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Dr Rosalia Daví Dr Vaclav Vavryčuk. Moment tensor inversion using observations of unknown amplification. Institute of Geophysics, Academy of Sciences, Praha, Czech Republic e-mail: [email protected] . - PowerPoint PPT Presentation
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Moment tensor inversion using observations of unknown amplification
Dr Rosalia DavíDr Vaclav Vavryčuk
Institute of Geophysics, Academy of Sciences, Praha, Czech Republice-mail: [email protected]
We propose a method for calibrating seismic networks in order to retrieve accurate moment tensors based on a joint inversion of large datasets of earthquakes for moment tensors and for amplifications of stations of the network.
The method is suitable for detecting technical problems at the stations (reverse polarities, incorrect orientation and amplification of sensors), for quantify local site effects and unify seismic networks.
Synthetic tests and numerical modeling (mapping the station distribution, the velocity model, the hypocenter locations of West-Bohemia).
Application in West-Bohemia (retrieval of highly accurate moment tensors).
umG
)(6
)(5
)(4
)(3
)(2
)(1
)2(6
)2(5
)2(4
)2(3
)2(2
)2(1
)1(6
)1(5
)1(4
)1(3
)1(2
)1(1
)(
)2(
)1(
.....................NNNNNNN GGGGGG
GGGGGG
GGGGGG
g
g
g
G
TMMMMMM 121323332211m
TNuuu )()2()1( ...u
METHODOLOGY
System of equations of the standard moment tensor inversion of amplitudes for one event
where
G is the Nx6 matrix of the Green’s function amplitudes
u is the N-vector of the displacement amplitudes observed at N stations
m is the 6-vector of moment tensor components
)(ilG is spatial derivatives of the Green’s tensor calculated for the ith station.
)1()1()1( NNN uCmg
0)1()1()1(
um
g
0GNNN Cu
If we incorporate into the inversion one uncalibrated station with index i = N+1 and unknown station amplification C(N+1)
Combining the equations we obtain:
IT IS IMPORTANT TO HAVE HIGH VARIABILITY OF FOCAL MECHANISMS
Generation of datasets of events with synthetic focal mechanisms.
Calculation of synthetic amplitudes.
Contamination of the amplitudes with random noise.
Numerical modeling
Multiplication of the noisy amplitudes by synthetic station amplifications.
Application of the procedure to calibrate the network and to retrieve the moment noise.
Partial network calibration
3 different datasets consisting of 10, 50 and 200 events with 2 station configurations defined as the sparse and dense configurations.
The synthetic P-wave amplitudes were contaminated with uniformly distributed random noise of 3 levels: up to 10%, 25% and 50% of the noise-free amplitude.
Events Fixed stations
Noise level [%] Δsparse Δdense
10 0.072 0.041
10 1 25 0.164 0.085
50 0.260 0.169
10 0.031 0.017
50 1 25 0.071 0.045
50 0.113 0.063
10 0.017 0.009
200 1 25 0.031 0.024
50 0.047 0.040
10 0.034 0.029
10 5 25 0.072 0.071
50 0.148 0.125
10 0.012 0.013
50 5 25 0.031 0.029
50 0.053 0.049
10 0.008 0.007
200 5 25 0.022 0.018
50 0.039 0.028
10 - 0.022
10 10 25 - 0.056
50 - 0.105
10 - 0.009
50 10 25 - 0.023
50 - 0.042
10 - 0.005
200 10 25 - 0.016
50 - 0.029
The inversion for the station amplifications is performed repeatedly 100 times for different random noise.
The mean and standard deviations of the retrieved station amplifications are calculated.
The inversion code perform better with a high number of stations with known amplifications, a low level of noise and a high number of jointly analyzed events.
Sensitivity to the station location
The stations located in the proximity to the nodal lines display higher standard deviations compared to the other stations.
If the condition of a variety of focal mechanisms is satisfied, the inversion yields accurate results independently of the station locations.
Complete network calibration
Simple initial guess
Calculation of the 1st station amplificationThe other amplifications are fixed
Normalization of the N retrieved amplifications
New set of station amplifications
Improved initial guess
Starting set of station amplifications
Difference in two successive sets of amplifications is small
Calculation of the 2nd station amplificationThe other amplifications are fixed
Calculation of the Nth station amplificationThe other amplifications are fixed
Repeating for all stations
Final set of station amplifications
Yes
No
New iteration
The complete network calibration can adjust station amplifications by including the local site effects at all stations.
The simplest way to calibrate the complete network (of N stations), is to perform the calibration in iterations.
Amplification of the 1st station is fixedThe other amplifications are calculated
All amplifications are normalized
N sets of N retrieved amplifications
Repeating for all stations
Improved initial guess of station amplifications
Amplification of the 2nd station is fixedThe other amplifications are calculated
All amplifications are normalized
Amplification of the Nth station is fixedThe other amplifications are calculated
All amplifications are normalized
Averaging of N amplifications for each station
Simple initial guess of station amplifications
2 4 6 8 10Itera tion
0.6
0.8
1
1.2
1.4
Cor
rect
ion
coef
ficie
nt
2 4 6 8 10Iteration
0.96
0.98
1.00
1.02
1.04
Co
rrec
tion
co
effic
ien
t
(a)
(b)
Simple initial guess
Improved initial guess
1) We assume a simple initial guess when the starting values of all station amplifications equal 1.
2) We estimate the starting values using the improved initial guess.
The iteration process with the improved initial guess (b) converges much faster.
Convergence
0 5 10 15 20
Station
0.4
0.8
1.2
1.6
2
Am
plifi
catio
n
(a)
(b)
0 5 10 15 20
Station
0
4
8
12
Am
plifi
catio
n e
rro
r [%
]
KAC
Accuracy
The retrieved amplifications are slightly biased from the true amplifications (noise in the data).
The lowest accuracy is achieved for station KAC (in the intersection of the nodal lines).
True station amplificationsRetrieved station amplifications
Difference between the true and retrieved amplifications in percent.
Data set DC [%]CLVD
[%]ISO
[%]abs(CLVD)
[%]abs(ISO)
[%] RMS
Uncorrected moment tensors
Noise-free data 77.6 -17.2 -4.7 17.7 4.7 0.248
Noisy data 77.5 -17.1 -4.6 17.8 4.8 0.266
Corrected moment tensors
Noise-free data 100.0 0.0 0.0 0.0 0.0 0.000
Noisy data 92.5 -0.7 0.1 5.6 1.8 0.115
Uncorrected moment tensors
0 40 80 120 160 200Event
0
0.1
0.2
0.3
0.4
0.5
RM
S
DC component Non-DC components RMS
Corrected moment tensors
DC component Non-DC components RMS
-60 -45 -30 -15 0 15 30C LVD [% ]
-20
-10
0
10
ISO
[%
]
-60 -45 -30 -15 0 15 30C LVD [% ]
-20
-10
0
10IS
O [
%]
0 40 80 120 160 200Event
0
0.1
0.2
0.3
0.4
0.5
RM
S
The focal mechanisms (left-hand plots) are better clustered for uncalibrated moment tensors (artificial).
The uncorrected moment tensors display significant false negative CLVD and ISO components.
The corrected moment tensors display smaller CLVD and ISO components and form a cluster centered around the origin of coordinates.
The RMS values are higher for the uncalibrated network.
The RMS values decrease for corrected moment tensors.
WEST BOHEMIA REGION
Epicentres of the 2008 swarm (red circles) .
Depth of 7.6 to 10.8 km.
22 short-period seismic stations (yellow triangles).
Czech Republic
Germany
200 micro-earthquakes: min 20 stations, high signal-to-noise ratio and highly accurate hypocenter locations.
(from Vavryčuk, 2011)
2 4 6 8 10Iteration
0.8
1
1.2
Cor
rect
ion
coef
ficie
nt
(a) Simple initial guess
(b) Improved initial guess
2 4 6 8 10Iteration
0.96
0.98
1.00
1.02
1.04
Cor
rect
ion
coef
ficie
nt
Iterations with the improved initial guess converge faster.
Good convergence of the iterations
and a reasonable accuracy of the station amplifications (the variability of the focal mechanisms is higher for observed data).
Convergence
Station Station nameRelative
amplification Abs. errorRel. error
[%]
1 BUBD 1.01 0.02 2.0
2 HOPD 1.24 0.03 2.2
3 HRC 0.62 0.02 3.5
4 HRED 1.16 0.06 5.6
5 KAC 0.85 0.05 6.0
6 KOC 0.65 0.01 2.2
7 KOPD 0.70 0.02 2.2
8 KRC 0.88 0.01 1.6
9 KVC 1.12 0.03 2.7
10 LAC 1.06 0.04 3.3
11 LBC 0.82 0.01 1.0
12 LOUD 1.45 0.02 1.3
13 NKC 1.00 0.01 1.5
14 NKCN 0.88 0.01 1.4
15 PLED 0.79 0.01 1.6
16 POC 1.40 0.04 2.7
17 POLD 1.04 0.02 1.9
18 SKC 1.02 0.02 2.3
19 SNED 0.80 0.01 1.1
20 TRC 1.90 0.04 2.3
21 VAC 0.84 0.01 0.9
22 ZHC 0.78 0.02 2.1
The accuracy of the amplification corrections was estimated using a jack-knife test (the iterative procedure was run 50 times on subsets of 100 randomly selected events).
The achieved accuracy of the station amplifications is ~ 4% for the majority of stations.
The only exceptions are stations KAC and HRED with accuracy of 6.0% and 5.6%.
Accuracy
0 5 10 15 20
Station
0.4
0.8
1.2
1.6
2
Am
plifi
catio
n
0 5 10 15 20
Station
0
2
4
6
8
Am
plifi
catio
n e
rro
r [%
]
KACHRED
TRC
KAC station (unfavorable position).
HRED station (rather high noise level).
No station with a reversed polarity.
TRC station (incorrect calibration of the sensor, incorrect value of the gain factor or an anomalous medium response).
The scatter of the amplification corrections is high: the values range from 0.62 to 1.45.
Accuracy
Uncorrected moment tensors
DC component Non-DC components RMS
Corrected moment tensors
DC component Non-DC components RMS
0 40 80 120 160 200Event
0
0.1
0.2
0.3
RM
S
-60 -45 -30 -15 0 15 30CLVD [% ]
-20
-10
0
10
20
ISO
[%]
0 40 80 120 160 200Event
0
0.1
0.2
0.3
RM
S
-60 -45 -30 -15 0 15 30CLVD [% ]
-20
-10
0
10
20
ISO
[%]
Dataset DC [%] CLVD [%] ISO [%] abs(CLVD) [%] abs(ISO) [%] RMS
Uncorrected moment tensors 76.3 -16.3 -2.3 19.0 4.6 0.191
Corrected moment tensors 83.8 -9.7 -1.5 12.5 3.7 0.112
The DC part of the moment tensors is rather stable.
The non-DC form a more compact cluster for corrected MT.
CLVD and ISO components are less compressive.
The average value of the CLVD changed from -16.3% to -9.7%. The average value of the RMS is reduced from 0.19 to 0.11 .
Conclusions
We propose a method for calibrating seismic networks in order to retrieve accurate moment tensors based on a joint inversion of large datasets of earthquakes for moment tensors and for amplifications of stations of the network.
The inversion works better for dense networks (good focal sphere coverage, high
variety of focal mechanisms and large datasets).
It detects: reverse polarities, incorrect orientation and amplification of sensors, anomalous local site effects at stations.
The tests (for accuracy and stability of the method) show that the moment tensors is retrieved with higher accuracy.
The inversion was applied to calibrate the WEBNET network (dataset of 200 micro-earthquakes that occurred in 2008).
The moment tensors retrieved using amplitudes of properly calibrated stations of the WEBNET network display lower RMS than the original moment tensors.
The focal mechanisms are not changed but the non-DC components of moment tensors changed significantly (one origins of spurious non-DC components might be linked to inaccurate amplifications).
The method is can be used for data gathered: (1) in laboratory experiments, (2) in boreholes or in mines (calibration and orientation are frequently unknown), or (3) in field experiments (networks are inhomogeneous).
Thank you for your attention!
