Least Squares Deconvolution Algorithm Implementation

Least squares deconvolution serves as a fundamental algorithm extensively applied in geophysical signal processing, primarily designed to eliminate wavelet effects from seismic records and enhance resolution. This algorithm achieves optimal solutions by minimizing the sum of squared prediction errors, effectively extracting subsurface reflection coefficient sequences. In MATLAB implementation, the algorithm typically involves several critical steps: First, constructing a Toeplitz matrix to represent the seismic wavelet, then establishing an objective function to solve for the least squares solution of reflection coefficients. Practical applications require regularization processing to avoid ill-conditioned matrix problems, commonly implemented through damping factors or sparse constraints. The MATLAB code typically utilizes built-in functions like `toeplitz()` for matrix construction and `lsqnonneg()` or custom optimization routines for constrained solutions. Compared to traditional methods, this deconvolution approach demonstrates superior numerical stability and noise resistance. Regarding algorithmic efficiency, MATLAB's matrix computation capabilities enable efficient processing of large-scale seismic data. However, careful attention must be paid to wavelet estimation accuracy as it directly impacts final deconvolution results. Practical deployment requires balancing computational complexity with memory usage through optimization techniques like matrix preconditioning and iterative solver implementations.