Focal Mechanism and Moment Tensor Analysis (2011)

Moment Tensor Inversion Assignment from Prof. Yagi

International Institute of Seismology and Earthquake Engineering, Building Research Institute

Prepared by Siti Norbaizura binti Mat Said (Seismology Group)

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Moment Tensor Inversion

Moment tensor is one of the most important information of earthquakes. From moment tensor solutions, we can obtain seismic moment (𝑀0 ), moment magnitude (Mw) and fault type of earthquakes and these information is necessary for investigation of detailed seismic source process (Yuji Yagi and Naoki Nishimura). It is desirable to determine earthquake source model in a more objective way such as using computer (other than the fault angle representation) because moment tensor is linearly related to ground displacement recorded by seismometer. This solution can be estimated by inversion analysis of seismic waveforms observed by local and global seismic networks ( e.g Dziewwonski et al.,1981; Kikuchi and Kanamori, 1991; Kawakatsu, 1995). The followings are the results obtained from the moment tensor inversion technique developed by Yuji Yagi and Naoki Nishimura (were applied for two large earthquakes and one medium earthquake as per Example1, Example2 and Example3 in MT_inversion folder given by Prof. Yagi) which is located at (42.357,144.557), (42.944,145.280) and (42.890,145.482) , respectively.

Example 1

Fig. 1 Results of moment tensor inversion for event in Example 1. (a) shows the focal mechanism

(top left-hand graph), the information of source parameters (top right-hand graph), and observed

and synthetic waveforms (black lines and red lines, respectively; bottom graph) . The numbers

below the station code indicate the maximum amplitude (in unit of cm/sec). A variance of 0.0559

was obtained with a seismic moment of 3.298x1018 N m. There is good agreement in both

waveform and amplitude shown by the synthetic and the real data. (b) shows the graph of

Variance vs Depth. Fourteen (14) depths were tried and a well defined global minima is observed

which gives the value of depth (35km) at variance of 0.0559.

(a)

(b)

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(a)

(b)

Fig. 2 Results of moment tensor inversion for event in Example 2. (a) shows the focal mechanism

(top left-hand graph), the information of source parameters (top right-hand graph), and observed

and synthetic waveforms (black lines and red lines, respectively; bottom graph) . The numbers

below the station code indicate the maximum amplitude (in unit of cm/sec). A variance of 0.0975

was obtained with a seismic moment of 1.490x1015 N m. Generally it is observed that both

synthetic and real data are having good agreement in waveform (as to exclude HID station for it

fails to produce complexity in observed data, especially the level of Pn energy on all tangential,

radial and vertical component). (b) shows the graph of Variance vs Depth. Fourteen (14) depths

were tried and lowest minimum variance (intersection) gives depth as 40.0 km . (will be better

defined with the removal of station in red Tr function).

Example 2

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(a)

Fig. 3 Results of moment tensor inversion for event in Example 3. (a) shows the focal mechanism

(top left-hand graph), the information of source parameters (top right-hand graph), and observed

and synthetic waveforms (black lines and red lines, respectively; bottom graph) . The numbers

below the station code indicate the maximum amplitude (in unit of cm/sec). A variance of 0.0812

was obtained with a seismic moment of 2.175x1019 N m. Both synthetic and real data are having

good agreement in waveform and amplitude. (b) shows the graph of Variance vs Depth. Fourteen

(14) depths were tried and a significant well defined global minima is observed which gives the

value of depth 50 km at variance of 0.0812 (will be better defined with the removal of station in

white Tr function).

(b)

Example 3

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Event Seismic Moment , 𝑴𝟎

(N m)

Moment Magnitude, 𝑴𝒘

Depth (km)

Half duration (sec)

Normalized L2 Norm

Example1 3.298x1018 6.3 35 4 0.0559 Event A 7.630x1018 6.5 35 6 0.1130

Ex ample2

1.490x1015

4.0

40

5

0.0975

Event C 2.4601015

4.2

40

4

0.1020

Example3

2.175x1019

6.8

50

7

0.0812

Event B 3.1801019 7.0 50 6 0.1290

Table 1 Comparison between source parameters obtained from this assignment

(Example 1, Example 2 and Example 3) with the ones extracted from research paper by

Prof Yagi and N. Nishimura (Event A, Event C and Event B)

Table 1 shows the seismic moment, moment magnitude, depth of centroid and the half duration

of source time function for each event with formulation of program set constructed by Yuji Yagi

and Naoki Nishimura for estimating moment tensor solutions using near source seismograms.

Difference is due to the change of filtering and structure information (where the lowest variance

who gives best solution for source parameters had to be found). It is observed that lower variance

gives lower value of both seismic energy, which reflect that filtering and structure information can

underestimate these values.

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References

Yagi, Y. and N. Nishimura, Moment Tensor Inversion of Near Source Seismograms.

Dreger, D.S., and Helmbeger, D.V., 1993, Determination of Source Parameters at Regional Distances

With Three-Component Sparse Network Data, Geophys. J. R., 98, B5, 8107 – 8125.

Y.Yagi, 2011,Focal Mechanism and Moment Tensor Analysis, IISEE Lecture Note 2010-2011, p.59

Appendix

Map shows the location of stations and earthquakes. The triangles

and the stars represent the location of stations and the epicenter,

respectively.