Geometric effects resulting from the asymmetry of dipping fault: Hanging wall/ footwall

Vol.21 No.3 (275~282) ACTA SEISMOLOGICA SINICA May, 2008 Article ID: 1000-9116(2008)03-0275-08 doi: 10.1007/s11589-008-0275-4 Geometric effects resulting from the asymmetry of dipping fault: Hanging wall/ footwall effects WANG Dong 1), ( 王栋 ) XIE Li-li 1,2) ( 谢礼立 ) HU Jin-jun 1) ( 胡进军 ) 1) Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China 2) School of Civil Engineering and Architecture, Harbin Institute of Technology, Harbin 150090, China Abstract Root-mean-square distance D rms with characteristic of weighted-average is introduced in this article firstly. D rms can be used to capture the general proximity of a site to a dipping fault plane comparing with the rupture distance D rup and the seismogenic distance D seis. Then, using D rup, D seis and D rms, the hanging wall/footwall effects on the peak ground acceleration (PGA) during the 1999 Chi-Chi earthquake are evaluated by regression analysis. The logarithm residual shows that the PGA on hanging wall is much greater than that on footwall at the same D rup or D seis when the D rup or D seis is used as site-to-source distance measure. In contrast, there is no significant difference between the PGA on hanging wall and that on footwall at the same D rms when D rms is used. This result confirms that the hanging wall/footwall effect is mainly a geometric effect caused by the asymmetry of dipping fault. Therefore, the hanging wall/footwall effect on the near-fault ground motions can be ignored in the future attenuation analysis if the root-mean-square distance D rms is used as the site-to-source distance measure. Key words: root-mean-square distance; rupture distance; hanging wall/footwall effects; peak acceleration attenuation relationship; near-fault ground motion CLC number: P315.9 Document code: A Introduction In some great earthquake occurred in recent years, there is a remarkable characteristics in near-fault ground motions, i.e., the hanging wall/footwall (HW/FW) effect (Abrahamson and Silva, 1997; Abrahamson and Somerville, 1996; YU and GAO, 2001; Shabestari and Yamazaki, 2003; XU et al, 2003; TAO and WANG, 2003; LIU et al, 2004; Chang et al, 2004; ZHANG et al, 2006; LI and XIE, 2007). The records of strong ground motion from 1994 Northridge earthquake and 1999 Chi-Chi earthquake in Chinese Taiwan show that the ground motions on HW are much greater than those on FW (YU and GAO, 2001; Chang et al, 2004; Abrahamson and Silva, 1997; Abrahamson and Somerville, 1996). Oldham is believed to be the first man who discovered the HW/FW effects on near-fault Received 2007-10-30; accepted in revised form 2008-03-28. Foundation item: Basic Science Research Foundation of Institute of Engineering Mechanics, China Earthquake Administration (2006B07); Natural Science Foundation of Heilongjiang Province (E2007-13) and Joint Seismological Science Foundation of China (C07025). Author for correspondence: wangdong@iem.ac.cn

276 ACTA SEISMOLOGICA SINICA Vol.21 ground motions. Oldham found that the ground motions on HW were greater than those on FW in 1899 in field survey after the great Assam, India earthquake (12 June, 1897) (Oglesby et al, 2000). Subsequently, Nason (1973), Brune (1996) and Allen (1998) also obtained the observational evidences of this effect individually during the field investigation of the 1971 San Fernando earthquake (Brune, 1996; Oglesby et al, 2000). Besides, Ruegg et al also got the same indication in 1982 when they investigated the El Asnam, Algeria earthquake (Oglesby et al, 2000). From all earthquakes mentioned above, the researchers found a mass of shattered rocks on HW together with many precarious rocks on FW. The shattered rocks on HW underwent a shock of high strain (2.5 10 3 ), which is large enough to crush them into pieces during the intense earthquakes (Brune, 1996). However, the precarious rocks on FW can be easily overturned with the strength of a single finger, and still kept balance after so large earthquakes (Brune, 1996). All these illuminate that much intense ground motions encountered on HW side and relative lower on FW. Nevertheless, the HW/FW effects have not attracted sufficient attention due to the lack of seismic records. Thrust earthquakes typically occur on the dipping (non-vertical) faults. For dipping fault, the side with the fault-dip δ less than 90 is defined as HW and the other side as FW. The definition of HW/FW effects is as follows: the ground motions on both sides of dipping fault are not expected to be the same. Definitely speaking, the sites located above the fault rupture on the HW will have larger ground motions than those at the same rupture distance located on FW because HW sites are closer to a larger area of the source than FW sites (Abrahamson and Silva, 1997; Abrahamson and Somerville, 1996). A previous study showed the HW/FW effects were observed in Chi-Chi earthquake regardless of the distance measures (Chang et al, 2004), such as D rup, D seis and the Joyner-Boore distance D jb (the shortest horizontal distance to the vertical projection of the rupture). That is to say, the ground motion on HW is larger than that on FW so long as they have the same D rup, D seis or D jb. The distance measures widely used before in attenuation analysis, such as D rup, D seis, D jb, the epicentral distance D epc, the hypocentral distance D hyp and so on, share a common disadvantage of being a distance between the recording site and a single point selected to represent the fault plane. These distances cannot represent the general proximity from the site to the dipping fault. In other words, even for the HW and FW site Figure 1 Scheme of source-to-site distance having the same distances mentioned above, the HW site is much closer to the rupture plane than FW site in general. So it s a good choice to use the weighted average distance Δ= [ Σ D γ (ζ, x)dσ/a] 1/γ to describe the whole proximity of the site to the fault plane. In which, Σ denotes the rupture plane, A is the total area of Σ, D(ζ, x) is the distance from the site x on free surface to a point ζ on rupture plane Σ (See Figure 1), and γ is weighted coefficient. Δ is the root-mean-square distance D rms when γ = 2, in which 2 is for consideration of the geometrical attenuation of seismic wave in a homogenous space. Generally speaking, D rms has the following advantages: 1 It can represent the general proximity between the site and the rupture plane accurately; 2 It can reflect the asymmetry degree of dipping fault, that is to say, for the HW and FW site at the same D rup, the larger their D rms difference is, the more obvious

No.3 WANG Dong et al: HANGING WALL/FOOTWALL EFFECTS 277 the asymmetry is. The goal of this paper is to examine whether the ground motion on HW and FW will be different if the same D rms is adopted. If there is no difference, the HW/FW effect is believed to be a geometric effect caused by the asymmetry of dipping fault. Firstly, the residuals of PGA are computed by regression method using D rms. Then comparing with the residuals got from the attenuation analysis based on the D rup and D seis, the cause of the HW/FW effect is investigated taking the 1999 Chi-Chi earthquake as an example. 1 Quantitative method of the HW/FW effects Firstly, for a well-recorded earthquake such as Chi-Chi earthquake, the empirical attenuation relation of PGA for this earthquake is developed by regression method with the full data set (including the HW sites, FW sites and the neutral sites outside of HW and FW). The recorded PGA is marked as a pg-obs and the values located on the attenuation curves at the corresponding distance are marked as a pg-pred. Then the logarithm residuals ln (a pg-obs /a pg-pred ) are used to quantify the HW/FW effects on PGA. Obviously, the larger the residual is, the larger the difference between the PGA on HW and the median level of PGA at corresponding distance is. However, if the residual approaches zero, the difference disappears, which indicates that there is no HW/FW effect on PGA. 2 HW/FW effects on PGA during the Chi-Chi earthquake 2.1 Data set of strong ground motions During the 1999 Chi-Chi earthquake, a total of 441 strong ground motions are recorded. According to the quality of records, a group of 298 accelerations belonging to A, B and C class are used in this research except the D class (not suitable for scientific research). Based on the defini tion of HW and FW zone (Abrahamson and Somerville, 1996), the 11 HW sites (triangles), 69 FW sites (open circles) and the neutral sites (stars) are classified and plotted in Figure 2. The three-component PGA of 11 HW sites are listed in Table 1. Then the D rms of stations are computed according to the definition of D rms and the finite-fault model of Chi-Chi earthquake (Iwata et al, 2000) with the surface projection of fault plane shown in Figure 2 (rectangle zone) Besides, since the site conditions of HW sites (belonging to site class D according to 1997 Uniform Building Code) and FW sites (belonging to site class C, D and E according to 1997 UBC) are similar (Lee et al, 2001), coupled with the scarcity of recordings on HW, the influence of site condition is not taken into consideration in this research. 2.2 Attenuation relations and curves of PGA Since there are a great number of recordings gotten during the Chi-Chi earthquake, the earthquake-specific attenuation relations are developed. The following regression model (Chang et al, 2004) is adopted in this research: Figure 2 Surface projection of finite-fault (Iwata et al, 2000) and the locations of HW and FW sites of Chi-Chi earthquake

278 ACTA SEISMOLOGICA SINICA Vol.21 ln( a pg ) = a + b ln( D + c) (1) In which, a pg is PGA with unit in m s 2, D is distance measure D rup D seis or D rms in km, the coefficients a, b and c for three-component PGA estimated using the ordinary-least-squares method together with the standard deviations σ are listed in Table 2. The attenuation curves of three-component PGA are plotted in Figures 3, 4 and 5, in which open circles denote the 11 HW sites, and the solid circles represent the FW and neutral sites. The HW sites uniformly locate up and down the attenuation curves based on D rms (see Figures 3a, 4a and 5a) without bias, which shows that the HW/FW effects are insignificant. In contrast, most of the HW sites locate above the attenuation curves based on the D rup or D seis (see Figures 3b, 3c, 4b, 4c, 5b and 5c), which indicates that the HW/FW effects are significant. Table 1 Three-component peak ground acceleration on the hanging wall Station code a pg-v /m s 2 a pg-ns /m s 2 a pg-ew /m s 2 TCU052 1.946 4.372 3.522 TCU068 5.202 3.531 4.944 TCU071 4.156 6.388 5.178 TCU072 2.760 3.601 4.669 TCU074 2.689 3.629 5.842 TCU078 1.704 3.019 4.336 TCU079 3.838 4.159 5.774 TCU084 3.124 4.228 9.892 TCU088 2.241 5.154 5.089 TCU089 1.913 2.247 3.470 CHY080 7.133 8.369 7.928 Note: a pg-v, a pg-ns and a pg-ew denote PGA component in vertical, north-south and east-west, respectively. Table 2 Attenuation coefficients of PGA for Chi-Chi attenuation curves using different distance measures Distance Component a b c σ measures D rms 5.82 1.48 6.49 0.044 a pg-v D rup 7.11 1.81 28.17 0.063 D seis 4.61 1.32 10.54 0.064 D rms 5.76 1.32 5.84 0.082 a pg-ns D rup 5.38 1.29 19.25 0.112 D seis 5.58 1.35 16.57 0.114 D rms 6.54 1.43 20.04 0.082 a pg-ew D rup 6.84 1.56 34.65 0.101 D seis 5.89 1.39 23.14 0.082 Note: a pg-v, a pg-ns, a pg-ew are the same as that in Figure 1. Figure 3 Attenuation curves of a pg-v using different source-to-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure 2.3 Hanging wall/footwall effects The logarithm residuals of three components of PGA are plotted in Figures 6, 7 and 8. In these figures, the FW and neutral sites (solid circles) are plotted at negative distances to separate

No.3 WANG Dong et al: HANGING WALL/FOOTWALL EFFECTS 279 Figure 4 Attenuation curves of a pg-ew using different source-to-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure Figure 5 Attenuation curves of a pg-ns using different source-to-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure them from HW sites (open circles). From Figures 6a, 7a and 8a based on D rms, the HW sites distribute symmetrically around the zero line without obvious bias, which indicates the HW/FW effects on PGA are insignificant when D rms is used. However, from Figures 6b, 6c, 7b, 7c, 8b and 8c based on D rup and D seis respectively, the PGA residuals appear to be biased to positive values, i.e., most HW sites locate above the zero line, which suggests the HW/FW effects on PGA are significant when D rup or D seis is used. In fact, the residuals of 11 HW sites based on D rms measure are much smaller than those based on D rup and D seis. As a comparison, the mean values R and variances S of residuals based on different distance measures are listed in Table 3, which shows the mean values based on D rms are all less than those based on D rup and D seis without exception. All these things indicate that the PGA on HW approxi-

280 ACTA SEISMOLOGICA SINICA Vol.21 Figure 6 Residuals of a pg-v using different source-to-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure Figure 7 Residuals of a pg-ew using different sourceto-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure Figure 8 Residuals of a pg-ns using different sourceto-site distance measure (a) D rms measure; (b) D rup measure; (c) D seis measure mates to the median attenuation for Chi-Chi earthquake at corresponding distance when D rms is used, that is to say, the HW/FW effects on PGA become insignificant. Based on the analysis above, for the HW and FW site having the same degree of general proximity to the fault plane (i.e., the same D rms ), there is no significant difference in PGA of these sites. However, in the case of the HW and FW site having the same D rup or D seis, the D rms of HW site is less than that of FW site (i.e., the HW site is much closer to the large area of the fault plane than the FW site), which leads to the PGA of the HW site being larger than that of FW site. In fact, with the increase of fault-dip, the asymmetry degree of dipping fault relieves, that is, the difference of D rms between the HW and FW site located at the same D rup or D seis reduces, which results

No.3 WANG Dong et al: HANGING WALL/FOOTWALL EFFECTS 281 in the HW/FW effects of PGA becoming insignificant. All these show that the HW/FW effect is a geometrical effect caused by the asymmetry of dipping fault. So, the HW/FW effects on the near-fault ground motions can be ignored when the D rms is used as source-to-site distance measure, however they can not be neglected when the other distance measures are used, such as D rup and D seis Table 3 Means R and variances S of residuals of HW sites using different distance measures during Chi-Chi earthquake Vertical EW NS Distance measure R S R S R S D rms 0.05 0.44 0.09 0.47 0.11 0.45 D rup 0.64 0.30 0.68 0.29 0.51 0.34 D seis 0.53 0.24 0.44 0.34 0.43 0.40 3 Discussion and conclusions The 1999 Chi-Chi earthquake occurred on dipping (non-vertical) fault, of which the fault-dip is 30 and the rupture broken up to the ground surface. The two sides of the fault (hanging wall and footwall) are obvious asymmetric relative to the rupture plane. The asymmetry includes the mass and volume difference between HW and FW, as well as the distance to the fault plane, which may be the potential causes of the HW/FW effects. Based on the regression analysis of the three components of PGA from the Chi-Chi earthquake, the following conclusions can be drawn. 1) The hanging wall/footwall effects on the PGA during the Chi-Chi earthquake is mainly a geometric effects caused by the asymmetry of dipping fault. The asymmetry mainly refers to D rms difference between the hanging wall site and footwall site at the same D rup. 2) The rupture distance D rup, the seismogenic distance D seis and the Joyner-Boore distance D jb can not accurately represent the general proximity from a site to the fault plane. For the hanging wall and footwall site at the same D rup, D seis or D jb, D rms of hanging wall site is much less than that of footwall site, which leads to the amplification of PGA on the hanging wall. The hanging wall/footwall effects on PGA are significant when D rup, D seis or D jb is used. 3) The root-mean-square distance D rms with characteristic of weighted average can accurately represent the general proximity from a site to the fault plane. Therefore, the hanging wall and footwall site at the same D rms have identical ground motions basically. The hanging wall/footwall effect on PGA is insignificant when D rms is used. 4) The hanging wall/footwall effects can be ignored when D rms is used in attenuation analysis, while they can not be neglected when the other distance measures are used, such as D rup and D seis. Acknowledgments The authors are grateful to the Central Weather Bureau of Taiwan for providing the strong ground motion records. References Abrahamson N A and Silva W J. 1997. Empirical response spectral attenuation relations for shallow crustal earthquakes [J]. Seism Res Lett, 68(l): 94-109. Abrahamson N A and Somerville P G.. 1996. Effects of the hanging wall and footwall on ground motions recorded during the Northridge earthquake [J]. Bull Seism Soc Amer, 86(1B): S93-S99. Brune J N. 1996. Precariously balanced rocks and ground-motion maps for southern California [J]. Bull Seism Soc Amer, 86(1A): 43-54. Chang T Y, Cotton F, Tsai Y B, et al. 2004. Quantification of hanging-wall effects on ground motion: Some insights from the 1999 Chi-Chi Earthquake [J]. Bull Seism Soc Amer, 94(6): 2 186-2 197. Iwata T, Sckiguchi H, Irikura K. 2000. Rupture process of the 1999 Chi-Chi, Taiwan, earthquake and its near-source strong ground motions [C]//Proc of International Workshop on Annual Commemoration of Chi-Chi Earthquake. Taipei, Taiwan: [s.n.]: 18-20, 36-46.

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