Fractional order electromagnetic anomalous diffusion three-dimensional simulation method of rational function approximation

Abstract

The invention relates to a fractional order electromagnetic anomalous diffusion three-dimensional simulation method of rational function approximation, and aims at calculating three-dimensional time-domain induction-polarization double field response of a fractional order Cole-Cole model. The method mainly comprises the steps of establishing a Cole-Cole model fractional order transfer function andan n-odrer rational approximation function based on a frequency domain rational function approximation method, and making the sum of the real part and the imaginary part of an error function as a target function; achieving linearization of the target function through an instrumental variable technique, and obtaining an optimal approximation rational function by adopting a linear programming approach; obtaining a time-domain mode of a conductivity by adopting a partial fraction expansion method and inverse laplace transformation; putting the time-domain mode in a Maxwell equation, deducing aniterative equation of an electromagnetic field based on a finite difference method, and achieving fractional order Cole-Cole model three-dimensional electromagnetic response value calculation. The fractional order electromagnetic anomalous diffusion three-dimensional simulation method of the rational function approximation has the advantages of fast and accurately simulating the fractional order Cole-Cole model three-dimensional time-domain electromagnetic response and providing theoretical foundation for research on abnormal electromagnetic diffusion in a polarization medium.

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 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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