A 3D Simulation Method of Fractional Electromagnetic Anomalous Diffusion Based on Rational Function Approximation

Abstract

The invention relates to a three-dimensional simulation method for fractional-order electromagnetic anomalous diffusion by rational function approximation, and aims to calculate the three-dimensional time-domain induction-polarization dual-field response of the fractional-order Cole-Cole model. It mainly includes constructing the Cole-Cole model fractional transfer function and the nth order rational approximation function based on the frequency-domain rational function approximation method, and using the sum of the absolute values ​​of the real and imaginary parts of the error function as the objective function; through the auxiliary variable method, the goal is achieved For the linearization of the function, the linear programming method is used to obtain the best approximation to the rational function; the time-domain form of the conductivity is obtained by using the partial fraction expansion method and the inverse Laplace transform; it is substituted into the Maxwell equation, and the electromagnetic field is derived based on the finite difference method The iterative equation realizes the numerical calculation of the three-dimensional electromagnetic response of the fractional Cole-Cole model. The beneficial effect of the invention is that the three-dimensional time-domain electromagnetic response of the fractional Cole-Cole model can be quickly and accurately simulated, and a theoretical basis is provided for the study of electromagnetic anomalous diffusion in polarized media.

Description

technical field [0001] The invention relates to a numerical simulation method for anomalous diffusion of time-domain electromagnetic fields with polarization effects in the field of geophysical forward modeling simulation, especially suitable for rapid calculation of fractional-order Cole-Cole model in time domain for three-dimensional space induction-polarization dual-field electromagnetic response. Background technique [0002] Transient-electromagnetic method (TEM for short) is a time-domain electromagnetic detection method based on the principle of electromagnetic induction and using artificial field sources as excitation sources. The transient electromagnetic method has the advantages of sensitive response to low-resistance bodies and high detection accuracy. It has gradually become a promising method and is widely used in the fields of hydrology and mineral exploration. However, when the center loop or overlapping loop is used for actual measurement, there is an abnor...

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Problems solved by technology

[0009] The key problem to be solved by the present invention is to provide a fractional-order electromagnetic anomalous diffusion three-dimensional simulation method for rational function approximation, and solve the best approximation of the fractional-order Cole-Cole model transfer function through the frequency-domain rational function approximation method and linear programming method Rational transfer function; using partial fraction expansion method and inverse Laplace transform to obtain the time-domain form of conductivity, the invention can overcome the problem of solving the extreme value of the fractional differential equation and the fitting process function of the finite difference method, and is applicable to any Fast Calculation of Induction-Polarization Dual Fields for Fractional Cole-Cole Model

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