Non-linear stochastic inversion of 2D gravity data using evolution strategy (ES)

In the current work, a 2D non-linear inverse problem of gravity data is solved using the evolution strategies (ES) to find the thickness of a sedimentary layer in a deep-water situation where a thick sedimentary layer usually exists. Such problems are widely encountered in the early stages of petroleum explorations where potential field data are used to find an initial estimate of the basin geometry. However, the gravity data are the non-unique problem, and classical deterministic inversions can only offer a single approximation of the solution. Conversely, ES and evolutionary algorithms in general due to their random nature can offer a range of solutions that all fit the data within the acceptable threshold. The inverse problem is formulated as a single objective unconstrained numerical optimization. In evolutionary algorithms, the random nature of the search follows the same rules of the Darwinian biological evolution. Hence, the search is not exhaustive and requires less computational resources compared to Monte Carlo methods. Herein, first, the algorithm is introduced, and a classical synthetic problem is formed and successfully solved in the presence of white Gaussian noise. Then, a two-layered synthetic oceanic crust is formed. ES is successfully tested for solving the formulated under-determined inverse problem of estimating both the base of the sedimentary layer and the crust (i.e., Moho boundary). Finally, using the proposed method, the thickness of the sedimentary layer of the Caspian basin is found along an E-W profile crossing the Caspian Sea. The results have a good agreement with the previous estimates by deep seismic sounding method. The proposed method could be of particular interest because, in deep-water situations, the high water content of sediments, and the expected large thickness of the sediments among other factors make the use of reflective seismic methods unfeasible.