### A Hybrid Strategy Based on Fast Iterative Shrinkage-Thresholding Algorithm and Very Fast Simulated Annealing: Application to the Prestack Seismic Inverse Problem

#### Abstract

With the purpose of characterizing the Earth subsurface, one of the objectives of the inversion of prestack seismic data is to determine contrasts between rock properties from the information contained in the variation of the amplitudes of the reflected compressional waves with the angle of incidence.

This amplitude-versus-angle (AVA) variation can be described by various approximations to the so-called Zoeppritz equations, a set of non-linear equations that depend on the physical characteristics of the medium at each side of the interface where the compressional wave strikes. The coefficients of such approximations constitute AVA attributes that may provide important information about fluid content, a key issue for the characterization of hydrocarbon reservoirs. In this work we present a new inversion strategy to estimate efficiently and accurately high-resolution AVA attributes from prestack data. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. Sparse solutions are desirable because they can be used to characterize significant and close reflectors more accurately than using conventional solutions. The inversion is carried out using a hybrid two-step strategy than combines Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Very Fast Simulated Annealing (VFSA). FISTA provides sparse solutions by minimizing both the misfit between the modeled and the observed data, and the l1-norm of the solution. VFSA is an stochastic computational algorithm to finding near-optimal solutions to hard optimization problems. At the first stage, FISTA sparse-solutions provide an estimate of the location in time of the main reflectors, information that is subsequently used as an initial guess for the second stage, where accurate reflectivity amplitudes are estimated by solving a more stable overdetermined inverse problem. The second stage also involves the use of VFSA for tuning the location in time of the main reflectors and the source wavelet. FISTA does not require the inversion of matrices in explicit form. At each iteration only matrix-vector multiplications are involved, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a result, the FISTA+VFSA strategy represents a simple and cost-effective new procedure to solve the high-resolution AVA inversion problem. Results on synthetic data show that the proposed hybrid method can obtain high-resolution AVA attributes from noisy observations, even when the number of reflectors is not known a priori and the utilized wavelet is inaccurate, making it an interesting alternative to conventional methods.

This amplitude-versus-angle (AVA) variation can be described by various approximations to the so-called Zoeppritz equations, a set of non-linear equations that depend on the physical characteristics of the medium at each side of the interface where the compressional wave strikes. The coefficients of such approximations constitute AVA attributes that may provide important information about fluid content, a key issue for the characterization of hydrocarbon reservoirs. In this work we present a new inversion strategy to estimate efficiently and accurately high-resolution AVA attributes from prestack data. The proposed technique promotes sparse-spike reflectivities that, when convolved with the source wavelet, fit the observed data. Sparse solutions are desirable because they can be used to characterize significant and close reflectors more accurately than using conventional solutions. The inversion is carried out using a hybrid two-step strategy than combines Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and Very Fast Simulated Annealing (VFSA). FISTA provides sparse solutions by minimizing both the misfit between the modeled and the observed data, and the l1-norm of the solution. VFSA is an stochastic computational algorithm to finding near-optimal solutions to hard optimization problems. At the first stage, FISTA sparse-solutions provide an estimate of the location in time of the main reflectors, information that is subsequently used as an initial guess for the second stage, where accurate reflectivity amplitudes are estimated by solving a more stable overdetermined inverse problem. The second stage also involves the use of VFSA for tuning the location in time of the main reflectors and the source wavelet. FISTA does not require the inversion of matrices in explicit form. At each iteration only matrix-vector multiplications are involved, making it easy to apply, economic in computational terms, and adequate for solving large-scale problems. As a result, the FISTA+VFSA strategy represents a simple and cost-effective new procedure to solve the high-resolution AVA inversion problem. Results on synthetic data show that the proposed hybrid method can obtain high-resolution AVA attributes from noisy observations, even when the number of reflectors is not known a priori and the utilized wavelet is inaccurate, making it an interesting alternative to conventional methods.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**