A stability-improved efficient deconvolution algorithm based on B-splines by appending a nonlinear regularization

Furthermore, through the study on two simulated cases with added data errors and an actual case, it is demonstrated that when the nonlinear regularization is appended, the stability of the deconvolution algorithm based on B-splines can be largely improved for mitigating the effect of data errors; besides, the stability-improved algorithm based on B-splines even exhibits higher stability than von Schroeter et al.'s algorithm that takes the same nonlinear regularization method, and the reason can be attributed to the superior properties of the representation of the wellbore pressure derivative (to be deconvolved) by B-spline functions in the numerical stability of computations and the inherent smoothness. Through the test of some simulated cases, it is also concluded that the stability-improved algorithm based on B-splines by appending the nonlinear regularization still has a high-level computation speed, which is nearly twenty times more than that of von Schroeter et al.'s algorithm. It can be attributed to the more undetermined coefficients and the computational complexity resulted from the z-function transformation in the formulation of von Schroeter et al.'s algorithm.