Logarithm Bidirectional Deconvolution Method With Regularization

In this paper, we theoretically discuss about regularization on logarithm bidirectional deconvolution proposed by Claerbout et al. (2011). We hope model fitting helps reduce the unwelcome strong precursors and noise in the bidirectional deconvolution results. INTRODUCTION Bidirectional deconvolution is an ill-posed and highly non-linear problem with many unexpected traps-local minima. When we test logarithm bidirectional deconvolution proposed by Claerbout et al. (2011) on one set of Common Offset gather, we notice the anti-causal part of the estimated wavelet is unexpectedly strong and the results contain high frequency noise. Thus, introducing additional information is needed in order to solve ill-posed problem and guide the result away from an unwelcome local minimum. Regularization, providing such information as restrictions for smoothness or bounds on the vector space norm becomes an important tool in bidirectional deconvolution. Therefore, we propose regularization be applied on logarithm bidirectional deconvolution method in order to reduce the strong precursors and noise. THEORY When we consider regularization in the logarithm bidirectional method, we need to change our objective function into J = hyp(r) + ε ‖W · u‖ = ∑