Refraction traveltime tomography using damped monochromatic wavefield

Abstract

For complicated earth models, wave-equation–based refraction-traveltime tomography is more accurate than ray-based tomography but requires more computational effort. Most of the computational effort in traveltime tomography comes from computing traveltimes and their Fréchet derivatives, which for ray-based methods can be computed directly. However, in most wave-equation traveltime-tomography algorithms, the steepest descent direction of the objective function is computed by the backprojection algorithm, without computing a Fréchet derivative directly. We propose a new wave-based refraction-traveltime–tomography procedure that computes Fréchet derivatives directly and efficiently. Our method involves solving a damped-wave equation using a frequency-domain, finite-element modeling algorithm at a single frequency and invoking the reciprocity theorem. A damping factor, which is commonly used to suppress wraparound effects in frequency-domain modeling, plays the role of suppressing multievent wavefields. By limiting the wavefield to a single first arrival, we are able to extract the first-arrival traveltime from the phase term without applying a time window. Computing the partial derivative of the damped wave-equation solution using the reciprocity theorem enables us to compute the Fréchet derivative of amplitude, as well as that of traveltime, with respect to subsurface parameters. Using the Marmousi-2 model, we demonstrate numerically that refraction traveltime tomography with large-offset data can be used to provide the smooth initial velocity model necessary for prestack depth migration.

Crust and Lithospheric Structure - Active Source Studies of Crust and Lithospheric Structure

“…For traveltime methods, formal treatment of Fresnel zones (Watanabe et al, 1999), adaptation of frequency-dependent sensitivity kernels from global seismology (Dahlen et al, 2000), and wave equation-based modeling (Pyun et al, 2005) will reduce the need for regularization and improve the stability of gradient methods. The derived models will contain more structure and increased resolution as a result of more accurately honoring the physics of wave propagation.…”

Laplace-domain waveform inversion versus refraction-traveltime tomography

“…2000; Hung et al . 2000; Pyun et al . 2005; Min & Shin 2006; Ellefsen 2009) overcomes some of these limitations.…”

“…2005; Min & Shin 2006; Ellefsen 2009) overcomes some of these limitations. In particular, Pyun et al . (2005) developed a first‐arrival traveltime tomography algorithm using damped monochromatic wave equation, which mimics the finite‐frequency traveltime tomography using single frequency component only.…”

“…In this study, we adopted the approach of Pyun et al . (2005) as a representation of refraction‐traveltime tomography because their algorithm is similar to Laplace‐domain waveform inversion that it can represent simple and multiple diffractions.…”

Refraction tomography using a waveform-inversion back-propagation technique

“…Most wave-based traveltime-tomography techniques extract phase differences of first arrivals by applying a time window or a connective function and computing the steepest-descent direction through a back-projection technique. Pyun et al ͑2005͒ proposed using damped monochromatic wavefields for calculating traveltime residuals and explicitly computed Fréchet derivatives using the reciprocity theorem in their refraction-tomography algorithm. Wave-based refraction tomography can give reliable solutions for a complicated and high-velocitycontrast model, but it requires more computational effort than the ray-based method.…”