## 175 Strong Motion Attenuation and Duration

The rate at which earthquake ground motion decreases with distance, termed attenuation, is a function of the regional geology and inherent characteristics of the earthquake and its source. Three

major factors affect the severity of ground shaking at a site: (1) source — the size and type of the earthquake; (2) path — the distance from the source of the earthquake to the site, and the geologic characteristics of the media earthquake waves pass through; and (3) site-specific effects — type of soil at the site. In the simplest of models, if the seismogenic source is regarded as a point then, from considering the relation of energy and earthquake magnitude, and the fact that the volume of a hemisphere is proportion to R3 (where R represents radius), it can be seen that energy per unit volume is proportional to C10aM R~3, where C is a constant or constants dependent on the earth's crustal properties. The constant C will vary regionally — for example, it has long been observed that attenuation in eastern North America (ENA) varies significantly from that in western North America (WNA) — earthquakes in ENA are felt at far greater distances. Therefore, attenuation relations are regionally dependent. Another regional aspect of attenuation is the definition of terms, especially magnitude, where various relations are developed using magnitudes defined by local observatories.

A very important aspect of attenuation is the definition of the distance parameter — since attenuation is the change of ground motion with location, this is clearly important. Many investigators use differing definitions — as study has progressed, several definitions have emerged: (1) hypocentral distance (i.e., straight line distance from point of interest to hypocenter, where hypocentral distance may be arbitrary, or based on regression rather than observation; (2) epicentral distance; (3) closest distance to the causative fault; and (4) closest horizontal distance from the station to the point on the earth's surface that lies directly above the seismogenic source. In using attenuation relations, it is critical that the correct definition of distance is consistently employed.

An extensive discussion of attenuation is beyond the scope of this chapter, and the reader is referred to Chen and Scawthorn for an extended discussion. However, for completeness, we present one attenuation relation, that of Campbell and Bozorgnia (2003 from which the following is excerpted), which can be represented by the expression:

ln Y = ci + fi (Mw) + c4 lnVf2(Mw, w S) + f3(F) + f4(S)+ f5(HW, Mw, rseis)+ e (17.15) where the magnitude scaling characteristics are given by fi(Mw) = c2Mw + c3(8.5 - Mw)2 (17.16)

The distance scaling characteristics are given by f2(Mw, rseis, S) = rs2eis + g(S)2 (exp [c8Mw + c9(8.5 - Mw)^)2 (17.17) in which the near-source effect of local site conditions is given by g (S) — c5 + c6(SVFS + SSR )c7SFR (17.18) The effect of faulting mechanism is given by f3(F) — (c1oFRv + CuFth) (17.19) The far-source effect of local site conditions is given by f4(S) — c12 Svfs + c13 Ssr + c14SFR (17.20) and the effect of the hanging wall (Hw) is given by f5 (HW, F, Mw,rseis) — HW f3(F)fHw(Mw)fHw(rseis) (17.21)

where

HW " \(SyFs + Ssr + Sfr) (5 - rp) /5 for j < 5 km and d < 70° (1722)

/hw(Mw) = < Mw - 5.5 for 5.5 < Mw < 6.5 (17.23)

and f tr \ f c15(rseis/8) for rseis< 8 km ,,71.v fHW(rseis)X c15 for rseis > 8 km (1724)

The parameter HW quantifies the effect of the hanging wall and will always evaluate to zero for firm soil and for a horizontal distance of 5 km or greater from the rupture plane. The standard deviation of ln Y is defined as a function of magnitude according to the expression:

or as a function of PGA according to the expression:

{c17 + 0.351 for PGA < 0.07g c17 - 0.132 ln(PGA) for 0.07g < PGA < 0.25g (17.26)

Tn (s) |
Cl |

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