CN110346835A - Magnetotelluric forward modeling method, forward modeling system, storage medium and electronic equipment - Google Patents
Magnetotelluric forward modeling method, forward modeling system, storage medium and electronic equipment Download PDFInfo
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Abstract
The application provides a kind of magnetotelluric forward modeling method, forward modeling system, storage medium and electronic equipment, and method comprises determining that zoning, zoning include abnormal body region；It is multiple units by zoning subdivision；Obtain the conductivity tensor and permeability tensor of each unit, wherein the conductivity and magnetic conductivity in abnormal body region are different from the region in zoning in addition to abnormal body region；Further determine that out the electric and magnetic fields of zoning；So that it is determined that the apparent resistivity and phase in zoning at earth's surface out.By the way that the anisotropy of conductivity and magnetic conductivity is taken into account in forward modeling method, it can be with quantitative analysis conductivity and influence of the magnetic conductivity anisotropy to MAGNETOTELLURIC RESPONSE ON, and the forward modeling system of this method and the actual electromagnetic response situation of magnetotelluric is applied more to coincide, basis can be provided for three-dimensional magnetotelluric conductivity and magnetic conductivity Anisotropic inversion, thus application range also can more extensively.
Description
Technical Field
The present application relates to the field of exploration geophysics, and for example, to a magnetotelluric forward modeling method, forward modeling system, storage medium, and electronic device.
Background
The geoelectromagnetic method is an important geophysical method and has wide application in the aspects of detection of the internal structure of the earth, exploration of mineral resources, search of underground water resources and the like. Currently, data simulation is continuously performed on the magnetotelluric observation data through inversion, so as to obtain the electrical structure of the underground medium. However, based on the existing forward system, the application range is relatively narrow under the condition that the inversion based on the forward system is required to have certain effectiveness.
Disclosure of Invention
In view of the above, the present application aims to provide a magnetotelluric forward modeling method, a forward modeling system, a storage medium and an electronic device, which are closer to practical situations, so that the forward modeling system applying the forward modeling method has a wider application range.
In order to achieve the above object, embodiments of the present application are implemented as follows:
in a first aspect, an embodiment of the present application provides a magnetotelluric forward modeling method, including:
determining a calculation region, wherein the calculation region comprises an abnormal body region for representing an abnormal body; subdividing the computing area into a plurality of cells; acquiring the conductivity tensor and the permeability tensor of each unit, wherein the conductivity and the permeability in the abnormal body area are different from those in the calculation area except for the abnormal body area; determining an electric field and a magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit; based on the electric and magnetic fields of each cell within the simulated body region, apparent resistivity and phase at the earth's surface within the calculated region are determined.
Because the actual geological conditions are complex and the electromagnetic response is complex, the influence of the anisotropy of the conductivity and the permeability on the magnetotelluric response can be quantitatively analyzed by considering the anisotropy of the conductivity and the permeability into a forward modeling method, and a forward modeling system applying the method is more consistent with the electromagnetic response conditions of the magnetotelluric under various actual geological conditions, so that the reflection of various actual geological conditions is more accurate. In addition, the anisotropy of the conductivity and the magnetic permeability is considered, a foundation is provided for the inversion of the anisotropy of the conductivity and the magnetic permeability of the three-dimensional magnetotelluric, the electromagnetic response of the geological structure is not required to basically accord with the isotropy of the magnetic permeability tensor, and therefore the application range can be wider.
With reference to the first aspect, in a first possible implementation manner of the first aspect, the subdividing the computation region into a plurality of units includes:
and dividing the calculation area into a plurality of units by adopting sparse grids, wherein the abnormal body area is uniformly divided, and the calculation area is divided by adopting gradually increased grids from the abnormal body area to the outside.
The abnormal body area is uniformly divided, and the areas outside the abnormal body area are divided by adopting gradually-increased grids, so that the whole calculation area is divided into a plurality of units, the influence of the abnormal body area on the outer boundary of the calculation area is ensured to be small to be ignored, and errors can be eliminated as far as possible. And by adopting the sparse grid configuration method, the dimensionality of the matrix equation can be reduced, the calculation time of the subsequent solving process can be saved, and the efficiency of the forward modeling method is improved.
With reference to the first aspect, in a second possible implementation manner of the first aspect, the acquiring a conductivity tensor and a permeability tensor of each cell includes:
obtaining the conductivity sigma of the x' main axis direction in the main axis anisotropic coordinate system of each unit in the calculation area1Y' ″ conductivity in the principal axis direction σ2Conductivity in the direction of the z' principal axis σ3And obtaining the angle alpha of each rotation in the three Euler rotation processesS、αDAnd alphaLAnd acquiring the magnetic susceptibility χ of the x' main shaft direction in the main shaft anisotropy coordinate system of each unit in the calculation area1Y' "magnetic susceptibility x in the direction of the main axis2Z' magnetic susceptibility in the main axis direction x3And obtaining the angle beta of each rotation in the three Euler rotation processesS、βDAnd betaL(ii) a According to σ of each cell1、σ2、σ3、αs、αDAnd alphaLDetermining the conductivity tensor of each cell, and, from the χ of each cell1、x2、χ3、βS、βDAnd betaLThe permeability tensor for each cell is determined.
By adopting a main axis anisotropic coordinate system, determining each main axis direction in the Euler rotation mode, and then determining the conductivity tensor and the permeability tensor of each unit, the conductivity tensor and the permeability tensor of each unit can be quickly and accurately obtained. The conductivity tensor and the magnetic permeability tensor determined by the method can show the anisotropy of the conductivity and the magnetic permeability, and are the basis for realizing the consideration of the anisotropy of the conductivity and the anisotropy of the magnetic permeability into a forward modeling method.
With reference to the first aspect, in a third possible implementation manner of the first aspect, the determining, according to the conductivity tensor and the permeability tensor of each unit, the electric field and the magnetic field of the calculation region includes:
determining an integral equation of the calculation area according to the conductivity tensor and the permeability tensor of each unit and by combining a Maxwell equation set; determining an overall coefficient matrix of the calculation area according to the integral equation; determining the electric field of each unit in the calculation area according to a preset boundary condition and the overall coefficient matrix; and determining the magnetic field of each unit in the calculation region according to the electric field of each unit in the calculation region, wherein the electric field and the magnetic field of all the units in the calculation region collectively represent the electric field and the magnetic field of the calculation region.
In this way, the electric field and the magnetic field of each unit can be calculated through the conductivity tensor and the permeability tensor. And each unit is analyzed to determine an integral equation so as to further obtain an overall coefficient matrix of the whole calculation area, so that the electric field and the magnetic field of the calculation area are determined, and the electric field and the magnetic field of the calculation area can be obtained as accurately as possible.
With reference to the third possible implementation manner of the first aspect, in a fourth possible implementation manner of the first aspect, the determining an integral equation of the calculation area according to the conductivity tensor and the permeability tensor of each cell includes:
determining an electric field double-rotation equation of each unit, including the conductivity tensor and the magnetic conductivity tensor, and integrating the whole calculation area after point-multiplying the variation of the electric field intensity to obtain an intermediate equation; and determining an integral equation of the calculation area according to the vector identity equation, the divergence theorem and the intermediate equation.
In this way, the integral equation of the calculation region can be accurately obtained.
With reference to the third possible implementation manner of the first aspect, in a fifth possible implementation manner of the first aspect, the determining an integral equation of the calculation area according to the conductivity tensor and the permeability tensor of each cell includes:
and according to the conductivity tensor and the permeability tensor of each unit, deducing a variational equation by adopting a Galiki weighted residue method to determine an integral equation of the calculation area.
And a Galiki weighted residue method is adopted to derive a variational equation, so that an integral equation can be accurately determined, and an electric field and a magnetic field with accurate calculation regions can be further obtained.
With reference to the third possible implementation manner of the first aspect, in a sixth possible implementation manner of the first aspect, when each cell is a hexahedron, an electric field is applied to an edge, and the determining, according to the integral equation, an overall coefficient matrix of the calculation region includes:
determining a unit equation of each unit according to the integral equation; and determining the overall coefficient matrix of the calculation area according to the coefficient matrix contained in the unit equation of each unit.
In this way, the electric field method phase component can be allowed to suddenly change at the electric discontinuity interface, which is more suitable for the actual situation. In addition, the mode considers the anisotropy of the conductivity and the magnetic conductivity, so that the forward system applying the method can be applied to wider fields and more practical environments and has higher accuracy.
In a second aspect, embodiments of the present application provide a magnetotelluric forward system, including:
the area acquisition unit is used for determining a calculation area, wherein the calculation area comprises an abnormal body area representing an abnormal body; a mesh division unit for dividing the calculation region into a plurality of cells; a tensor acquisition unit configured to acquire a conductivity tensor and a permeability tensor of each cell, wherein conductivity and permeability in the abnormal body region are different from conductivity and permeability in a region other than the abnormal body region in the calculation region; the forward processing unit is used for determining an electric field and a magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit; and determining apparent resistivity and phase at the earth's surface within the calculation region based on the electric and magnetic fields of the calculation region.
In a third aspect, an embodiment of the present application provides a storage medium, where the storage medium includes a stored program, where, when the program runs, a device where the storage medium is located is controlled to execute the first aspect or any one of the first to sixth possible implementation manners of the first aspect.
In a fourth aspect, an embodiment of the present application provides an electronic device, including a memory and a processor, where the memory is configured to store information including program instructions, and the processor is configured to control execution of the program instructions, where the program instructions are loaded and executed by the processor to implement the steps of the magnetotelluric forward modeling method according to the first aspect or any one of the first to sixth possible implementation manners of the first aspect.
In order to make the aforementioned objects, features and advantages of the present application more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and it will be apparent to those skilled in the art that other related drawings can be obtained from the drawings without inventive effort.
Fig. 1 shows a flowchart of a magnetotelluric forward modeling method according to an embodiment of the present disclosure.
Fig. 2 shows a schematic diagram of a calculation region provided in an embodiment of the present application.
Fig. 3 shows a block diagram of a hexahedral unit according to an embodiment of the present disclosure.
Fig. 4 illustrates a euler rotation method provided in an embodiment of the present application.
Fig. 5 shows a schematic diagram of a vector finite element method applied to a hexahedral unit according to an embodiment of the present application.
Fig. 6 shows a block diagram of a forward system of magnetotelluric provided in an embodiment of the present application.
Fig. 7 shows a block diagram of an electronic device according to an embodiment of the present application.
The figure is as follows: 10-forward system of magnetotelluric electricity; 11-a zone establishing unit; 12-a mesh partitioning unit; 13-tensor acquisition unit; 14-a forward processing unit; 20-an electronic device; 21-a memory; 22-a communication module; 23-a bus; 24 processor.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
Currently, the forward system of magnetotelluric is mostly established based on the assumption that the earth medium is isotropic, and has many researches and applications. The anisotropy of the earth medium is objectively present due to the influence of various macroscopic and microscopic factors, such as the earth formation stress field, the deformation band of the earth medium, and the crystal orientation arrangement, for example, the rocks in nature have different degrees of anisotropy, and thus, the interpretation capability of the assumption that the earth medium is isotropic is limited.
For magnetotelluric, the anisotropic rock structure can be a micron-sized mineral and rock structure, or a periodically arranged mineral vein of tens to hundreds of meters or a directionally arranged water-filled crack, or even a rock ring structure of several kilometers to tens of kilometers. The anisotropy phenomenon of the physical properties of the solid earth medium has been proved and accepted by the geophysical world at home and abroad, and the geophysical theory and method technology developed on the basis of the physical phenomenon have been primarily applied in some fields, but the wide-range application of distance systematicness has a plurality of problems. The inventor of the application finds that when the numerical simulation is carried out on the actual observation data of the complex geology on the basis of the existing magnetotelluric forward modeling system, if anisotropy is ignored, deviation and even errors can be brought to the inversion result, so that when the existing magnetotelluric forward modeling method is applied to a wider range, the forward modeling effectiveness can not be reliably guaranteed. Based on this, the inventors of the present application have made the present application through creative efforts.
Wherein, the forward evolution: the method is a process of solving the response of a given model according to a certain physical principle under the action of a certain excitation source; and (3) inversion: refers to a mathematical physical process that retrofits the information inherent in the system that generated the data based on the measured data.
Referring to fig. 1, fig. 1 is a flowchart of a method for forward modeling of magnetotelluric electricity according to an embodiment of the present disclosure, where the method for forward modeling may include: step S10, step S20, step S30, step S40, and step S50.
First, step S10 may be performed.
Step S10: determining a calculation region, wherein the calculation region comprises an abnormal body region for representing an abnormal body.
In this embodiment, simulation data may be acquired, and in a forward modeling system to which the forward modeling method provided by the present application is applied, a calculation region may be established based on the acquired simulation data, and the calculation region may include an abnormal body region, where the abnormal body region refers to a region represented by an abnormal body in the calculation region. The abnormal body refers to a geologic body causing geophysical exploration abnormity, such as a different density body causing gravity abnormity, a magnetic body causing magnetic abnormity, a geologic body with electrical difference causing electrical abnormity, and the like.
For example, referring to fig. 2, fig. 2 is a schematic diagram of a calculation region established in a forward system. In a computing area, a variety of different material regions may be included, such as air, ground, and subsurface media, where anomalies are typically present.
It is understood that in other embodiments, the calculation regions may also be preset, for example, in a magnetotelluric forward system, models of some regions may be preset and stored, and when a calculation region needs to be obtained, the forward system may call a corresponding model without obtaining data immediately to establish a calculation region. Therefore, the present application should not be considered as limited herein.
After the calculation region including the abnormal body region is determined, step S20 may be performed.
Step S20: and dividing the calculation area into a plurality of units.
In this embodiment, the calculation region may be divided into a plurality of units by using a sparse grid, where the abnormal region is uniformly divided, and the calculation region is divided by using a gradually increasing grid from the abnormal region to the outside.
Illustratively, the calculation region may be a region including an abnormal body region and extending outward from the abnormal body region. And uniformly subdividing the abnormal body region by using a sparse grid, gradually increasing the size of the grid from the abnormal body region outwards, and subdividing the whole calculation region into a plurality of units until the influence of the abnormal body region on the outer boundary of the calculation region is small to be ignored.
Continuing to refer to fig. 2, specifically, a regular hexahedral sparse grid may be used to uniformly subdivide the abnormal body region, and then the size of the subdivided grid is continuously increased from the abnormal body region to the outside along the three directions x, y, and z until the influence of the abnormal body region on the outer boundary of the calculation region is negligible. Each resulting cell may be a rectangular block as shown in fig. 3.
Of course, in some other alternative manners, the calculation region may be subdivided in other manners to obtain a plurality of units. For example, a tetrahedron subdivision cutting method may be adopted to subdivide the calculation region to obtain a plurality of tetrahedrons. Therefore, the present application should not be considered as limited herein.
After the calculation region is divided into a plurality of cells, step S30 may be performed.
Step S30: and acquiring the conductivity tensor and the permeability tensor of each unit cell, wherein the conductivity and the permeability in the abnormal body area are different from those in the calculation area except for the abnormal body area.
In this embodiment, as for the anomalous body of the conductivity and permeability anisotropy, the conductivity tensor and the permeability tensor can be obtained by euler rotation from the principal axis anisotropy. Hereinafter, a detailed description will be given of an example in which the principal axis anisotropy coordinate system is obtained by euler rotation based on the measurement coordinate system.
Specifically, referring to FIG. 4, a measurement coordinate system (x, y, z) may be determined for each cell. Then, the measurement coordinate system is rotated clockwise along the z axis by an angle alphaSObtaining a coordinate system (x ', y', z); the coordinate system (x ', y ', z) is then rotated clockwise around the x ' axis by an angle αDObtaining a coordinate system (x ', y ", z'); then the coordinate system (x ', y', z ') is rotated around the z' axis by an angle alphaLAnd obtaining a principal axis anisotropic coordinate system (x ', y ' ″, z ').
After the main axis anisotropic coordinate system (x ', y' ″, z ') is determined, the conductivity sigma of the main axis direction x' in the main axis anisotropic coordinate system can be obtained1Y' ″ conductivity in the principal axis direction σ2Conductivity in the direction of the z' principal axis σ3And, obtaining the angle alpha of each rotation in three Euler rotation processess、αDAnd alphaL(ii) a Wherein alpha isS: the angle of the anisotropy of the direction of the flow,αD: angle of anisotropic inclination, αL: the angle of anisotropy tendency.
Similarly, three euler rotations of the measurement coordinate system are performed to obtain a principal axis anisotropy coordinate system (x ", y '", z'). Can obtain the magnetic susceptibility x of the x' main shaft direction in the main shaft anisotropic coordinate system1Y' ″ magnetic susceptibility in the main axis direction χ2Magnetic susceptibility χ in the direction of the z' principal axis3And, obtaining the angle beta of each rotation in three Euler rotation processesS、βDAnd betaLWherein, βS: angle of anisotropy, betaD: anisotropic angle of inclination, betaL: the angle of anisotropy tendency. In addition, β is the same unitS、βD、βLAnd alphaS、αD、αLThe rotation angles can be different.
The above parameter (σ)1、σ2、σ3、μ1、μ2、μ3、αs、αD、αL、βS、βDAnd betaL) The setting can be performed in a preset mode or by means of user input. After the parameters are determined, the sigma of each unit can be determined1、σ2、σ3、αS、αDAnd alphaLDetermining the conductivity tensor of each cell, and, from the χ of each cell1、χ2、χ3、βS、βDAnd betaLThe permeability tensor for each cell is determined.
Specifically, in the present embodiment, σ according to each cell1、σ2、σ3、αS、αDAnd alphaLThe manner in which the conductivity tensor for each cell is determined may be by rotating a transformation matrix through each rotation. Wherein, the measuring coordinate system is rotated clockwise along the z-axis by an angle alphaSObtaining a coordinate system (x ', y', z), and recording a corresponding rotation transformation matrix as R1(αS) (ii) a The coordinate system (x ', y'Z) clockwise about the x' axis by an angle of rotation alphaDObtaining a coordinate system (x ', y ', z '), and recording a corresponding rotation transformation matrix as R2(αD) (ii) a Rotating the coordinate system (x ', y', z ') around the z' axis by an angle alphaLObtaining a principal axis anisotropy coordinate system (x ', y ' ″, z '), and recording a corresponding rotation transformation matrix as R3(αL). Wherein R is1(αS)、R2(αD) And R3(αL) Respectively as follows:
in this way, the overall rotational transformation matrix can be determined:
R＝R1(αS)R2(αD)R3(αL)····(4)，
and the total rotational transformation matrix R satisfies the following condition (i.e., equation (5)):
RRT＝I························(5)，
wherein R isTIs the transpose of R, and I is the identity matrix.
From this, R is an orthogonal matrix, and from the characteristics of the orthogonal matrix, R is knownT＝R-1，R-1Is the inverse matrix of R.
In anisotropic media, the conductivity is a tensor of 3 × 3 orders in size. After the total rotation transformation matrix is determined, the relationship between each physical quantity in the measurement coordinate system and each physical quantity in the main axis anisotropic coordinate system can be further obtained:
J’＝RJ························(6)，
E’＝RE······················(9)，
wherein J, E andcurrent density, electric field and conductivity tensor under a measurement coordinate system respectively; j ', E' andthe current density, electric field and conductivity tensor are respectively under the main axis anisotropic coordinate system.
Further, it can be determined from equations (6) to (9):
wherein, conductivity tensor under the principal axis anisotropy coordinate system:
thus, the conductivity tensor can be determined as:
and the conductivity tensor is composed of three conductivities a1、σ2、σ3And three Euler rotation angles alphaS、αD、αLCollectively, any anisotropy may be expressed. Wherein each element is respectively:
σzz＝sin2αD(sin2αLσ1+cos2αLσ2)+cos2αDσ3··········(15)，
while the conductivity tensor is symmetrically positive, in addition, the resistivity tensorIs the conductivity tensorInverse of (2):
thus, it can be determined from maxwell's equations, ignoring the effects of displacement current here:
in this embodiment, the manner of determining the permeability tensor is also similar to the manner of determining the conductivity tensor, and is not described here again. The determined conductivity tensor and permeability tensor can be expressed as follows respectively:
wherein,is the conductivity tensor, σ is the conductivity;is the permeability tensor; mu.s0Is the magnetic permeability in air, and χ is the magnetic susceptibility.
In the present application, euler rotation is used to obtain the anisotropic conductivity tensor and the anisotropic permeability tensor, and rotation is performed in the order of the z-axis, the x-axis, and the z-axis, but in some realizable embodiments, rotation may be performed by another rotation axis and rotation order, and the anisotropic conductivity tensor and the anisotropic permeability tensor may be obtained, which is not limited herein.
The electric conductivity and magnetic permeability in the abnormal body region are different from those of the region outside the abnormal body region in the calculation region, but the electric conductivity tensor and magnetic permeability tensor of each cell in the abnormal body region may be the same or different, and are not limited herein.
After the conductivity tensor and permeability tensor are determined, step S40 may be performed.
Step S40: and determining the electric field and the magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit.
In this embodiment, an integral equation of the calculation region may be obtained based on the conductivity tensor and the permeability tensor by using the determined conductivity tensor and permeability tensor and using a galileo weighted residue method.
For example, the equation may be derived by using maxwell's equations according to the determined conductivity tensor and permeability tensor, and thereby the electric field bi-rotation equation and the magnetic field bi-rotation equation may be derived:
wherein,is a Hamiltonian, E is the electric field intensity, H is the magnetic field intensity, omega is the frequency, i is an imaginary number,equation (23) represents the electric field bispherical equation, and equation (24) represents the magnetic field bispherical equation.
Because the derived electric field bispin degree equation only contains an electric field and the magnetic field bispin degree equation only contains a magnetic field, on the premise of obtaining the electric field, the corresponding magnetic field can be obtained based on the determined electric field; similarly, on the premise of obtaining the magnetic field, the corresponding electric field can be obtained based on the determined magnetic field. In the present embodiment, a method of determining a magnetic field by solving an electric field will be described in detail as an example, but in other realizable forms, a method of determining an electric field by solving a magnetic field may be used, and therefore, the present invention is not limited thereto.
In this embodiment, after the electric field double rotation equation is determined, the electric field double rotation equation may be point-multiplied by δ E, and then the whole calculation area is integrated, so as to obtain:
wherein δ E is a variation of E, and δ E ═ δ Ex+δEy+δEz，δExRepresents the component of δ E in the x-axis direction, δ EyDenotes E in the y-axis directionComponent of direction, δ EzRepresents the component of δ E in the z-axis direction; integral multiple ofvdv denotes the integration over the entire calculation area.
The vector identity is combined according to the equation after integrating the whole calculation area, i.e. equation (25):
further, equation (26) may be combined with the divergence theorem (or gaussian theorem):
since the inner boundary integrals of the calculation regions can cancel each other out, the outer boundary of the calculation regions can adopt the preset first type boundary condition. In this way, the amount of calculations required can be reduced as much as possible. On this basis, the integral equation can be determined as:
by using the Galiki weighted residue method, the integral equation of the calculation area can be further determined quickly and accurately through the conductivity tensor and the permeability tensor of each unit, so that the calculation time is saved, and the efficiency is improved. It should be noted that, in some other implementations, an integral equation of the calculation area may be further derived based on the conductivity tensor and the permeability tensor of each cell by deriving a variational equation, which is not limited herein.
After the integral equation of the calculation region is determined, one unit in the calculation region can be analyzed, and the analyzed unit is expanded to the whole calculation region to complete the analysis of the calculation region.
Exemplarily, taking fig. 5 as an example, fig. 5 shows the structure and parameters of a hexahedral unit, the side lengths in the three directions of x, y and z are respectively denoted as a, b and c, and the origin coordinate is (x)0，y0，z0). In this embodiment, a tangent vector field can be assigned to an edge, and field component vectors in three directions can be represented as:
where N is the Whitney interpolation basis function (an interpolation function where Whitney is the name of a person).
Specifically, the method comprises the following steps:
and E on a cell can be expressed as the sum of the vector basis function multiplied by the value of the field on the edge:
the entire calculated area integral can then be decomposed into the unit integrals as follows:
thus, within one cell there are:
after the coefficient matrix in one unit is determined, the coefficient matrix in one unit can be expanded based on the coefficient matrix in the unit, and the coefficient matrix is expanded to all units in the calculation area, so that the overall coefficient matrix of the calculation area is obtained:
wherein E is E of all nodesx，Ey，EzThe column vector of (2).
Based on delta ETThe overall coefficient matrix of the calculation region can be obtained:
KE＝0·············(46)。
after the overall coefficient matrix of the calculation area is determined, a preset first type boundary condition can be added. In order to improve the calculation accuracy, the preset first class boundary condition can be added to the equation (46) by a direct method without loss of accuracy, so as to obtain an equation system:
at a known phi3＝p3，φ5＝p5，φ6＝p6Then the system of equations to be solved (i.e., equation (47)) may be equivalent to solving the following system of equations:
the boundary conditions are added through a direct method, the quantity of the first type of boundary conditions in the equation is eliminated, the dimensionality of the equation can be effectively reduced, and the method is suitable for the condition that the known quantity is large. In addition, the dimensionality of the matrix equation is reduced by adding the boundary conditions by a direct method, the processing speed can be increased, and the operation efficiency of the magnetotelluric forward modeling method is improved.
After adding the boundary condition, the overall coefficient matrix becomes:
KE＝P·············(49)，
solving the equation system can obtain the electric field value on each edge of all the units. Here, the electric fields of all the cells in the calculation region can be obtained by preprocessing with SSOR (Symmetric super-Relaxation iteration) and solving the equation with a bicgsab (conjugated gradient stabilized method, generally abbreviated as bicgsab).
And after the electric fields of all the units in the calculation area are obtained, the magnetic field of each unit in the calculation area can be determined according to the electric field of each unit in the calculation area. Specifically, the method comprises the following steps:
after the electric field and the magnetic field of each unit in the calculation area are determined, the electric field and the magnetic field of the calculation area can be obtained. Thus, step S50 may be performed.
In this embodiment, the tensor impedance Z of each cell can be determined based on the electric field and the magnetic field of each cell:
wherein Z isxx、Zxy、Zyx、ZyyRespectively as follows: the tensor impedances in xx, xy, yx, yy modes.
From the tensor impedance of each cell, the apparent resistivity and phase at the earth's surface within the computed area can be determined:
in this embodiment, the apparent resistivity and phase at the earth surface within the region are calculated to characterize the electromagnetic response of the anomaly, i.e., the forward evolution of magnetotelluric power on the anomaly region. Wherein the earth's surface refers to the surface at the interface of air and the underground medium in the calculation area.
By applying the magnetotelluric forward modeling method, the conductivity anisotropy and the magnetic conductivity anisotropy can be considered at the same time, the electromagnetic response is closer to the electromagnetic response of actual geological conditions, and a forward modeling system established based on the forward modeling method can adapt to more geological types, so that the forward modeling method has a wider application range.
The following describes the application effect of the forward modeling method provided by the present application with reference to specific examples.
In this embodiment, a magnetic susceptibility model may be calculated by a forward modeling system applying the forward modeling method provided in the embodiment of the present application, and compared with a one-dimensional analytic solution.
As shown in table 1, a magnetic susceptibility ground layer was included in one isotropic uniform half space of resistivity, the half space had a resistivity of 100 Ω · m, the magnetic susceptibility of the magnetic permeability layer was 1, the thickness was 100m, and the depth of burial was 140 m.
TABLE 1
Three frequency points are calculated, namely 100Hz, 50Hz and 20 Hz. The calculation results are shown in table 2, and it can be seen that the numerical solution is consistent with the analytic solution (1D is a one-dimensional analytic solution; 3D is a numerical solution calculated by the forward modeling system), and the maximum relative error is less than 0.3%. It is also known that a positive magnetic susceptibility leads to high apparent resistivity values.
TABLE 2
Through the principle introduction and the application effect description of the forward modeling method containing the conductivity anisotropy and the permeability anisotropy, it can be seen that the forward modeling method for the magnetotelluric provided by the application can be used for simulating a forward modeling model of the conductivity anisotropy and the permeability anisotropy, can quantitatively analyze the influence of the conductivity anisotropy and the permeability anisotropy on magnetotelluric response, provides a basis for inversion of the conductivity anisotropy and the permeability anisotropy of the magnetotelluric, and is wider in application range.
Referring to fig. 6, an embodiment of the present application further provides a magnetotelluric forward system 10, including:
the region acquiring unit 11 is configured to determine a calculation region, where the calculation region includes an abnormal body region representing an abnormal body; a mesh dividing unit 12 for dividing the calculation region into a plurality of cells; a tensor acquisition unit 13 configured to acquire a conductivity tensor and a permeability tensor of each cell, where conductivity and permeability in the abnormal body region are different from conductivity and permeability in a region other than the abnormal body region in the calculation region; the forward modeling processing unit 14 determines an electric field and a magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit; and determining apparent resistivity and phase of the earth surface in the calculation region based on the electric field and the magnetic field of each unit in the calculation region, wherein the apparent resistivity and the phase of the earth surface in the calculation region are forward results of the abnormal body.
In this embodiment, the mesh dividing unit 12 is further configured to:
and dividing the calculation area into a plurality of units by adopting sparse grids, wherein the abnormal body area is uniformly divided, and the calculation area is divided by adopting gradually increased grids from the abnormal body area to the outside.
In this embodiment, the tensor acquiring unit 13 is further configured to:
obtaining the conductivity sigma of the x' main axis direction in the main axis anisotropic coordinate system of each unit in the calculation area1Y' ″ conductivity in the principal axis direction σ2Conductivity in the direction of the z' principal axis σ3And obtaining the angle alpha of each rotation in the three Euler rotation processesS、αDAnd alphaLAnd acquiring the magnetic susceptibility χ of the x' main shaft direction in the main shaft anisotropy coordinate system of each unit in the calculation area1Y' "magnetic susceptibility x in the direction of the main axis2Z' mainMagnetic susceptibility χ in axial direction3And obtaining the angle beta of each rotation in the three Euler rotation processesS、βDAnd betaL(ii) a According to σ of each cell1、σ2、σ3、αS、αDAnd alphaLDetermining the conductivity tensor of each cell, and, from the χ of each cell1、χ2、χ3、βS、βDAnd betaLThe permeability tensor for each cell is determined.
In this embodiment, the forward processing unit 14 is further configured to:
determining an integral equation of the calculation area according to the conductivity tensor and the permeability tensor of each unit and by combining a Maxwell equation set; determining an overall coefficient matrix of the calculation area according to the integral equation; determining the electric field of each unit in the calculation area according to a preset boundary condition and the overall coefficient matrix; and determining the magnetic field of each unit in the calculation region according to the electric field of each unit in the calculation region, wherein the electric field and the magnetic field of all the units in the calculation region collectively represent the electric field and the magnetic field of the calculation region.
In this embodiment, the forward processing unit 14 is further configured to:
determining an electric field double-rotation equation of each unit, including the conductivity tensor and the magnetic conductivity tensor, and integrating the whole calculation area after point-multiplying the variation of the electric field intensity to obtain an intermediate equation; and determining an integral equation of the calculation area according to the vector identity equation, the divergence theorem and the intermediate equation.
In this embodiment, the forward processing unit 14 is further configured to:
and according to the conductivity tensor and the permeability tensor of each unit, deducing a variational equation by adopting a Galiki weighted residue method to determine an integral equation of the calculation area.
In this embodiment, when each unit is a hexahedron, an electric field is applied to the edge, and the forward processing unit 14 is further configured to:
determining a unit equation of each unit according to the integral equation; and determining the overall coefficient matrix of the calculation area according to the coefficient matrix contained in the unit equation of each unit.
Referring to fig. 7, an electronic device 20 is provided in the embodiments of the present application, where the electronic device 20 may be a server, such as a database server, a web server, a cloud server, or a server assembly composed of multiple sub-servers; and the terminal can also be a personal computer, a tablet computer, a smart phone and the like. The above listed devices are only illustrative and should not be considered as limiting the present application.
In this embodiment, the electronic device 20 may include: memory 21, communication module 22, bus 23, and processor 24. The processor 24, the communication module 22 and the memory 21 may be connected by a bus 23. The memory 21 may store therein a program required for executing the magnetotelluric forward modeling method; the communication module 22 can enable communication with the outside; bus 23 may facilitate communication and data transfer between the various modules connected by bus 23; and processor 24 may execute executable modules (e.g., computer programs for magnetotelluric forward modeling) stored in memory 21.
The processes disclosed in this embodiment, or the methods that the apparatus defined in this embodiment needs to perform, may be implemented by the processor 24. For example, after the processor 24 receives a corresponding execution instruction (e.g., an instruction for executing the magnetotelluric forward modeling method), the bus 23 may call the program of the magnetotelluric forward modeling method stored in the memory 21, and the processor 24 controls the communication module 22 through the bus 23, thereby implementing the execution of the magnetotelluric forward modeling method.
In summary, embodiments of the present application provide a magnetotelluric forward modeling method, a forward modeling system, a storage medium, and an electronic device, which can take the anisotropy of electrical conductivity and the anisotropy of magnetic conductivity into account in the forward modeling system to establish a new forward modeling method. Because the actual geological conditions are complex, a plurality of different electromagnetic responses exist in the same survey area, the influence of the anisotropy of the conductivity and the permeability on the magnetotelluric response can be quantitatively analyzed by considering the anisotropy of the conductivity and the permeability into a forward modeling method, and a forward modeling system applying the method is more consistent with the electromagnetic response conditions of the magnetotelluric under various geological conditions in practice, so that the reflection of various geological conditions in practice is more accurate. In addition, the anisotropy of the conductivity and the magnetic permeability is considered, a foundation is provided for the inversion of the anisotropy of the conductivity and the magnetic permeability of the three-dimensional magnetotelluric, the electromagnetic response of the geological structure is not required to basically accord with the isotropy of the magnetic permeability tensor, and therefore the application range can be wider.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A magnetotelluric forward modeling method is characterized by comprising the following steps:
determining a calculation region, wherein the calculation region comprises an abnormal body region for representing an abnormal body;
subdividing the computing area into a plurality of cells;
acquiring the conductivity tensor and the permeability tensor of each unit, wherein the conductivity and the permeability in the abnormal body area are different from those in the calculation area except for the abnormal body area;
determining an electric field and a magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit;
based on the electric and magnetic fields of the calculation region, apparent resistivity and phase at the earth's surface within the calculation region are determined.
2. The forward modeling method of claim 1, wherein the subdividing the computation region into a plurality of cells comprises:
and dividing the calculation area into a plurality of units by adopting sparse grids, wherein the abnormal body area is uniformly divided, and the calculation area is divided by adopting gradually increased grids from the abnormal body area to the outside.
3. The forward modeling method of claim 1, wherein the obtaining the conductivity tensor and permeability tensor for each cell comprises:
obtaining the conductivity sigma of the x' main axis direction in the main axis anisotropic coordinate system of each unit in the calculation area1Y' ″ conductivity in the principal axis direction σ2Conductivity in the direction of the z' principal axis σ3And obtaining the angle alpha of each rotation in the three Euler rotation processesS、αDAnd alphaLAnd acquiring the magnetic susceptibility χ of the x' main shaft direction in the main shaft anisotropy coordinate system of each unit in the calculation area1Y' ″ magnetic susceptibility in the main axis direction χ2Magnetic susceptibility χ in the direction of the z' principal axis3And obtaining the angle beta of each rotation in the three Euler rotation processesS、βDAnd betaL；
According to σ of each cell1、σ2、σ3、αS、αDAnd alphaLDetermining the conductivity tensor of each cell, and, from the χ of each cell1、χ2、χ3、βS、βDAnd betaLThe permeability tensor for each cell is determined.
4. The forward modeling method of claim 1, wherein the determining the electric and magnetic fields of the computed area from the conductivity tensor and permeability tensor of each cell comprises:
determining an integral equation of the calculation area according to the conductivity tensor and the permeability tensor of each unit and by combining a Maxwell equation set; and the number of the first and second groups,
determining an overall coefficient matrix of the calculation area according to the integral equation;
determining the electric field of each unit in the calculation area according to a preset boundary condition and the overall coefficient matrix; and the number of the first and second groups,
and determining the magnetic field of each unit in the calculation region according to the electric field of each unit in the calculation region, wherein the electric field and the magnetic field of all the units in the calculation region collectively represent the electric field and the magnetic field of the calculation region.
5. The forward modeling method of claim 4, wherein the determining an integral equation for the calculated area based on the conductivity tensor and permeability tensor for each cell comprises:
determining an electric field double-rotation equation of each unit, including the conductivity tensor and the magnetic conductivity tensor, and integrating the whole calculation area after point-multiplying the variation of the electric field intensity to obtain an intermediate equation;
and determining an integral equation of the calculation area according to the vector identity equation, the divergence theorem and the intermediate equation.
6. The forward modeling method of claim 4, wherein the determining an integral equation for the calculated area based on the conductivity tensor and permeability tensor for each cell comprises:
and according to the conductivity tensor and the permeability tensor of each unit, deducing a variational equation by adopting a Galiki weighted residue method to determine an integral equation of the calculation area.
7. The forward modeling method of claim 4, wherein an electric field is applied to the edges when each cell is a hexahedron, and determining the global coefficient matrix of the calculation area according to the integral equation comprises:
determining a unit equation of each unit according to the integral equation;
and determining the overall coefficient matrix of the calculation area according to the coefficient matrix contained in the unit equation of each unit.
8. A magnetotelluric forward-acting system, comprising:
the area acquisition unit is used for determining a calculation area, wherein the calculation area comprises an abnormal body area representing an abnormal body;
a mesh division unit for dividing the calculation region into a plurality of cells;
a tensor acquisition unit configured to acquire a conductivity tensor and a permeability tensor of each cell, wherein conductivity and permeability in the abnormal body region are different from conductivity and permeability in a region other than the abnormal body region in the calculation region;
the forward processing unit is used for determining an electric field and a magnetic field of the calculation area according to the conductivity tensor and the permeability tensor of each unit; and determining apparent resistivity and phase at the earth's surface within the calculation region based on the electric and magnetic fields of the calculation region.
9. A storage medium, characterized in that the storage medium comprises a stored program, wherein the program, when running, controls a device in which the storage medium is located to execute the magnetotelluric forward modeling method according to any one of claims 1 to 7.
10. An electronic device comprising a memory for storing information including program instructions and a processor for controlling execution of the program instructions, characterized in that: the program instructions, when loaded and executed by a processor, implement the steps of the method of magnetotelluric forward modeling of any one of claims 1 to 7.
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