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 frequencies. 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, longperiod pulses in velocities, and complex randomness in accelerations. The nearsource directivity effects are also confirmed; the fault-normal components are dominant 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.

Three‐dimensional dense strong motion waveform inversion for the rupture process of the 1999 Chi‐Chi, Taiwan, earthquake

“…Here, the rupture may have encountered an asperity, requiring more time to overcome the resistance. This phenomenon is different from what has been inferred in previous rupture inversions [e.g., Hisada , 2001] and some models of dynamic rupture propagation. However, Dalguer et al [2001] also suggested a slower rupture velocity at the northern part of the fault where the largest asperity occurred during the Chi‐Chi earthquake.…”

Kinematic source models for long-period ground motion simulations of megathrust earthquakes: validation against ground motion data for the 2003 Tokachi-oki earthquake

“…The resultant source model agrees with the omegasquare model of the source spectra and the slip spectra model by Mai and Beroza (2002). Spatial heterogeneities in the slip and rupture velocity are theoretically necessary for the omega-square model as presented by Hisada (2001).…”

Implications of the 26 December 2004 Sumatra–Andaman Earthquake on Tsunami Forecast and Assessment Models for Great Subduction-Zone Earthquakes

“…Tsunami generation models used for tsunami assessments such as presented here have been modified from models previously used for strong ground motion studies (Herrero and Bernard, 1994;Berge et al, 1998;Somerville et al, 1999;Hisada, 2000Hisada, , 2001Honda and Yomogida, 2003). At low wavenumbers, stochastic slip distributions are scaled relative to average slip or static stress drop.…”

“…Each of the slip distributions conform to a k ‫2מ‬ radial-wavenumber spectrum for k Ͼ k c where k c scales with the characteristic rupture dimension (Herrero and Bernard, 1994;Tsai, 1997;Somerville et al, 1999;Hisada, 2000Hisada, , 2001Mai and Beroza, 2002). For the more general case of a k ‫␣מ‬ spectrum, Zeng et al (2005) note that scaling of ū with rupture length (L) is physically related to the degree of slip heterogeneity (␣) and indicate that linear scaling between ū and L occurs only for relatively smooth slip distributions.…”