Fréchet kernels for body-wave amplitudes

Abstract

Summary We derive a 3D Fréchet sensitivity kernel relating the rms amplitude of a far‐field, broad‐band body‐wave pulse to laterally heterogeneous seismic slowness variations within the earth. Unlike the ‘banana–doughnut’ sensitivity kernel for a cross‐correlation traveltime, the amplitude Fréchet kernel for a turning wave is maximally sensitive, rather than completely insensitive, to the 3D slowness perturbation along the central source‐to‐receiver ray. In the asymptotic limit of an infinite‐frequency pulse, our 3D amplitude kernel formulation is consistent with the dominant 1D integral involving the cross‐path curvature of the slowness perturbation along the unperturbed geometrical ray.

Computing traveltime and amplitude sensitivity kernels in finite-frequency tomography

“…The aspect ratio of either the ellipse or the hyperbola becomes larger as the cross-section gets closer to the caustics, because the aspect ratio is determined by the ratio jH 11 /H 22 j, and as the cross-section approaches the caustics, jH 11 j goes to infinity with H 22 remaining finite (Paper I). Similar plots of K c T and K c A have earlier been presented by Hung et al [7] and Dahlen and Baig [3].…”

“…Ray theory ignores wave scattering and wavefront healing effects, which render the traveltime anomalies dependent on the Earth structure in a 3D region around the geometrical ray, rather than limiting the sensitivity to an infinitesimally narrow ray path. Recently, Dahlen et al [4,3] formulated efficient theories for 3D traveltime and amplitude sensitivity (or Fréchet) kernels, using the paraxial approximation and dynamic ray tracing [19] to reduce the computational effort. Dynamic ray tracing software to compute the geometrical spreading factors and second derivatives of the traveltime along the wavefront, which are the parameters needed for the computation of finite-frequency kernels, was described by [18], hereafter referred to as Paper I.…”

Full-Wave Seismic Data Assimilation: Theoretical Background and Recent Advances

“…In traditional broadband cross-correlation analysis, the travel-time shift DT of an isolated waveform is estimated using the location of the cross-correlogram peak (LUO and SCHUSTER 1991;WOODWARD and MASTERS 1991;DAHLEN et al 2000;ZHAO et al 2000) and the amplitude anomaly can be determined from the maximum amplitudes of the cross-correlograms (DAHLEN and BAIG 2002;RITSEMA et al 2002). The seismogram perturbation kernels for broadband cross-correlation travel-time shift and amplitude anomaly are presented in CHEN et al (2007a).…”

Muon tomography: Plans for observations in the Lesser Antilles

“…The finite angular resolution of each detection direction r m,n implies that the integration (1) is not actually done along a mathematical line but, instead, in a conical volume with a square cross-section. This situation is already considered in other geophysical tomography problems, like seismic imaging where the Fresnel zone is sometimes used instead of the "line-like" asymptotic rays (e.g., Dahlen et al, 2000;Dahlen and Baig, 2002).…”