**Focal Depth Determination for Moderate and Small Earthquakes by Modeling Regional Depth Phases** *sPg***,** *sPmP***, and** *sPn*

Shutian Ma *Carleton University Canada* 

### **1. Introduction**

142 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

Chen, W.S., Yang, C.C., Yen, Y,C., Lee, L.S., Lee, K.J., Yang, H.C., Chang, H.C., Ota Y., Lin,

Chen, W.S., Lee, K.J., Lee, L.S., Streig, A.R., Chang, H.C., Lin, C.W. (2007b) Paleoseismic

Chen, Y.G., Chen, Y.M., Chen W.S., Lee, K.J., Lee, L.S., Lu, S.T., Lee, Y.H., Watanuki, T., Lin,

source fault of the 1999 Chi-Chi earthquake, Taiwan, *Quat. Int.* 199, 25–33. Chiu, H.T. (1971) Folds in the Northern Half of Western Taiwan, *Petrol. Geol. Taiwan* 8, 7–19. Dominguez, S., Avouac, J.P., Michel, R. (2003) Horizontal coseismic deformation of the 1999

Hardy, S., Ford, M. (1997) Numerical modeling of trishear fault-propagation folding,

Kao, H., and W.P. Chen (2000) The Chi-Chi Earthquake sequence: active, out-of-sequence

Lai, K.Y., Chen, Y.G., Hung, J.H., Suppe, J., Yue, L.F., Chen, Y.W. (2006) Surface deformation

Machette, M.N., Personius, S.F., Nelson, A.R. (1992) Paleoseismicity of the Wasatch Fault

Ota. Y., Chen, Y.G., Chen, W.S. (2005) A review on paleoseismological and active fault study

Pathier, E., Fruneau, B., Deffontaines, B., Angelier, J., Chang, C.P., Yue, S.B., Lee, C.T. (2003)

Streig, A.R., Rubin, C.M., Chen, W.S., Chen, Y.G., Lee, L.S., Thompson, S., Madden, C., Lu,

Suppe, J. (1981) Mechanics of mountain building and metamorphism in Taiwan, *Geol. Soc.* 

Wang, C.Y., Li, C.L., Su, F.C., Leu, M.T., Wu, M.S., Lai, S.H., Chern, C.C. (2002) Structural

Yue, L.F., Suppe, J., Hung, J.H. (2005) Structural geology of a classic thrust belt earthquake: The 1999 Chi-Chi earthquake Taiwan (Mw = 7.6), *J. Struct. Geol.* 27, 2058–2083.

Front, Utah, *U.S. Geol. Surv. Professional Paper* 1500, p. A1–A30. Mitra, S. (2002) Fold-accommodation faults, *Am. Asso. Petrol. Geol. Bull.* 86, 4, 671–693. Ota, Y., Huang, C.Y., Yuan, P.B., Sugiyama, Y., Lee, Y.H., Watanabe, M., Sawa, H., Yanagida, M.,

the Chelungpu Fault, Taiwan, *West. Pacific Earth Sci.* 1, no. 4, 487–498.

Chushan excavation site, *Bull. Seism. Soc. Am.,* 97(1B), 1–13.

earthquakes, central Taiwan, *J. Asian Earth Sci.* 31, 204–213.

Erslev, E.A. (1991) Trishear fault-propagation folding, *Geology* 19, 617–620.

thrust faulting in Taiwan, *Science* 288, 2346–2349.

and co-seismic slips, *Quat. Int.*147, 44–54.

in Taiwan, *Tectonophysics* 408, 63–77.

methods, *Terr. Atmo. Ocea. Sci.* 13, 211–226.

dori:10.1029/2006JB004493.

*China Mem.* 4, 67–89.

73–88.

B2, 2083, doi:10.1029/2001JB000951

*Tectonics* 16, 841–854.

C.W., Lin, W.H., Shih, T.S., Lu, S.T. (2007a) Late Holocene paleoseismicity of the southern portion of the Chelungpu fault, central Taiwan: Evidence from the

evidence for coseismic growth-fold in the 1999 Chichi earthquake and earlier

Y.N. (2009) Optical dating of a sedimentary sequence in a trenching site on the

Chi-Chi earthquake measured from SPOT satellite images: Implications for the seismic cycle along the western foothills of central Taiwan, *J. Geophy. Res.* 108, no.

related to kink-folding above an active fault: Evidence from geomorphic features

zones: a summary of recent investigation, interpretations and conclusions, In Gori, P.L. (Ed.), Assessment of regional earthquake hazards and risk along the Wasatch

Sasake, S., Tanifuchi, K. (2001). Trenching study at the Tsaotun site in the central part of

Coseismic displacements of the footwall of the Chelungpu fault caused by the 1999, Taiwan, Chi-Chi earthquake from InSAR and GPS data, *Earth Planet. Sci. Lett*. 212,

S.T. (2007) Evidence for prehistoric coseismic folding along the Tsaotun segment of the Chelungpu fault near Nan-Tou, Taiwan, *J. Geophy. Res.* 112, B03S06,

mapping of the 1999 Chi-chi earthquake fault, Taiwan by seismic reflection

Earthquake focal depth is a critical parameter for seismological research, seismotectonic study, seismic hazard assessment, and event discrimination. For most earthquakes with *M*<sup>W</sup> ≥4.5, the focal depth can be estimated from the arrival times of the teleseismic depth phase *sP* (or *pP*) and its reference phase *P*. Many seismologists have studied how to detect and use teleseismic depth phases to estimate focal depth (e.g., Goldstein and Dodge, 1999). For smaller earthquakes, focal depths can be estimated jointly while being located with the arrival times of the *Pg* and *Sg* phases recorded at close stations. Because stations in a regional network are generally not dense enough to control focal depth, operators often use default focal depths for regional events.

If regional depth phases can be identified, an alternative solution for moderate and small earthquakes is to use regional depth phases to estimate focal depth. The *P* portion of regional waveform records contains three major parts: (1) the *P*-wave travels directly to the station; (2) the *P-* or *S*-wave travels upward to the surface in the source region, is reflected or converted at the surface and then travels downward to the Moho (or interfaces), is reflected or refracted there, and then travels upward to the station; and (3) the *P*-wave travels downward to the Moho (or interfaces), is reflected there and then travels upward to the station. One feature of *P*- and *S*-waves is that the amplitude of the *S*-wave radiated from the source is generally stronger than that of the *P*-wave by about five times (Aki and Richards, 1980) and the period of the *S*-wave is longer than that of the *P*-wave on the same record.

From this analysis we know that there are regional depth phases in the *P* portion of the record and the usable regional depth phases are (1) *sPg* (the *S*-wave travels upward to the surface, is converted to a *P*-wave at the critical angle, then the *P*-wave travels along or close the surface to the station), (2) *sPmP* (the *S*-wave travels upward to the surface, is converted to a *P*-wave, then the *P*-wave travels downward to the Moho, is reflected there and travels upward to the station; Langston *et al*., 2003), and (3) *sPn* (the *S*-wave travels upward to the surface, is converted to a *P*-wave, then the *P*-wave travels along the *Pn* path to the station;

 This chapter is adapted from the paper "Focal Depth Determination for Moderate and Small Earthquakes by Modeling Regional Depth Phases *sPg*, *sPmP*, and *sPn"*, *Bull. Seism. Soc. Am*. **100,** 1073-1088

Zonno and Kind, 1984). Fig. 1 (Ma and Eaton, 2011) shows the sketch paths of these regional depth phases. Many scientists have studied regional depth phases to some extent (e.g., King, 1979; Helmberger and Engen, 1980; Langston, 1987, 1996; Mulder and Lamontagne, 1990; Zhao and Helmberger, 1991, 1993; Bock, 1993; Ebel, 1995; Bock *et al*., 1996; Zhu and Helmberger, 1997; Saikia, 2000; Saikia *et al*., 2001; Bent and Perry, 2002; Savage *et al*., 2003; Uski *et al*., 2003).

Fig. 1. Sketch figures for regional depth phase *sPg* (upper panel), *sPmP* (middle), and *sPn* (bottom).

Regional depth phases (*sPg*, *sPmP,* and *sPn*) can be used to estimate focal depth if they and their reference phases (*Pg*, *PmP,* and *Pn*) can be correctly identified. Following Langston (1987) and Bock *et al*. (1996), we developed a method to use the regional depth phases to determine focal depths. The principle is: (1) calculate synthetics with the reflectivity method (Randall, 1994) at a station with a reasonable range of depths; (2) compare the synthetics with the observed values at the same station; and (3) take as the focal depth of the earthquake the depth at which the synthetic and the observation have similar time differentials (regional depth phase to its reference phase).

We previously reported some aspects of the regional depth-phase modeling (RDPM) method (e.g., Ma *et al*., 2003; Ma and Atkinson, 2006). Here we introduce the RDPM method more systematically and describe the principles and features of the three depth phases in detail. We have proved that the assumptions of depth phase *sPmP* and its reference phase *PmP* are correct, and by conducting several tests, found in which regions the regional depth phases are developed and in which they are not, and which factors contribute to errors in the modeled focal depths. We also found that the contents of *PmP* and *sPmP* come from different interfaces beneath the source. These findings are useful for researchers who want to use the RDPM method, and especially for identifying the regional depth phases and their reference phases.

Because we use regional synthetics as a "ruler" to measure focal depth from observed waveforms, we first describe how to generate synthetics that are suitable to be used as the "ruler" and discuss some features of the regional depth phases.

Zonno and Kind, 1984). Fig. 1 (Ma and Eaton, 2011) shows the sketch paths of these regional depth phases. Many scientists have studied regional depth phases to some extent (e.g., King, 1979; Helmberger and Engen, 1980; Langston, 1987, 1996; Mulder and Lamontagne, 1990; Zhao and Helmberger, 1991, 1993; Bock, 1993; Ebel, 1995; Bock *et al*., 1996; Zhu and Helmberger, 1997; Saikia, 2000; Saikia *et al*., 2001; Bent and Perry, 2002; Savage *et al*., 2003;

Fig. 1. Sketch figures for regional depth phase *sPg* (upper panel), *sPmP* (middle), and *sPn*

differentials (regional depth phase to its reference phase).

"ruler" and discuss some features of the regional depth phases.

Regional depth phases (*sPg*, *sPmP,* and *sPn*) can be used to estimate focal depth if they and their reference phases (*Pg*, *PmP,* and *Pn*) can be correctly identified. Following Langston (1987) and Bock *et al*. (1996), we developed a method to use the regional depth phases to determine focal depths. The principle is: (1) calculate synthetics with the reflectivity method (Randall, 1994) at a station with a reasonable range of depths; (2) compare the synthetics with the observed values at the same station; and (3) take as the focal depth of the earthquake the depth at which the synthetic and the observation have similar time

We previously reported some aspects of the regional depth-phase modeling (RDPM) method (e.g., Ma *et al*., 2003; Ma and Atkinson, 2006). Here we introduce the RDPM method more systematically and describe the principles and features of the three depth phases in detail. We have proved that the assumptions of depth phase *sPmP* and its reference phase *PmP* are correct, and by conducting several tests, found in which regions the regional depth phases are developed and in which they are not, and which factors contribute to errors in the modeled focal depths. We also found that the contents of *PmP* and *sPmP* come from different interfaces beneath the source. These findings are useful for researchers who want to use the RDPM method, and especially for identifying the regional depth phases and their

Because we use regional synthetics as a "ruler" to measure focal depth from observed waveforms, we first describe how to generate synthetics that are suitable to be used as the

Uski *et al*., 2003).

(bottom).

reference phases.
