First-arrival traveltime tomography based on the adjoint-state method

Abstract

Classical algorithms used for traveltime tomography are not necessarily well suited for handling very large seismic data sets or for taking advantage of current supercomputers. The classical approach of first-arrival traveltime tomography was revisited with the proposal of a simple gradient-based approach that avoids ray tracing and estimation of the Fréchet derivative matrix. The key point becomes the derivation of the gradient of the misfit function obtained by the adjointstate technique. The adjoint-state method is very attractive from a numerical point of view because the associated cost is equivalent to the solution of the forward-modeling problem, whatever the size of the input data and the number of unknown velocity parameters. An application on a 2D synthetic data set demonstrated the ability of the algorithm to image near-surface velocities with strong vertical and lateral variations and revealed the potential of the method.

Interferometría de ruido sísmico para la caracterización de la estructura de velocidad 3D de un talud en la 3ª Sección del Bosque de Chapultepec, Ciudad de México

“…Una revisión de la aproximación clásica de este método es presentada por Taillandier et al (2009). En este método se construye un modelo de estructura del subsuelo con las variaciones de velocidad producidas por el ajuste de los tiempos de viaje observados con aquellos derivados por el trazado de rayos.…”

An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media

“…For high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, it is important to compute first-arrival traveltimes in the presence of anisotropy (Baofu et al, 2008;Taillandier et al, 2009;Al-Shuhail et al, 2013). First-arrival traveltimes satisfy the eikonal equation, which is obtained from the high-frequency asymptotic approximation of the wave equation.…”

Wavefront picking for 3D tomography and full-waveform inversion

“…The adjoint of the Jacobian matrix J † smears the traveltime residuals along the raypaths computed using the traveltime tables (Dessa et al, 2004). This back-projection approach is preferred to the back projection using the adjoint-state method (Sei and Symes, 1994;Leung and Qian, 2006;Taillandier et al, 2009), due to the small number of rays, which is faster to trace.…”