Modelling curved surface wave paths: membrane surface wave synthetics

Abstract

Earth's heterogeneity near the surface is so severe that surface waves with period 20 s exhibit complicated propagation effects such as curved paths and multiple rays.In order to take account of these effects, a new method to analyse surface waves is developed. The method, which we call the membrane surface wave method, is an approximation t o the Green's function method in a 3-D medium and is valid for a laterally, smoothly varying media. We also present the formulae to invert the seismograms. As an example, we apply the method to a preliminary California model. Use of the method for the forward calculation shows that heterogeneity in the model is so severe that the wavefront due to the Whittier Narrows earthquake is split in two by the time it feaches the San Francisco Bay area. The kernels in the inverse formula to the six Berkeley stations show curved paths, multipathings and finite wavelength effects and visually demonstrate how waves sample the medium.The method is attractive in that these complications cause no problems in its application.

Imaging near-surface heterogeneities by natural migration of surface waves

“…The relations between the model perturbation m and the backscattered surface waves d can be linearized by the Born approximation d = Lm, where L is the forward modeling operator for a known background velocity (Snieder, 1986;Tanimoto, 1990). To get the model perturbation m, Riyanti (2005) used an iterative optimization method to approximate the solution, and Snieder (1986) and Yu et al (2014) applied the adjoint of the forward modeling operator L † to backscattered data to obtain the migration image.…”

Wave-equation dispersion inversion

“…Here, f(x, s, ω) i for i ∈ (1, 2, 3) is the downgoing source field at x that originates at s, and B(x, s, ω) i for i ∈ (1, 2, 3) represents the backprojected field at x. If the membrane model is assumed (Tanimoto 1990;Tromp & Dahlen 1993), then the Fréchet derivative assumes a simplified scalar form similar to that of the acoustic wave equation.…”

Double-difference adjoint seismic tomography

“…1. We use membrane surface waves (Tanimoto 1990;Peter et al 2007) as an analogue for short-period (10-20 s) surface waves. We use SPECFEM2D (Komatitsch & Vilotte 1998) to model the wavefield.…”