CN116822305A - Magnetotelluric three-dimensional forward modeling method for resistivity and magnetic susceptibility anisotropic medium - Google Patents
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Abstract
The application provides a magnetotelluric three-dimensional forward modeling method of a resistivity and magnetic susceptibility anisotropic medium, and relates to the field of geophysics. The magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that a research model is the anisotropic medium, and the relation between magnetic induction intensity B and magnetic field intensity H is as follows: b=μh (1); where μ is the permeability of the medium, in a susceptibility anisotropic medium the susceptibility of the medium is no longer a scalar but expressed as a second order tensor, changing the equation (1) to:wherein the method comprises the steps ofAs the magnetic permeability tensor,i is the identity matrix,is the magnetic susceptibility tensor. The application solves the problem that the response calculation has deviation under the influence of resistivity and magnetic susceptibility anisotropy in the process of the geoelectromagnetic forward modeling.
Description
Technical Field
The application relates to the field of physics, in particular to a magnetotelluric three-dimensional forward modeling method of a resistivity and magnetic susceptibility anisotropic medium.
Background
Resistivity and magnetic susceptibility are two important electromagnetic parameters of an underground medium, and in conventional earth electromagnetic forward modeling, only the resistivity parameters are studied, usually assuming that the underground medium has no magnetic susceptibility anomalies. In order to better analyze the actual underground construction situation, acquiring reliable electrical structures guides the geological exploration work, and it is necessary to explore the magnetotelluric theory in terms of resistivity and susceptibility anisotropy. Early studies on resistivity anisotropy focused mainly on the effect of one-and two-dimensional principal axis anisotropic media on magnetotelluric response. With the rapid development of computer technology and mesh dissection technology, research hotspots gradually change from two dimensions to three dimensions and from principal axis anisotropy to arbitrary anisotropy. The range of applications is also extended from magnetotelluric models to marine magnetotelluric models, models with terrain or with oblique sounding, etc. The accuracy and effect of the simulation result of the magnetotelluric forward modeling will directly affect the authenticity and reliability of the inversion result. However, magnetotelluric related studies that consider both resistivity and susceptibility anisotropy are less. Therefore, there is a need for a three-dimensional forward method of magnetotelluric based on resistivity and susceptibility anisotropy to solve the problem of bias in response calculation under the influence of resistivity and susceptibility anisotropy in the magnetotelluric forward process.
Disclosure of Invention
The application aims to provide a magnetotelluric three-dimensional forward modeling method of a resistivity and magnetic susceptibility anisotropic medium, which can solve the problem that response calculation has deviation under the influence of resistivity and magnetic susceptibility anisotropy in the magnetotelluric forward modeling process.
In order to solve the technical problems, the application adopts the following technical scheme:
the magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that a research model is the anisotropic medium, and the relation between magnetic induction intensity B and magnetic field intensity H is as follows:
B＝μH (1)；
where μ is the permeability of the medium, in a susceptibility anisotropic medium the permeability or susceptibility of the medium is no longer a scalar but expressed as a second order tensor, changing the formula (1) to:
wherein the method comprises the steps ofIs magnetic permeability tensor->For the relative permeability tensor, I is the identity matrix, < >>Is the magnetic susceptibility tensor.
Further, in the present application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium of resistivity and magnetic susceptibility comprises the steps ofExpressed as:
wherein χ is ij (i, j=x, y, z) are different susceptibility tensor elements.
Further, in the application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that the expression of the relative permeability tensor is as follows:
further, in the application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that the expression of the magnetic permeability tensor is:
wherein mu ij (i, j=x, y, z) are different permeability tensor elements.
Further, in the present application, the magnetotelluric three-dimensional forward method of the above-mentioned resistivity and susceptibility anisotropic medium comprises the steps of, in the resistivity anisotropic medium, a resistivity tensorThe expression is:
wherein ρ is ij (i, j=x, y, z) are different resistivity tensor elements.
Compared with the prior art, the application has at least the following advantages or beneficial effects:
the application develops a forward algorithm which simultaneously considers the anisotropic medium of resistivity and magnetic susceptibility, designs related calculation examples, and shows that the analysis of the calculation examples simultaneously considers the anisotropic medium of resistivity and magnetic susceptibility to obtain a more real forward response of the underground electrical structure. The application adopts unstructured tetrahedral mesh subdivision calculation area, respectively carries out forward result verification based on resistivity anisotropic medium and susceptibility anisotropic medium, design resistivity lamellar model and susceptibility lamellar model, compares calculation result with analytic solution, and verifies the accuracy of developed algorithm. A single abnormal body model which simultaneously considers resistivity and magnetic susceptibility anisotropy is designed, relevant parameters of the resistivity and the magnetic susceptibility are modified by a variable control method, and analysis shows that a forward result with higher precision can be obtained by simultaneously considering the resistivity and the magnetic susceptibility anisotropy. And the effectiveness and practicality of the algorithm are verified by applying the algorithm to the actual model case. The forward modeling is a foundation of inversion, and in order to research the magnetotelluric response rule of the anisotropic medium with conductivity and magnetic susceptibility and lay a forward modeling foundation for subsequent inversion, the application develops the magnetotelluric three-dimensional forward modeling research of the anisotropic medium with resistivity and magnetic susceptibility, and has important significance for promoting the fine inversion interpretation of the actual magnetotelluric data.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic representation of a three-layer resistivity laminar model according to example 1 of the present application;
FIG. 2 shows the xy and yx components of (a) apparent resistivity and (b) phase, (c) relative error of apparent resistivity and analytical solution, and (d) absolute error of phase and analytical solution for different resistivities of example 1 of the present application;
FIG. 3 is a schematic diagram of a three-layer magnetic susceptibility layered model according to example 2 of the present application;
FIG. 4 shows (a) apparent resistivity and (b) phase, (c) apparent resistivity versus error curve and (d) phase absolute error curve for different magnetic susceptibility of example 2 of the present application;
FIG. 5 is a schematic diagram of a single anomaly model in embodiment 3 of the present application;
FIG. 6 is a plot of the magnetotelluric response at z=0 km for model 1, model 3, model 4, example 3 of the present application;
FIG. 7 is a plot of the magnetotelluric response at z=0 km for model 2, model 3, model 5, example 3 of the present application;
FIG. 8 is a plot of apparent resistivity and phase response for example 3 of the present application;
FIG. 9 is a schematic diagram of an actual model of embodiment 4 of the present application;
FIG. 10 is a schematic diagram of an initial model of a prior art inversion tool according to example 4 of the present application;
FIG. 11 is a grid subdivision schematic of a prior art inversion tool of example 4 of the present application;
FIG. 12 is a comparative graph of the inversion results of the actual model synthesis data of example 4 of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
The embodiment of the application discloses a magnetotelluric three-dimensional forward modeling method of a resistivity and magnetic susceptibility anisotropic medium, which comprises the following steps of researching the relationship between magnetic induction intensity B and magnetic field intensity H as an anisotropic medium:
B＝μH (1)；
where μ is the permeability of the medium, in a susceptibility anisotropic medium the permeability or susceptibility of the medium is no longer a scalar but expressed as a second order tensor, changing the formula (1) to:
wherein the method comprises the steps ofIs magnetic permeability tensor->For the relative permeability tensor, I is the identity matrix, < >>Is the magnetic susceptibility tensor.
Further, in the present application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium of resistivity and magnetic susceptibility comprises the steps ofExpressed as:
wherein χ is ij (i, j=x, y, z) are different susceptibility tensor elements.
Further, in the application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that the expression of the relative permeability tensor is as follows:
further, in the application, the magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility comprises the following steps that the expression of the magnetic permeability tensor is:
wherein mu ij (i, j=x, y, z) are different permeability tensor elements.
Further, in the present application, the above-mentioned resistivity and magnetizationThe magnetotelluric three-dimensional forward modeling method of anisotropic medium comprises the following steps ofThe expression is:
wherein ρ is ij (i, j=x, y, z) are different resistivity tensor elements.
Example 1
In the embodiment of the application, the resistivity lamellar model is taken as an example for verification, and as shown in fig. 1, the three-layer resistivity model provided by the embodiment of the application is shown, and the magnetic susceptibility of each layer in the model is 0. The first layer of the model is isotropic, the resistivity is 300 Ω & m, and the thickness is 2km; the second layer is an electric anisotropic layer, and has principal axis resistivity ρ x /ρ y /ρ z 10/100/10Ω·m, rotation angle α S /α D /α L 30 DEG/0 DEG, the thickness is 4km; the bottom layer is a uniform half space with the resistivity of 300 omega-m; the resistivity of the air layer was set to 10 8 Omega.m. The logarithmic number is equally spaced at 10 -1 Hz～10 3 Forward responses at 21 frequencies between Hz.
As shown in fig. 2, which shows the comparison of the magnetotelluric response results with the analytical solution, fig. 2 (a) and (b) show the apparent resistivity and phase curves varying with the period, wherein the triangle marks are the responses in the xy mode of the present algorithm, the diamond marks are the responses in the yx mode of the present algorithm, and the solid lines are the responses in the xy mode and the yx mode of the analytical solution. The solid triangles in fig. 2 (c) and (d) represent the relative (absolute) errors of apparent resistivity and phase calculated by the algorithm and the analytical solution when resistivity anisotropy is introduced in xy mode, and the solid diamonds represent the relative errors of response calculated by the algorithm and the analytical solution in yx mode. From the graph, the apparent resistivity and the phase calculated by the algorithm are well fitted with the analytic solution, the relative error of the apparent resistivity and the analytic solution is not more than 1%, the absolute error of the phase and the analytic solution is not more than 1 degree, and the accuracy of the algorithm when resistivity anisotropy is introduced is verified.
Example 2
The embodiment of the application shown in fig. 3 designs a three-layer model with the resistivity of the first layer of 20 Ω·m, the magnetic susceptibility χ of 0, and the thickness of 20m for the case where only the influence of magnetic anomalies is considered; the second layer is a magnetic susceptibility variable layer, the resistivity is 100 omega-m, the magnetic susceptibility χ is 0 and 0.5, and the thickness is 1000m; the bottom layer is a uniform half space with the resistivity of 1000 omega-m and the magnetic susceptibility χ of 0; the resistivity of the air layer was set to 10 8 Omega.m, magnetic susceptibility χ is 0. The logarithmic number is equally spaced at 10 -3 Hz～10 3 Forward responses at 31 frequencies between Hz.
Fig. 4 (a) and (b) are graphs of apparent resistivity and phase change with frequency for different magnetic susceptibility, where the triangle label is the response of the calculated second layer magnetic susceptibility χ of the algorithm when 0, the diamond label is the response of the calculated second layer magnetic susceptibility χ when 0.5, and the solid line is the analytical solution response of the calculated second layer magnetic susceptibility χ when 0 and 0.5. When the solid triangle mark in fig. 4 (c) and (d) is that the magnetic susceptibility χ of the second layer is equal to 0, the apparent resistivity and the relative (absolute) error of the phase and the analytical solution calculated by introducing the magnetic susceptibility χ are introduced; the solid diamond marks the relative (absolute) error of the calculated response and the analytical solution when the second layer susceptibility χ is equal to 0.5. As can be seen from the graph, no matter the magnetic susceptibility χ of the second layer is equal to 0 or 0.5, the apparent resistivity and the phase calculated by introducing the magnetic susceptibility χ are good in fitting with the analytical solution, the relative error of the apparent resistivity and the analytical solution is not more than 1%, and the absolute error of the phase and the analytical solution is not more than 1 °. In addition, as can be seen from fig. 4, when the magnetic susceptibility changes, the apparent resistivity and the phase also change, and the solution fit with the corresponding analysis is very good, thus verifying the accuracy of the forward result when the magnetic susceptibility χ is introduced.
Example 3
Embodiments of the present application provide a three-dimensional two-parameter anisotropic model as shown in fig. 5, (a) horizontal slice at z=0 km; (b) vertical slice at y=0 km. The abnormal body has a resistivity of 100 Ω·m and a magnetic susceptibility of 0In the half space, blue square blocks in the figure are abnormal bodies, and the resistivity of the blue square blocks is ρ a Magnetic susceptibility of χ a The size of the abnormal body is 10km×10km×5km, and the top is 2km from the ground. Air has a magnetic susceptibility of 0 and a resistivity of 10 8 Omega.m. Resistivity ρ of abnormal body a And magnetic susceptibility χ a All taken as principal axis anisotropy tensors.
(1) Spindle resistivity ρ y And spindle susceptibility χ x Influence of (2)
In order to study the influence of the change of the principal axis resistivity and the magnetic susceptibility parameters on the forward result, ρ is taken y And x is a variable, and electromagnetic anisotropy parameters of an abnormal body are set according to the table 1, so that the magnetotelluric response at the ground surface at the moment is analyzed.
TABLE 1 Anisotropic parameter setting of resistivity and susceptibility of abnormal bodies
Note that: alpha in the table S 、α D And alpha L For rotation angle, alpha, in resistivity anisotropy characterization parameters S1 、α D1 And alpha L1 The rotation angle in the parameter is characterized for susceptibility anisotropy.
As can be seen from Table 1, the variable between the different models is the principal axis resistivity ρ y And the magnetic susceptibility χx of the main shaft, and other parameters are the same. The resistivity anisotropy parameter settings of the model 1 and the model 3 are the same, and the susceptibility anisotropy parameter settings are different; the resistivity anisotropy parameter settings of the model 2 and the model 5 are the same, and the susceptibility anisotropy parameter settings are different; the resistivity anisotropy parameter settings of model 3 and model 4 are different, and the susceptibility anisotropy parameter settings are the same; the resistivity anisotropy parameter settings of model 3 and model 5 are different and the susceptibility anisotropy parameter settings are the same.
FIG. 6 shows the results of calculations for different models at a frequency of 1Hz. Apparent resistivitySusceptibility χ of main shaft y Sensitivity, apparent resistivity->Susceptibility χ of main shaft x Sensitive and->Resistivity ρ to principal axis x Sensitive (I)>Resistivity ρ to principal axis y Sensitivity is also due to the fact that the variable between different models is the principal axis resistivity ρ y And spindle susceptibility χ x So the apparent resistivity in FIG. 6 +.>And phase->Is not dependent on ρ y Or χ x Is changed by a change in (a). FIG. 6 (a) is a response of model 1 because ρ y Low resistance relative to the resistance value of surrounding rock, magnetic susceptibility of 0, abnormal body +.>Manifested as low resistance abnormality, & lt & gt>Greater than 45 °; FIG. 6 (b) shows the response result ρ of model 3 y Is uniform half space relative to surrounding rock, χ x Is of high magnetism +.>Manifested as high resistance abnormality and->Less than 45 °; FIG. 6 (c) shows the response result ρ of model 4 y Relative to surrounding rockLow resistance, χ x Is of high magnetism, is in the center of the abnormal body +.>Is expressed as nearly uniform half space,/->Approximately 45 deg..
FIG. 7 is a calculation of models 2, 3 and 5, with a frequency of 1Hz, and with anisotropic parameters of models 2, 5 compared to models 1, 4, ρ alone y The low resistance is changed into high resistance, and other parameters are unchanged. In model 2, because ρ y Is high-resistance, so at the center of the abnormal bodyManifested as high resistance abnormality, phase +.>Less than 45 deg., as shown in fig. 7 (a). In FIG. 7 (c), the +.in the center of the abnormal body>Is manifested as a high resistance abnormality and is larger than the abnormal value in FIG. 7 (a), (b), +.>The angle value of (a) is smaller than 45 deg. and smaller than in fig. 7 (a), (b).
(2) Anisotropic rotation angle alpha S Influence of (2)
The above analysis shows the effect of the change in spindle resistivity and spindle magnetic susceptibility on the response characteristics, and the rotation angle alpha is added based on the above S . Specifically, the influence of the anisotropic rotation angle on the surface response was studied by setting the anisotropic parameters according to table 2.
TABLE 2 Anisotropic parameter setting of resistivity and susceptibility of abnormal bodies
FIGS. 8 (a) - (e) are the results of calculations for models 1-5, respectively, at different rotational angles α S The apparent resistivity and phase response cut at z=0 km, frequency 0.1Hz. In the figure, the red solid line is aligned with the low apparent resistivity and high phase direction, and the white solid line is aligned with the high apparent resistivity and low phase direction. From Table 2, it can be seen that the principal axis resistivity ρ x Is of low resistance, ρ y High resistance, spindle magnetic susceptibility χ x 、χ y All are high magnetic, and according to the conclusion, when two electromagnetic parameters influencing apparent resistivity are respectively low-resistance high magnetic, the high magnetic can counteract the effect of low-resistance on response; when two electromagnetic parameters affecting apparent resistivity are high resistance and high magnetism, the high magnetism can enhance the effect of high resistance on response. FIG. 8 (a) is a response graph when the angle is equal to 0, and the response anomalies are not deflected at this time; when the rotation angle alpha S Is 0 degree alpha S1 At 30 °, the apparent resistivity is deflected by a random angle in response to anomaliesSlightly decreasing, +.>As shown in fig. 8 (b); when alpha is S Is 30 degrees alpha S1 At 0 deg., deflection occurs in response to the abnormality, the angle of deflection being about 30 deg., and +.>Is increased by (a) abnormal value (b)>As shown in fig. 8 (c); when alpha is S 、α S1 At 30 ° each, the deflection occurs in response to an abnormality, the deflection angle being about 30 °, as shown in fig. 8 (d), compared to fig. 8 (c), the +_in the center of the abnormality body>Is reduced in the abnormal value of (1),/>the abnormal value of (2) is increased, and the phase change range is not large; when alpha is S Is 60 degrees alpha S1 At 30 DEG, the deflection angle is approximately 60 DEG in response to the occurrence of deflection of the abnormality, at which time the +_ at the center of the abnormality body>Is changed into high resistance abnormality, +.>Becomes slightly smaller than the background abnormality as shown in fig. 8 (e).
As can be seen from fig. 8 (b), (d) and (e), α S1 Unchanged, alpha S Gradually increasing from 0 DEG, at the center of the abnormal bodyDeflection occurs and the abnormal value gradually decreases, +.>Deflection occurs, the abnormal value is gradually increased, and the abnormal value change of the phase is not obvious; in FIGS. 8 (c) and (d), when α S Unchanged, alpha S1 When changing from 30 DEG to 60 DEG, the center of the abnormal body is +.>Is reduced, the anomaly value at the center of the anomaly is +.>Is increased, the deflection angle of the response is unchanged, and is still approximately equal to alpha S Is a value of (2).
From the above analysis, it can be seen that the rotation angle α in the susceptibility anisotropy parameter when the resistivity is the principal axis anisotropy S1 The deflection effect on the response is no longer noticeable; when the magnetic susceptibility is the principal axis anisotropy, the rotation angle α in the resistivity anisotropy parameter S The deflection effect on response still existsAnd the responsive deflection angle is approximately the angle of rotation; when alpha is S And alpha S1 At the same time, the response still has deflection effect, and the deflection angle is approximately equal to alpha S . So when alpha S Unchanged, alpha S1 When increasing, the abnormal body is at the centerIs reduced, the anomaly value at the center of the anomaly is +.>Is increased; when alpha is S1 Unchanged, alpha S In case of enlargement, the center of the abnormal body is +.>Is increased by the abnormal value of +.>Is reduced; the deflection angle in response to anomalies is mainly defined by alpha S Is determined by the angle of (a).
Example 4
The embodiment of the application provides an actual model designed based on engineering exploration results, and adopts an audio magnetotelluric method to carry out metal ore detection work, so that audio magnetotelluric field data of 422 measuring points are obtained in total, and two-dimensional isotropy nonlinear conjugate gradient inversion is carried out, so as to obtain an electrical structure model under the region. An actual earth model was constructed from the results of the isotropic inversion interpretation of the field data described above, as shown in fig. 9. And adding resistivity and magnetic susceptibility anisotropy into the model, performing forward modeling to generate theoretical synthesis data of an actual model, and performing inversion test work by adopting the existing magnetotelluric three-dimensional isotropy and three-dimensional electrical anisotropy inversion program so as to check whether the existing inversion tool can recover real abnormal distribution characteristics.
As shown in FIG. 9, the actual model has an isotropic low-resistance coating layer with a thickness of 40m, a resistivity of 50Ω.m and a susceptibility of 0 on a shallow surface, and an abnormal body with complicated resistivity and susceptibility anisotropy having a principal axis resistivity of 30/1/1 Ω.m and a principal axis susceptibility of 0/1 is buried in a uniform isotropic half space with a resistivity of 100deg.Ω.m and a susceptibility of 0 at a distance of 240m from the surface. The model profile extends infinitely in the y-direction, with the model parameters unchanged.
The projection of the central axis of the abnormal body on the ground surface is taken as a symmetrical point, 11 measuring lines are arranged in a research area, the direction is perpendicular to the trend of the abnormal body, the interval between the measuring lines is 200m, 41 measuring points are arranged on each measuring line, and the measuring point interval is 100m. At a frequency of 10 4 16 points are selected at equal logarithmic intervals between Hz and 1Hz, the unstructured grid subdivision is carried out on the actual model by adopting the com in consideration of the skin depth corresponding to the distribution of the measuring points and the frequency points, the number of grid units is 628635, and the total impedance tensor (Z) is calculated based on the set measuring points, the frequency points and the grid xx 、Z xy 、Z yx And Z yy ) In response, 1% gaussian random error was added as the inverse synthetic data.
Inversion is carried out by adopting a mature modularized three-dimensional parallel inversion program ModEM, and comprises a three-dimensional isotropic version and a three-dimensional electrical anisotropy version, forward modeling of the two versions is realized by adopting a staggered sampling finite difference method, and inversion is carried out by adopting a nonlinear conjugate gradient method to carry out optimization solution on the following objective functions:
wherein m is a model, d is data, f (m) forward responses, m 0 Is a priori model; c (C) d As a data covariance matrix, C m Is a model covariance matrix; lambda is a regularization factor; t is the transpose operation.
The initial model was a two-layer model (as shown in FIG. 10), the first layer being a low-resistance layer 40m thick and having a resistivity of 50Ω·m, and the second layer being a uniform isotropic half-space of 100deg.OMEGA·m. The inversion horizontal grid is evenly split in the central area with the size of 80m multiplied by 100m, then 10 expansion grids are added with a 1.8 times scale factor, the first layer of the vertical grid is 10m, and then 1.1The scale factor of 2-1.3 times is increased, the total finite difference grid cells are 81×47×57, fig. 11 is a schematic diagram of inversion grid subdivision, (a) horizontal direction, (b) vertical direction, and red dots in the figure represent measurement points. The standard deviation of the impedance data is 1% × +|Z xy Z yx | a. The application relates to a method for producing a fibre-reinforced plastic composite. The model covariance factors in the three directions are all taken to be 0.5, and the regularization factors of the model smoothing terms are all taken to be 100.
The inversion result of the actual model synthesis data is shown in fig. 12, and the black dotted line indicates the position of the abnormal body. Of these, fig. 12 (a) shows the three-dimensional isotropic inversion result (resistivity isotropy, magnetic susceptibility is 0), and fig. 12 (b 1) and (b 2) show the three-dimensional electric anisotropy inversion result (resistivity anisotropy, principal axis resistivity ρ) x And ρ y Magnetic susceptibility of 0). As can be seen from fig. 12 (a), the three-dimensional isotropic inversion can better locate the position of the abnormal body, recover the low-resistance characteristic of the abnormal body, but recover the obvious high-resistance false anomaly above the abnormal body, is inconsistent with the real abnormal body model, and cannot embody the difference of the conductive characteristics of the abnormal body in different directions; as can be seen from fig. 12 (b 1) and (b 2), the three-dimensional electric anisotropy inversion is performed at the principal axis resistivity ρ y The position and resistance of the abnormal body are better recovered in the result of (a) as shown in FIG. 12 (b 2), while the resistivity ρ at the principal axis x In the results of (a), the position of the abnormal body has a certain reaction, but the inversion resistance is high, as shown in fig. 12 (b 1).
In order to study the influence degree of the magnetic susceptibility anisotropy parameter on the inversion result, the magnetic susceptibility parameter in the model is set to 0/0/0, namely, the magnetic susceptibility anomaly is not considered, only the resistivity anomaly (30/1/1 omega-m) is considered, forward calculation is carried out to obtain synthetic data, and three-dimensional electric anisotropy inversion is carried out on the data. FIGS. 12 (c 1) and (c 2) are three-dimensional electrical anisotropy inversion results, and as can be seen by comparing FIGS. 12 (b 1) and (b 2), the recovered principal axis resistivity ρ is inverted with or without consideration of the resultant data of susceptibility anomalies y Substantially uniform, but principal axis resistivity ρ x The difference exists, the main manifestation is that the resistance value of the inversion of the synthesized data without considering the magnetic susceptibility abnormality is relatively low, the result is closer to a real model, and the influence of the magnetic susceptibility abnormality is not enoughNeglecting.
In addition, functional modules in the embodiments of the present application may be integrated together to form a single part, or each module may exist alone, or two or more modules may be integrated to form a single part.
Due to various geological effects, in some magnetite-rich rock regions, the subsurface medium exhibits not only resistivity anisotropy but also susceptibility anisotropy. When inversion interpretation is carried out on the magnetotelluric actual model data influenced by resistivity and magnetic susceptibility anisotropy, if only the resistivity anisotropy is researched, the inversion result is easy to generate errors or even generate errors, and other exploration and development work conducted by referring to the result is misled. The study of susceptibility anisotropy is similar to the study of resistivity anisotropy, and follows a rule from shallow to deep and from simple to complex. The magnetic susceptibility anisotropy is extremely widely applied in the geological field, and can be used for researching the directional arrangement of magnetic minerals caused by ancient flow direction, the directional recrystallization, the directional arrangement, the ductile deformation and the like of the magnetic minerals in the rock caused by the structural stress effect. The magnetic anisotropy has a great influence on the morphology of magnetic anomalies on the magnetized body, and is not negligible when applied to research in geophysics. The introduction of resistivity and susceptibility anisotropy makes both the resistivity and susceptibility scalar parameters in the isotropic numerical simulation theory tensor parameters. The problem is more complex than the isotropic case, where the number of model parameters increases dramatically.
In order to research the magnetotelluric response rule of the anisotropic medium with conductivity and magnetic susceptibility, a forward basis is laid for the subsequent inversion. The application develops a forward algorithm that considers both resistivity and susceptibility anisotropy. And related calculation examples are designed, and analysis of the calculation examples shows that the resistivity and the magnetic susceptibility anisotropy are considered at the same time, so that a more real forward response of the underground electrical structure can be obtained. And then the effectiveness and the practicability of the algorithm are verified by applying the algorithm to an actual model case.
The embodiment of the application designs the layered models of resistivity and magnetic susceptibility respectively, and compares the layered models with the analytic solutions of the corresponding layered models to respectively verify the forward accuracy when the resistivity anisotropy and the magnetic susceptibility anisotropy are introduced. A single abnormal body model with resistivity and magnetic susceptibility anisotropy being considered is designed, relevant parameters of the resistivity and the magnetic susceptibility are modified through a variable control method, and analysis shows that more accurate forward modeling results can be obtained by considering the resistivity and the magnetic susceptibility anisotropy at the same time.
In summary, the magnetotelluric three-dimensional forward modeling method based on resistivity and susceptibility anisotropy provided by the embodiment of the application develops a forward algorithm which simultaneously considers resistivity and susceptibility anisotropy, and designs related examples, and analysis of the examples shows that the forward modeling response of a more real underground electrical structure can be obtained by simultaneously considering resistivity and susceptibility anisotropy. The application adopts unstructured tetrahedral mesh subdivision calculation area, respectively carries out forward result verification based on resistivity anisotropic medium and susceptibility anisotropic medium, design resistivity lamellar model and susceptibility lamellar model, compares calculation result with analytic solution, and verifies the accuracy of developed algorithm. A single abnormal body model which simultaneously considers resistivity and magnetic susceptibility anisotropy is designed, relevant parameters of the resistivity and the magnetic susceptibility are modified by a variable control method, and analysis shows that a forward result with higher precision can be obtained by simultaneously considering the resistivity and the magnetic susceptibility anisotropy. And the effectiveness and practicality of the algorithm are verified by applying the algorithm to the actual model case. The forward modeling is a foundation of inversion, and in order to research the magnetotelluric response rule of the anisotropic medium with conductivity and magnetic susceptibility and lay a forward modeling foundation for subsequent inversion, the application develops the magnetotelluric three-dimensional forward modeling research of the anisotropic medium with resistivity and magnetic susceptibility, and has important significance for promoting the fine inversion interpretation of the actual magnetotelluric data.
The above description is only of the preferred embodiments of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (5)
1. The magnetotelluric three-dimensional forward modeling method of the anisotropic medium with resistivity and magnetic susceptibility is characterized by comprising the following steps,
the research model is an anisotropic medium, and the relation between the magnetic induction intensity B and the magnetic field intensity H is as follows:
B＝μH (1)；
where μ is the permeability of the medium, in a susceptibility anisotropic medium the permeability or susceptibility of the medium is no longer a scalar but expressed as a second order tensor, changing the formula (1) to:
wherein the method comprises the steps ofIs magnetic permeability tensor->For the relative permeability tensor, I is the identity matrix, < >>Is the magnetic susceptibility tensor.
2. The magnetotelluric three-dimensional forward method based on resistivity and susceptibility anisotropy as defined in claim 1, comprising the steps ofExpressed as:
wherein χ is ij (i, j=x, y, z) are different susceptibility tensor elements.
3. The magnetotelluric three-dimensional forward method based on resistivity and susceptibility anisotropy of claim 2, comprising the steps of:
4. a magnetotelluric three-dimensional forward method based on resistivity and susceptibility anisotropy as defined in claim 3, comprising the steps of:
wherein mu ij (i, j=x, y, z) are different permeability tensor elements.
5. The magnetotelluric three-dimensional forward method of resistivity and susceptibility anisotropy as defined in claim 4, comprising the step of, in a resistivity anisotropic medium, a resistivity tensorThe expression is:
wherein ρ is ij (i, j=x, y, z) are different resistivity tensor elements.
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| CN113221393A (en) * | 2021-01-29 | 2021-08-06 | 吉林大学 | Three-dimensional magnetotelluric anisotropy inversion method based on non-structural finite element method |
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| CN113221393A (en) * | 2021-01-29 | 2021-08-06 | 吉林大学 | Three-dimensional magnetotelluric anisotropy inversion method based on non-structural finite element method |
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