A Theoretical Omega-Square Model Considering Spatial Variation in Slip and Rupture Velocity. Part 2: Case for a Two-Dimensional Source Model

Abstract

The theoretical basis of the x-squared model and the characteristics of near-source broadband strong ground motions are investigated using a 2D source model with spatial variations in slip and rupture velocity. This is an extension of a study by Hisada (2000a), who used 1D source models for the same purpose. First, Hisada's slip-velocity function (2000a) is modified by superposing scalene triangles to construct Kostrov-type slip-velocity functions with arbitrary combinations for the source-controlled f max and the slip duration. Then, it is confirmed that the Fourier amplitudes of these slip velocities fall off as the inverse of x at frequencies lower than f max (Hisada, 2000a). Next, the effects of 2D spatial distributions of slip and rupture time on the source spectra are investigated. In order to construct a realistic slip distribution, the hybrid slip model is proposed, which is the combination of the asperity model at lower wavenumbers and the k-squared model (Herrero and Bernard, 1994) at higher wavenumbers. The source spectra of the proposed 2D models, which have the k-squared distribution for slip and rupture time, fall off as the inverse of x, when the slip is instantaneous. This result also agrees with Hisada (2000a). Therefore, the x-inverse-squared model, which consists of the combination of the Kostrov-type slip velocity proposed here and the k-squared distributions for both slip and rupture time, is not only consistent with the empirical x-squared model, but also provides the theoretical basis for constructing realistic 2D source models at broadband fre- quencies. In addition, it is confirmed that the proposed source model successfully simulates most of the well-known characteristics of the near-fault strong ground motions at broadband frequencies, that is, permanent offsets in displacements, long- period pulses in velocities, and complex randomness in accelerations. The near- source directivity effects are also confirmed; the fault-normal components are dom- inant over the fault-parallel components, especially at the forward rupture direction. However, the ratio between the fault-normal and fault-parallel components is roughly independent of frequency, which is contradictory to empirical models. This suggests that a 3D faulting model is necessary to represent more realistic near-source strong motions at broadband frequencies.