismic displacement at station s, Fp is

the force applied in p-direction, Mpq is the pq-component of the moment tensor, Gnps

is the

Green tensor which relates the nth-component of impulsive force at the source position,

and Gnp,qs

indicate the spatial differentiation with respect to the q-coordinate of the Green

tensor. In this case we have 9-free parameters, 6 for the moment tensor and 3 for the

single forces. Nakano and Kumagai (2005) proposed an approach to reduce the number

of free parameters considering a predefined set of source geometries. This method is

particularly appropriate when a small number of stations are used. We inverted our signals

for the 2 most likely volcanic seismic source geometries; a crack and a pipe. The appendix

gives the Cartesian components of the moment tensors for a crack and pipe. If we form

the column vector d containing all the data components for all the stations, the matrix G

containing the Green's functions and m the column vector containing the free parameters,

then equation (1) can be rewritten in matrix form:

d=Gm (2)

Equation (2) is solved by minimizing the misfit function between data and synthetics

defined by R=|d-Gm|/|d| where |.| denotes the L2 norm. The best location corresponds to

a point with the smallest misfit. The Green's function between a point source and a station

location is the solution of the wave equation for an impulse force. The complete Green's

tensor can be computed by solving the wave equation using impulse forces in the x, y and

z direction. Using the reciprocity theorem, the Green's tensor can be computed by putting

the single forces at the station locations and taking the wavefield at a source position. This

allows us to compute the Green's tensor between the station and several source positions

with only 3 simulations. These Green's functions are calculated only once for each point of

a 3-D grid for each station and are then subsequently used for all inversions. We used 6

stations yielding 18 simulations to compute the complete Green's tensor necessary for our

inversion (IGP2 waveform was not used in this work). Without information about the 3-D

structure of Ubinas volcano, our calculation of Green's function assumes a homogeneous

medium including the topography. The P-wave velocity is set to 3,500 m/s, the S-wave

velocity to 2,000 m/s and the density to 2,500 kg/m3. The medium is sampled every 20 m

over 576 x 501 x 240 grid nodes. We used a 3D discrete Elastic Lattice Method to

calculate the full 3-D wavefield (O'Brien and Bean, 2004) where we computed the Green's

functions in a 3-D grid spaced 80 m x 80 m x 60 m under the volcanic crater with a total of

12,000 points for the inversion (Figure 1a).

Data inversion

A linear inversion of displacement has been performed in the frequency domain at

each point in the 3-D grid under the crater. The misfit function is computed at each node

and is mapped in order to locate the minimum residual. In our case, two areas show a

value below 0.25, Figure 1b. The first zone is situated 100 m below the crater and the

second is situated in the northern flank of Ubinas volcano. The most probable solution is a

source location situated under the crater. A point in this area was therefore chosen in

order to perform a waveform inversion for the moment tensor and single force, for the

moment tensor only, for a crack and finally for a pipe. The misfit function value for moment

tensor and single forces is 0.22 for the source location under the crater.

Figure 3. Left column, waveform fits for 3 components of all stations, the real data are in blue, the synthetics are in red. The solution for all free parameters, moment tensor and single force is displayed in the middle. The right column displays the solution for moment tensor only.

The misfit value increases for the moment tensor with no single forces to 0.43.

Figure 3 displays the waveform fits for the all free parameters and solutions for the

moment tensor and single force and for the moment tensor only. In both cases, the

moment tensors are similar, but the amplitude is about 10 times lower for the inversion

with the moment tensor only. Bean et al. (2008) demonstrated that in case of uncertainties

in the uppermost part of the velocity structure, inverting signals for the moment tensor and

single forces yields an incorrect source orientation and strong spurious single forces. They

show that an acceptable solution can be obtained by following the procedure of Nakano

and Kumagai (2005), where waveforms are inverted for a set of pre-assumed possible

source geometries like a pipe or crack. The misfit function then depends on the dip θ and

the azimuth ϕ for both crack and pipe source mechanism. The best solution obtained was

for a crack with θ = 40,ϕ = 75 and for a pipe with θ = 35,ϕ = 50. The misfit value for the crack is

0.885 and for the pipe is 0.908.

Figure 4. Ubinas topography and source geometry for a crack (plane) and for a pipe (cylinder) from two different aspects.

Conclusion

We performed a moment tensor inversion for explosions recorded on Ubinas

Volcano from June to August 2006. We inverted a stacked signal representative of the

explosive activity during this period. We calculated Green's function using full waveform

modelling in a homogeneous medium taking into account Ubinas topography. First, we

inverted for a moment tensor with single forces for all points in the 3-D grid situated under

the crater. The misfit function gave a low value just below the crater, as expected, for the

possible source location of the explosion activity. Then we performed an inversion for two

assumed source mechanisms using the previous location. We obtained two possible

orientations for a pipe and a crack with comparable misfit values. Figure 4 indicates the

source geometry inside the volcano. The pipe orientation is orthogonal to the crater

direction. The crack is centered 100 m below the bottom of crater and about 250 m to the

East. Results suggest the most likely solution is the crack with a normal vector oriented

N15°E in the horizontal plane and 40° from the vertical axis. The crack plane could

correspond to the regional trend identified by Thouret et al. (2004) oriented NNW-SSE.

References

Aki, K., and P. G. Richard (1980), Quantitative seismology, 932 pp, W. H. Freeman, New York.

Bean, C., Lokmer, I. and O'Brien, G. (2008) 'Influence of near-surface volcanic structure on long-period seismic signals and on moment tensor inversions: Simulated examples from Mount Etna'. Journal of Geophysical Research-Solid Earth, 113, B08308Chouet et al., 2005

Hidayat, D., Chouet, B., Voight, B., Dawson, P. and Ratdomopurbo, A., 2002. Source mechanism of very-long-period signals accompanying dome growth activity at Merapi volcano, Java, Indonesia. Geophys. Res. Lett. 29 23, p. 2118 (DOI 10.1029/2002GL015013)

Kumagai, H., Chouet, B.A. and Nakano M., (2002) Waveform inversion of oscillatory signatures in long-period events beneath volcanoes, J. Geophys. Res. 107, p. 2301

Legrand, D., Kaneshima, S. and Kawakatsu, H., (2000). Moment tensor analysis of near-field broadband waveforms observed at Aso, Japan. J. Volcanol. Geotherm. Res., 101: 155-169.

Lokmer, I., Bean, C. J., Saccorotti, G., Patane, D., (2007) 'Moment-tensor inversion of LP events recorded on Etna in 2004 using constraints obtained from wave simulation tests'. Geophysical Research Letters, 34, L22316

Nakano, M. and Kumagai, H., Waveform inversion of volcano-seismic signals assuming possible source geometries, Geophys. Res. Lett. 32 (2005), p. L12302

Neuberg, J., Baptie, B., Luckett, R. and Stewart, R., (1998). Results from the broadband seismic network on Montserrat. Geophys. Res. Lett., 25(19): 3661-3664.

Neuberg, J., (2000). Characteristics and causes of shallow seismicity in andesite volcanoes. Phil. Trans. R. Soc. Lond., A 358: 1533-1546.

O'Brien, G. S.; Bean, C. J (2004) 'A 3D discrete numerical method for wave propagation in heterogeneous media including topography'. Geophysical Research Letters, 31 (14).

Simkin T, and Siebert L (1994). Volcanoes of the World, 2nd edition. Geoscience Press, Tucson, 349 p

Rivera M, Thouret JC, Gourgaud A (1998) Ubinas, el volcán más activo del sur del Perú desde 1550: Geología y evaluación de las amenazas volcánicas. Bol Soc Geol Perú 88:53–71.

Thouret J.-C., Rivera M., Wörner G., Gerbe M.-C., Finizola A., Fornari M., Gonzales K., (2005). Ubinas: evolution of the historically most active volcano in Southern Peru. Bull. Volc., 67, 557-589.

Taipe, E., Analisis de la actividad sismica del volcan Ubinas para el periodo marzo-abril 1998, Tesis, Universidad San Agustin, Arequipa, 2008.

Waite, G.P., B.A. Chouet, and P.B. Dawson (2008), Eruption dynamics at Mount St. Helens imaged from inversion of broadband waveforms: interaction of the shallow magmatic and hydrothermal system, J. Geophys. Res., 113, B02305

Appendix

The Cartesian components of the moment tensors for a crack and pipe from Nakano and

Kumagai (2005).

A crack

M xx ω( )= M0 ω( ) λ / µ + 2sin2θcos

2ϕ( ),

M yy = M 0 λ /µ + 2sin2θsin

2ϕ( ),

M zz = M 0 λ /µ + 2cos2θ( ),

M xy = M yx = M 0 sin2θsin2ϕ( ),

M xz = M zx = M0 sin2θcosϕ( ),

M yz = M zy = M0 sin2θsinϕ( ).

A pipe

M xx = M 0 λ /µ + cos2θcos

2ϕ +sin2 ϕ( ),

M yy = M 0 λ /µ + 2cos2θsin

2ϕ + cos2ϕ( ),

M zz = M 0 λ / µ +sin2θ( ),

M xy = M yx = −

1

2M0 sin2θsin2ϕ( ),

M xz = M zx = −

1

2M0 sin2θcosϕ( ),

M yz = M zy = −

1

2M0 sin2θsinϕ( ).

M0 represents the scalar seismic moment and λ and µ are the elastic Lamé's constants.

The angles θ and φ are the dip and the azimuth for both a crack and a pipe source

mechanism. If we assume a value for λ µ then the free parameters in the moment tensor

for both the crack and the pipe are M0, θ and ϕ .