Surface wave tomography: finite-frequency effects lost in the null space

Abstract

S U M M A R YWe compared surface wave tomography models obtained using finite-frequency kernels and ray theory. We systematically changed regularization in both cases and plotted data misfit against the number of independent parameters in the solution. Our tests show that models from finite-frequency kernels and ray-theoretical kernels are statistically similar. This means that any model obtained using one forward theory can be obtained using the other one by appropriately changing the damping constant. It is clear that finite-frequency theory is a better forward theory to represent the wavefield, but the associated inverse problem is not less ill posed. Indeed, current data coverage is such that the solution is dominated by the chosen regularization. This prevents us from achieving a resolution of the order of the Fresnel zone, or beyond, and noticing the benefits of a better forward theory.

Lateral Variations of Rayleigh-Wave Dispersions in the Philippine Sea Region

“…A few studies stressed that tomographic results using the finite-frequency theory are superior to those using the traditional ray theory (a great-circle path assumption under high-frequency approximation) (e.g., Zhou et al 2005). However, other studies (Sieminski et al 2004;Levshin et al 2005;Trampert and Spetzler 2006) found that results using the ray theory are similar to those of the finite-frequency theory when utilizing reasonable ray coverage in the study region. Sieminski et al (2004) further pointed out that finite-frequency effects can be counterbalanced by a physically-based regularization of the tomographic inversion or dense ray coverage in the study region (e.g., Levshin et al 2005).…”

“…Sieminski et al 2004;Levshin et al 2005;Trampert and Spetzler 2006). Also, the relationship between lateral velocity variation and azimuthal variation is weak (cf.…”

“…Sieminski et al (2004) further pointed out that finite-frequency effects can be counterbalanced by a physically-based regularization of the tomographic inversion or dense ray coverage in the study region (e.g., Levshin et al 2005). Trampert and Spetzler (2006) also stated that tomographic models from finite-frequency theory and ray theory are statistically similar. Experiments of Sieminski et al (2004) stressed that regional surface-wave tomography can be safely conducted using the great-circle ray theory assumption when good path coverage and short path length are used.…”

Validation of first-order diffraction theory for the traveltimes and amplitudes of propagating waves

“…While in seismology, these benefits are still overshadowed by incomplete data coverage ͑Van der Hilst and De Hoop, 2005;Trampert and Spetzler, 2006͒, the seismic applications clearly suffer less from lack of data. This is illustrated by two examples of finite-frequency wave theory in seismic imaging experiments.…”

An objective rationale for the choice of regularisation parameter with application to global multiple-frequency <i>S</i>-wave tomography

“…In parallel, several studies questioned whether the benefits from using BDT, rather than simple RT, could be smaller than the uncertainty posed by the subjective regularisation of the inverse problem (e.g. Sieminski et al, 2004;Trampert and Spetzler, 2006;Van der Hilst and de Hoop, 2005;Boschi et al, 2006). It seems pertinent that tomographers ask what are the consequences on seismic models of the subjectivity inherent to the choice of regularisation parameter.…”