A MATLAB-based inversion program, b-Spline Polynomial Approximation using Differential Evolution Algorithm (SPODEA), is introduced to recover the concealed basement geometry under heterogeneous sedimentary basins. Earlier inversion techniques used the discretized subsurface interface topography into a grid of juxtaposed elementary prisms to estimate the basement depth of a basin. Such discretization leads to the failure of depth profile continuity and requires a higher number of inversion parameters for achieving the desired accuracy. The novel approach of SPODEA overcomes such limitations of earlier inversion techniques. SPODEA is based on the segment-wise b-spline optimization technique to estimate the basement depth by using high-order polynomials.Moreover, it can achieve an optimal misfit with a minimal parametric information, which reduces the computational expense. The proposed inversion approach uses the differential evolution (DE) algorithm that provides real parametric optimization and uses b-splines for an accurate estimation of continuous depth profiles. The efficiency of the proposed algorithm is illustrated with two complex synthetic sedimentary basin models comprised of constant and depth varying density distributions. Furthermore, the uncertainty analysis of the proposed inversion technique is evaluated by incorporating white Gaussian noise into the synthetic models. Finally, the utility of SPODEA is illustrated by inverting gravity anomalies for two different real sedimentary basins. It produces geologically reasonable outcomes that are in close agreement with basement structures from previously reported results.
Quintic B-spline polynomial for Solving Bagely-Torvik Fractional Differential Problems
