A new 2D/3D accurate geophysical forward modelling technique: sub-domain Chebyshev spectral method

Abstract

A new numerical approach, called the ?sub-domain Chebyshev spectral method?, has been developed to calculate differentiations in a curved coordinate system, which may be employed for 2D/3D geophysical forward modelling. The new method utilises non-linear transformations defined by the free-surface topography and subsurface interfaces and incorporates cubic-spline interpolations to convert the global domain into subdomains, and applies Chebyshev points in the model discretisation and computation of the spatial derivatives. Such effort makes the numerical differentiations have ?spectral accuracy? inside the subdomains whose boundaries match the free-surface topography and subsurface interfaces. 2D and 3D synthetic experiments have been performed with two geological models, both having different free-surface topographies and sub-surface interfaces. The computational errors of the new approach were compared with traditional finite-difference schemes, and the results show that the sub-domain Chebyshev spectral method is superior to traditional finite-difference method in its accuracy and applicable for all of the geophysical forward modelling problems.