Non-stationary deconvolution via stochastic simulated annealing optimization

Summary Deconvolution is one of the significant steps in seismic signal processing for obtaining high resolution images of subsurface. In this paper, a new nonstationary deconvolution is developed to retrieve the impulse response of the earth and remove the earth attenuation effects from it via a simulated annealing (SA) optimization. The time location of each spike and the corresponding quality factor is estimated by the SA method and its amplitude is calculated using a least-squares method. All three parameters of the reflection coefficient, time lag, and the quality factor for each layer are estimated simultaneously. Available information from well-logs can also be incorporated as a priori information. Numerical examples from simulated and field seismic data show high performance of the proposed algorithm for estimating the reflectivity structure and the model of the quality factor. Numerical examples confirm promising applicability of the new method for processing and interpretation of seismic data. The goal of non-stationary deconvolution is to remove the effects of the source wavelet and the attenuation filter from the data to retrieve the earth impulse response with an enhanced temporal resolution.
Introduction High resolution images of subsurface, obtained from seismic studies, can serve an important role in the oil and gas exploration industry. One of the main steps in seismic signal processing is deconvolution to increase the temporal resolution of the data. Beside the blurring effect of the source generated pulse, the inhomogeneity and anelasticity of the earth causes a decrease in the resolution of the acquired data due to the absorption and dispersion mechanisms. While propagation, the absorption decreases the strength of the pulse and dispersion leads to a gradual change in its shape. These effects deteriorate the resolution of the subsurface images and need appropriate processing tools for compensating their effects. Simultaneous compensation of these effects is a non-linear and ill-posed problem. In this paper, based on SA, a new algorithm is developed for this task. The performance of the method is tested via numerical examples.
Methodology and Approaches Many approaches have been proposed for solving non-linear optimization problems such as the hill climbing, the genetic algorithm and the SA methods. One of the advantages of these methods in comparison with the gradient based solvers is their ability to find the global minimizer. Here, we employ the SA method for solving the non-stationary seismic deconvolution. This method escape from trapping in local minima by adding random amounts to the solution space. Most of the algorithms avoid approaching false solutions which may cause trapping in local minima. The SA method, however, prefers evaluating possibly incorrect solutions and calculating its correctness using a probability distribution function based on the amount of the cost function. The other advantage of the SA method is that the uncertainty of the parameters can also be calculated by applying the algorithm several times for searching the whole model space in order to obtain a set of solutions, which fit the data and satisfy the constraints.
Results and Conclusions In this paper, a stochastic SA-based algorithm, was proposed to solvinge the non-stationary seismic deconvolution problem for simultaneous compensation of the blurring effect of the wavelet and the Q-filtering effects of the earth. The Q-model of the earth is also estimated during the deconvolution. Numerical examples of synthetic and field data confirmed high-performance of the proposed algorithm.