Background velocity estimation using non‐linear optimization for reflection tomography and migration misfit

Abstract

We show that it is possible to estimate the background velocity for prestack depth migration in 2D laterally varying media using a non‐linear optimization technique called very fast simulated annealing (VFSA). We use cubic splines in the velocity model parametrization and make use of either successive pairs of shot gathers or several constant‐offset sections as input data for the inversion. A Kirchhoff summation scheme based on first‐arrival traveltimes is used to migrate/model the input data during the velocity analysis. We evaluate and compare two different measures of error. The first is defined in the recorded data or (x,t) domain and is based on a reflection‐tomography criterion. The second is defined in the migrated data or (x,z) domain and is based on a migration‐misfit criterion. Depth relaxation is used to improve the convergence and quality of the velocity analysis while simultaneously reducing the computational cost. Further, we show that by coarse sampling in the offset domain the method is still robust. Our non‐linear optimization approach to migration velocity analysis is evaluated for both synthetic and real seismic data. For the velocity‐analysis method based on the reflection‐tomography criterion, traveltimes do not have to be picked. Similarly, the migration‐misfit criterion does not require that depth images be manually compared. Interpreter intervention is required only to restrict the search space used in the velocity‐analysis problem. Extension of the proposed schemes to 3D models is straightforward but practical only for the fastest available computers.

Waveform-based simulated annealing of crosshole transmission data: a semi-global method for estimating seismic anisotropy

“…While extremely robust, global and semi-global inverse methods have not been widely adopted in traveltime or waveform tomography, although examples do exist (Sen & Stoffa 1991;Varela et al 1998;Sambridge & Mosegaard 2002;Kaufl et al 2013). This is mainly due to the extreme size of the parameter space, and the significant amount of time needed to perform the forward modelling.…”

“…Of specific relevance to this paper is the semi-global method of simulated annealing (Rothman 1985(Rothman , 1986Kirkpatrick et al 1987;Mosegaard & Vestergaarad 1991;Sen & Stoffa 1991;Varela et al 1998). The concepts behind simulated annealing are borrowed from statistical mechanics, specifically from the analysis of a solid cooling in a heat bath.…”

Global Optimisation of Time Domain Electromagnetic Data Using Very Fast Simulated Annealing

“…For the interpretation of TEM data we utilise very fast simulated annealing (VFSA) as it is more efficient and takes less computing time than other global converging algorithms (SEN and STOFFA, 1995, p. 267). In the VFSA algorithm, the temperature schedule for the acceptance rule is exponentially faster than the one used in conventional simulated annealing (VARELA et al, 1998). An energy (objective) function and governing equations of the process used in the present study are briefly reviewed below.…”

Optimization and geophysical inverse problems

“…Its use in numerical optimization problems began with Kirkpatrick et al (1983) and its first use in geophysical problems appears to be Rothman (1985Rothman ( , 1986. A review of the method and its application to geophysical problems can be found in Sen and Stoffa (1995) and examples of its use in Sen and Stoffa (1991), Mosegaard and Vestergaard (1991), and Varela et al (1998).…”