oa Spiking Deconvolution by Means of Adaptive Simulated Annealing

Convolution of seismic wavelet with reflectivity of the earth yields seismic trace which also involves additive noise. Sparse spike deconvolution can remove wavelet effect from seismic noisy data and recover impulse response of the earth. The problem of deconvolution can be viewed as an inversion problem which consists of two main steps. The first stage is to find locations of spikes and the second one is to calculate amplitudes of them. Indeed, desired solution is a set of spikes with appropriate amplitudes such that when convolved with known seismic wavelet fit the data within a predetermined misfit error. Detection of spikes time lags is a nonlinear optimization problem that can be solved using Adaptive Simulated Annealing (ASA). ASA is one of the global stochastic optimization methods which can find the global minimum of complex cost functions with good accuracy. Here for a given seismic trace we locate spikes one by one and after achieving the optimized set of spikes, amplitudes are evaluated using linear least squares.