Geophysical Inversion Method Based on Functional Reconstruction Under the Constraints of Modified Total Variational Model

Abstract

The invention discloses a geophysics inversion method based on a generic function reconstruction under a modified total variation model constraint. The method comprises the following steps: (1) constructing an inversion objective function aiming at the problem of regularized inversion of the modified total variation model constraint; (2) performing a generic function reconstruction on stable function terms of the modified total variation; (3) iteratively solving a calculation formula of a new model on the model itself according to an objective function minimization equation; and (4) setting inversion parameters, repeating the iteration to obtain a desired model result, and the result is used for inferring geological structures or positioning geological anomaly bodies. According to the geophysics inversion method based on the generic function reconstruction under the modified total variation model constraint, a generic function reconstruction method is innovatively provided, and the constraint property of the stable function term on the model is reserved, thereby greatly simplifying the numerical calculation difficulty caused by the high nonlinearity to the inversion; the inversionadopts a solution mode which is iterative to the model itself, and compared with a solution mode which is iterative to the correction amount of the model, the regularization directly applies a stablefunction constraint on the model, thereby obtaining a more reasonable model result.

Description

technical field [0001] The invention relates to the technical field of geophysical exploration, in particular to a geophysical inversion method based on functional reconstruction under the constraint of a modified total variation model. Background technique [0002] Inversion occupies a very important position in the field of geophysics. Geophysical inversion problems solve source bodies based on measured data or observed geophysical fields to infer geological structures or locate anomalous bodies. The model parameters to be solved by inversion represent the physical properties of geological bodies, which can be density, magnetic permeability, electrical conductivity, elasticity, thermal conductivity, and radioactivity. The corresponding exploration methods are gravity exploration, magnetic exploration, and electrical exploration. Exploration, Seismic Exploration, Geothermal Exploration, Nuclear Exploration. Since the amount of observed data is usually less than the number...

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Problems solved by technology

This solution is still much more complex than other inversion problems under the constraints of stable functionals, therefore, the modified total variational stable functionals have not been widely used in the field of geophysical inversion

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