Moment tensor inversion using observations of unknown amplification

Rosalia DavíVáclav Vavryčuk

Institute of Geophysics, Academy of Sciences, Praha, Czech Republice-mail: rosi.davi@ig.cas.cz

Green’s functions and Moment tensor

The moment tensor represents the stresses acting on the point and describes the physical forces generated by the source.

txun , represents the n component of the displacement

pqM is the pq element of the moment tensor

qnpG ,represents the spatial differentiation along the q direction of the np element of the Green’s functions

un(x,t)=Mpq*Gnp,q

The Green’s functions represent the Earth’s response to an impulsive force acting at a certain point (source location) and propagating to the receiver location

(1)

Moment tensor inversion

Wuu

GmuWGmuT

T

R=

WuGWGGm T1Test

WuGm 1-est

Misfit between calculated and observed data

Solution for noise-free data

Solution for noisy data

3

2

1

23

13

12

33

22

11

321

333231

232221

131211

3,23,12,13,32,21,1

3,323,312,313,332,321,31

3,223,212,213,232,221,21

3,123,112,113,132,121,11

2

1

.

.

.

.

F

F

F

M

M

M

M

M

M

ggg

ggg

ggg

ggg

gggggg

gggggg

gggggg

gggggg

u

u

u

NNNNNNNNNN

amplitudes amplitude ratios full waveforms

• Moment tensor inversion can be performed using:

• The inversion for waveform amplitude

linear allows the use of several input data (P, S or P and S waves) the convolution is reduced into multiplication (waveform is neglected) un(x)=Mpq Gnp,q

• The inversion technique is normally very sensitive to

Lack of sufficient structural information Hypocentres location Quantity and quality of the data

High number of stations with good coverage and high signal to noise ratio are required

Focal sphere

stations

Joint inversion for amplifications and moment tensor

MT INVERSION 6 unknowns

JOINT INVERSIONfor MT and AMPLIFICATION

data recorded by 10 working stations

6 +1 unknownsdata recorded by 9 working stations + 1 with amplification problems

JOINT INVERSIONfor MT and AMPLIFICATION

6 +5 unknownsdata recorded by 5 working stations + 5 with amplification problems

FOR ONE EVENT

10 EQUATIONS

10 EQUATIONS

10 EQUATIONS

METHODOLOGY

IT IS IMPORTANT TO HAVE HIGH VARIABILITY OF FOCAL MECHANISMS

METHODOLOGY

MT INVERSION 600 unknowns

JOINT INVERSIONfor MT and AMPLIFICATION

data recorded by 10 working stations

600 +1 unknownsdata recorded by 9 working stations + 1 with amplification problems

JOINT INVERSIONfor MT and AMPLIFICATION

600 +5 unknownsdata recorded by 5 working stations + 5 with amplification problems

FOR 100 EVENTS

1000 EQUATIONS

1000 EQUATIONS

1000 EQUATIONS

Synthetic tests with noisy data3 levels of noise with 100 realizations (noise level = 0.1, 0.25, 0.50 )

2 main focal mechanisms with variation of 15 degrees

Different station configurations

4 sets of events (number of events = 10, 25, 50, 100)

Sparse configuration Dense configuration

LAC

KOPD

TRC

POLD

KRC

LBC

HRC

ZHC

KAC

VAC

LAC

KOPD

TRC

POLD

KRC

LBC

HRC

ZHC

KAC

VAC

LOUD

SKC

BUBDPOC

KOCNKCN

PLEDHOPDHRED

KVC

SNED

Number of stations with known amplification

noise = 0.5

noise = 0.25

noise = 0.1

Sparse configuration

number of stations with known amplification

Dense configuration

noise = 0.5

noise = 0.25

noise = 0.1

Unknown stations

1 known station 5 known stations

10 known stations 17 known stationsNoise = 0.50 Noise = 0.25 Noise = 0.1

For stations close to the nodal lines the std is high and the amplitude is small

Dense configuration

Noise = 0.50

Noise = 0.25

Noise = 0.1

station order

Results from synthetic tests

Lower noise values gives lower and less scattered standard deviation

Higher number of stations with known amplifications gives smaller standard deviation

For a high variability of the focal mechanisms the results are insensitive to station locations on the focal sphere

Joint inversion with real events

We considered catalogue amplitudes of the 441 real events (Boušková et al., 2011)

22 stations (with only one with unknown amplification – jack-knife test)

Results shows that the majority of our stations have good amplifications values

In order to confirm our results we calculated the RMS as an average of all the events at each station

WEST BOHEMIA REGION

Topographic map of the West-Bohemia/Vogtland region (from Vavryčuk, 2011)

• Epicentres of the 2008 swarm (red circles)

• Depth of 7.6 to 10.8 km

• 22 short-period seismic stations (yellow triangles)

Two principal focal mechanisms

Most common focal mechanism (left lateral strike-slip with a strike of 169o)

Second focal mechanism (right lateral strike-slip with a strike of 304o)

(from Vavryčuk, 2011)

Tectonic structure

The red lines indicate the directions of the two principal faults

Their associate focal mechanisms are also shown (Vavryčuk, 2011).

LOUD and HOPD HAVE WRONG CALIBRATION !

ZHC and TRC are noisy stations

RMS is the misfit between calculated and observed data

Conclusions The joint inversion for focal mechanism and station amplifications is a poweful

tool to perform moment tensor inversion

Results of the synthetic tests (with and without noisy data) show the reliability of our inversion code

Standard deviations decrease with higher number of events and stations with known amplification

Results of the inversions for real events confirm that stations with high amplifications and RMS values are affected by problems (e.g. instrumental problems such as calibration; site effects)

Stations with high RMS values but low amplifications are generally affected by problems strictly related to the inversion (e.g. noisy data or positions)

Acknowledgements

We thank Josef Horálek, Alena Boušková and other colleagues from the WEBNET group for providing us with the data from the 2008 swarm activity and for kind help with their preprocessing.