Optimized approximate inverse Laplace transform for geo-deformation computation in viscoelastic Earth model

Integral transformations, especially the inverse Laplace transform, are powerful techniques for resolving a wide range of geophysical and geodynamic simulation problems in viscoelastic materials. The exact location or distribution range of poles of the image function in a complex plane is usually necessary for applying numerical algorithms such as contour integration. Unfortunately, there are innumerable poles (such as those of post-seismic deformations) in a realistic Earth model with continuous stratification, finite compressibility and self-gravitation. Here, an optimized method to effectively calculate the inverse Laplace transform is presented. First, the integral kernel is approximated as a rational function with two parameters (a and m). Thereafter, the residue theorem is analytically applied to the approximated integrand. Finally, a series formula of the inverse Laplace transform sampling of image functions along a contour line parallel to the image axis is obtained. The proposed approximate scheme of the inverse Laplace transform is discussed by some common geophysical signals and the optimized selection of two parameters (a = 6 and m = 4) is conducted after a detailed analysis. The proposed method is anticipated as being able to help performing certain theoretical studies related to geodynamic problems with viscoelastic deformations.