A Fast and Reliable Method for Surface Wave Tomography

Abstract

Ð We describe a method to invert regional or global scale surface-wave group or phasevelocity measurements to estimate 2-D models of the distribution and strength of isotropic and azimuthally anisotropic velocity variations. Such maps have at least two purposes in monitoring the nuclear Comprehensive Test-Ban Treaty (CTBT): (1) They can be used as data to estimate the shear velocity of the crust and uppermost mantle and topography on internal interfaces which are important in event location, and (2) they can be used to estimate surface-wave travel-time correction surfaces to be used in phasematched ®lters designed to extract low signal-to-noise surface-wave packets.The purpose of this paper is to describe one useful path through the large number of options available in an inversion of surface-wave data. Our method appears to provide robust and reliable dispersion maps on both global and regional scales. The technique we describe has a number of features that have motivated its development and commend its use: (1) It is developed in a spherical geometry; (2) the region of inference is de®ned by an arbitrary simple closed curve so that the method works equally well on local, regional, or global scales; (3) spatial smoothness and model amplitude constraints can be applied simultaneously; (4) the selection of model regularization and the smoothing parameters is highly¯exible which allows for the assessment of the eect of variations in these parameters; (5) the method allows for the simultaneous estimation of spatial resolution and amplitude bias of the images; and (6) the method optionally allows for the estimation of azimuthal anisotropy.We present examples of the application of this technique to observed surface-wave group and phase velocities globally and regionally across Eurasia and Antarctica.

Seismic structure beneath the Gulf of California: a contribution from group velocity measurements

“…In order to determine the reliability of an azimuthal anisotropy calculation in the case of our study, we calculate the azimuthal distribution of ray paths at each gridpoint. For this purpose, following Barmin et al (2001), ray paths are distributed across a fixed number n of azimuthal bins from 0 to 180 • . The resulting histogram of the azimuthal distribution of rays is then used to calculate the function χ = i=1,n f i n max f i where f i is the density of azimuths within the ith bin; max f i is the maximum of f i at a given point, which may be in any of the n azimuthal bins.…”

“…Considering that the possible range is [1/n, 1], a perfectly uniform ray path distribution implies χ = 1, whereas χ = 1/n implies all rays are concentrated along one direction. Barmin et al (2001) assume that values of χ < 0.3 do not provide a reliable estimate of anisotropy. In their study, χ is used to damp azimuthal anisotropy in regions with poor azimuthal coverage based on the ray paths at a given point.…”

“…2(b). The value of 0.3 is subjective and based on the value used in Barmin et al (2001). Considering that the azimuthal density is clearly nonuniform ( Fig.…”

Ambient noise surface wave tomography of the Iberian Peninsula: Implications for shallow seismic structure

“…The tomography method is that of Barmin et al [2001], which approximately accounts for the spatially extended frequency-dependent sensitivity of the waves by using Gaussian lateral sensitivity kernels. Although the use of spatially extended sensitivity kernels has only a small effect on the estimated maps at the periods considered [Ritzwoller et al, 2002], they help to provide a more accurate estimate of spatial resolution.…”

Lateral variation of Lg wave propagation in southern Mexico

“…Obviously, the problem of Q tomography in southern Mexico is mixed determined, since some areas have a high path coverage, while other areas are poorly covered. We follow the approach presented by Barmin et al [2001], who described a fast and reliable method to solve twodimensional tomography problems applying simple regularization conditions.…”