Synthetic examination

The superior resolution of the 2D MUSIC BP applying to shallow earthquakes has already been demonstrated by (Meng et al., 2011, 2012a, 2012b). In this section, we further evaluate the reliability of 3D MUSIC BP imaging on several rupture

propagation scenarios inspired by the BP results of 2013 Okhotsk deep earthquake sequence. Each hypothetical earthquake source model consists of several subevents to simulate the rupture propagation with presumed rupture speed ranging from 3 to 4.5 km/sec. The NA and EU seismic stations shown in Figure 3.2d are taken as our test arrays. The synthetic waveforms are calculated by the FK method (Zhu and Rivera, 2002) which includes all seismic phases with all ranges of slowness excited by the velocity structure and has better simulation on the nonstationary seismic wave properties than the synthetic waveforms from ray tracing method of WKBJ.

Our first vertical resolution experiment is motivated by the depth difference between two rupture stages of mainshock and fast downward ruptures of two

aftershocks. We set up two rupture scenarios which both consist of 6 subevents at the same epicenters with focal depths and gradually move upward or downward. To have more realistic simulation, we set later subevents having much smaller magnitudes which can imitate the poorer coherency of the waveforms and push this examination more difficult to recover. The focal depth is set from 600 to 645 km. Figure 3.8 shows the recovered 3D BP images of vertical rupture experiments. The combined P- and pP-waves 3D BP images retrieve the epicenters of subevents precisely for both upward and downward rupture tests. The cross-sections (insets of Figure 3.8) demonstrate the

spatial uncertainty of the combined BP images which is reduced significantly comparing with those from P- or pP-wave BP images. As the focal depth, the

combined BP images apparently recover the rupture propagation better than the P-only or pP-only BP images do. Whereas, in overall, the P- or pP-wave only MUSIC BP images seem obtain more reliable subevent hypocenters when the propagation direction is against the ray path (Figure 3.8b&f). In other words, the rupture

propagating close to the ray path tends to result in stronger smearing effects and less reliability of BP images (Figure 3.8c&e). In more realistic circumstance, it is typical that we only have P-wave to perform BP imaging (Figure 3.8b&e), hence the P-wave BP results achieve acceptable resolution for recovering both the epicenters and focal depths although we will see larger spatial uncertainty for the downward rupture scenario. For the pP-wave BP image, as we expected, it’s more un-reliable than the P-wave BP image. Because of more energy decaying in high frequency, the pP-waves holding more lower frequency contents and longer period signals usually suffer stronger swimming and smearing effects (Meng et al., 2012b) which also explains the great uncertainty of pP-wave BP results for the 2013 Okhotsk deep earthquake (Figure 3.4b).

Figure 3.8 Synthetic tests of vertical rupture scenarios.

Map and cross-sections showing the 3D BP results for (a)-(c) downward and (d)-(e) upward rupture scenarios. (a) & (d) show the resultant BP images by combining those obtained by P- and pP-waves, respectively. (b) & (e) are the BP images of P-wave. (c) & (f) are the BP images of pP-wave. The stars showing the subevent hypocenters are colored and scaled by the hypothetical occurrence time after the 1^st subevent and with corresponding magnitude. The inset in each figure shows the cross-section along the latitude. The resultant BP images are shown with the symbols the same with those in Figure 3.3.

The second experiment is an overall Southwestern-dipping scenario which is inspired by the high-frequency 3D BP imaging result from EU seismic array (Figure 3.3b). We like to examine whether the NA seismic array is capable to recover this rupture scenario if this is the true 1^st rupture propagation of the mainshock. This testing model includes 5 subevents with a rupture speed of 4 km/s. In order to set up more

sophisticated rupture experiment, as shown in Figure 3.9, after the rupture initiates, a smaller subevent located at the north of the epicenter, then the rupture gradually moves to SE-ward direction and the focal depths of subevents also increase from 600 to 645 km at the same time. Figure 3.9a shows great agreements in both horizontal and vertical direction between the presumed and recovered subevents from the combined BP images of P- and pP-waves. As the result from pP-wave only shown in Figure 3.9c, the BP imaging only retrieves reliable initial NE-ward rupture (subevent 1 & 2). The P-wave BP result is overall consistent with the input rupture model although there are few unrealistic source radiators which falls to the range parallel to the source-to-array path. This unavoidable bias accompany with large smearing zone occurs because the BP tends to project those subsequently low coherent wavetrains inside the smearing area which has long axis parallel to the source-to-array path. Similar biases are also observed in the vertical rupture experiment at the end of the rupture (Figure 3.8). In general, disregarding those weak source radiators accompany with large spatial uncertainties, the P-wave BP result retrieves the hypocenters of input subevents

correctly including the focal depths (Figure 3.9b). After briefly summery this synthetic test results with the BP imaging of the mainshock from two arrays that we believe NA seismic array should also observe the SE-ward propagation as EU array does if the 2013 Okhotsk deep earthquake do rupture toward SE direction during the 1^st rupture stage.

Figure 3.9 Synthetic tests of SE-ward dipping rupture scenario.

The recovered BP image snapshots by (a) combined, (b) P-wave and (c) pP-wave BP images. Insets: the cross-section along the Profile AA’. The symbol configurations are the same as Figure 3.8.

The last synthetic experiment, based on the 3D BP results of the mainshock from NA seismic array, is a complex rupture scenario having total 13 subevents comprising two subhorizontal ruptures against to each other. Figure 3.10a-c shows the BP imaging results from NA seismic array. The first one goes to NE-direction at depth of 609 km and the SSW-ward one propagates at depth of 645 km. As expected, the P-wave BP is capable to recover the input subevent hypocenters well (Figure 3.10b) even though we notice some errors on estimating the focal depth for the initial NE-ward rupture. It’s also not surprise to see the BP results of pP-wave having biased radiators recovery for the second SSW-ward rupture (Figure 3.10c) because of strong swimming and

smearing effects as discussed earlier. Nevertheless, the integrated BP images of P- and pP-wave (Figure 3.10a) recovered scenario precisely and approved the reliability and stability of the 3D BP images likewise.

Figure 3.10 Synthetic tests of two-stage anti-parallel rupture scenarios.

Map and cross-sections showing the 3D BP results with circles and diamonds are obtained from the (a)-(c) NA and (d)-(e) EU seismic arrays, respectively. Insets: the cross-section along the Profile AA’.

The layout and symbol configurations are the same as Figure 3.8 & Figure 3.7.

To have cross-reference, we also examine whether the EU seismic array is capable to resolve this anti-parallel rupture scenario (Figure 3.10d-f). Instead of getting the NE-direction propagation of 1^st rupture stage, the EU seismic array projects the wavetrains to an East-ward propagation rupture which is literally parallel to the source-to-array (EU) direction. Summarizing the BP results shown in Figure 3.9b and Figure 3.10e, we found one of the disadvantages of BP imaging is the near

perpendicular geometry between source-to-array path and rupture propagation. The undesirable geometry perfectly explains the inconsistent 1^st rupture stage of 2013 Okhotsk earthquake from NA and EU arrays (Figure 3.3). By our rupture scenario experiments, we are able to confirm that the East-ward propagation of 1^st rupture stage observed by EU BP images is deviated from the true rupture propagation.

Taking a compressive view of above synthetic experiments (Figure 3.9b & Figure 3.10b), For the late arriving less coherent and weak wavetrains, the BP imaging

becomes unstable and tends to back project the energy radiators along the

source-to-array path rather than to the true propagation when the rupture direction is nearly perpendicular to the source-to-array path. We believe the biased BP result is related with the less coherent wavetrains, the stronger smearing and swimming effects which are contributed together to make the source energy been projected to the error locations along the ray path. This particular phenomenon could be treated as an important indicator for us to examine and verify the BP images carefully if the tempo-spatial distribution aligns parallel to the ray path. In practical, it’s easy to encounter poor geometry of propagation with the ray path when performing the BP.

Other than the instability of horizontal locations of subevents, the cross-sections of all

synthetic tests indicate that the focal depths of subevents recovered by combined MUSIC BP images of P- and pP-waves are reliable and stable. For the synthetic results from P-wave only BP images, we also approve the reliability on resolving the focal depth of subevents, even in the circumstance of undesirable geometry between the rupture direction and ray path (Figure 3.9b and Figure 3.10e).

Our synthetic experiments demonstrate the importance of combining P-wave and depth phases BP images to cope with the perpendicular geometry of rupture

propagation with the ray path (Figure 3.8~Figure 3.10) and approve the depth

difference of two-stage antiparallel subhorizontal ruptures of 2013 Okhotsk mainshock and fast subvertical ruptures of two aftershocks.