Line source time domain electromagnetic response numerical calculation method based on meshless method

Abstract

The invention relates to a line source time domain electromagnetic response numerical calculation method based on meshless method, particularly a numerical simulation which can overcome dependence on mesh in the conventional numerical calculation method and is suitable for time domain electromagnetic surveying under complex terrain. In the line source time domain electromagnetic response numerical calculation method based on meshless method, based on a governing equation and a definite condition which the transient electromagnetic method satisfies, a generic function of a two-dimensional line source boundary value problem is established, essential boundary conditions are loaded through a penalty method, a paraxial approximate equation is provided to eliminate reflected waves at truncated boundaries, time discretization is carried out through a Crack-Nicolson format, and a recurrence equation is obtained. Based on an isoparametric element thought, units with regular shape in local coordinates are discretized to be irregular solving objects of which nodes are distributed at random. The recurrence equation is solved through a LU decomposition method, and finally, a field value of each node in a solving region is obtained. Calculation result shows that, with the method provided by the invention, a shape function has good smoothness, simulation precision is high, maximum error is not more than 1*10<-3>, and electromagnetic method high-accuracy numerical calculation is realized.

Description

technical field

[0001] The invention relates to an electromagnetic field numerical calculation method in the field of geophysical exploration, in particular to a line source time-domain electromagnetic response numerical calculation method based on a gridless method. Background technique

[0002] Time domain electromagnetic methods, or transient electromagnetic methods, is an artificial source electromagnetic detection method based on the principle of electromagnetic induction. At present, this method is widely used in metal ore exploration, coal mine hydrogeological survey and engineering exploration and other fields.

[0003] Electromagnetic field numerical simulation is the basis of data processing and inversion interpretation, and plays a fundamental and global role in geophysical numerical calculations. The existing transient electromagnetic numerical calculation methods mainly include integral equation method (IEM), finite difference method (FDM), finite element metho...

Examples

Embodiment

[0034] see Figure 5 combine figure 1 As shown, a numerical calculation method of time-domain electromagnetic response of line source based on mesh-free method, including:

[0035] 1) Set model parameters, including node settings, electrical parameter settings, background grid settings, and initial field value settings;

[0036] Such as figure 1 Meshless Gaussian points, field nodes, domain of influence Ω shown I , the local domain Ω x A schematic diagram of the background unit, including the solution domain Ω in the background integral network 1, including nodes 3 represented by black dots, and Gaussian integration points or calculation points 2 represented by hollow circles, within the solution domain Ω of a background integral network 1, Influence domain Ω I Refers to the influence area of ​​a node, the influence domain Ω I The center of is the field node, and the local domain Ω x Then it is the area selected for the least square fitting of the calculation point, and...

technical field

[0001] The invention relates to an electromagnetic field numerical calculation method in the field of geophysical exploration, in particular to a line source time-domain electromagnetic response numerical calculation method based on a gridless method. Background technique

[0002] Time domain electromagnetic methods, or transient electromagnetic methods, is an artificial source electromagnetic detection method based on the principle of electromagnetic induction. At present, this method is widely used in metal ore exploration, coal mine hydrogeological survey and engineering exploration and other fields.

[0003] Electromagnetic field numerical simulation is the basis of data processing and inversion interpretation, and plays a fundamental and global role in geophysical numerical calculations. The existing transient electromagnetic numerical calculation methods mainly include integral equation method (IEM), finite difference method (FDM), finite element metho...

Examples

Embodiment

[0034] see Figure 5 combine figure 1 As shown, a numerical calculation method of time-domain electromagnetic response of line source based on mesh-free method, including:

[0035] 1) Set model parameters, including node settings, electrical parameter settings, background grid settings, and initial field value settings;

[0036] Such as figure 1 Meshless Gaussian points, field nodes, domain of influence Ω shown I , the local domain Ω x A schematic diagram of the background unit, including the solution domain Ω in the background integral network 1, including nodes 3 represented by black dots, and Gaussian integration points or calculation points 2 represented by hollow circles, within the solution domain Ω of a background integral network 1, Influence domain Ω I Refers to the influence area of ​​a node, the influence domain Ω I The center of is the field node, and the local domain Ω x Then it is the area selected for the least square fitting of the calculation point, and...

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