CN117538945B - Three-dimensional magnetotelluric multi-resolution inversion method, device, equipment and medium - Google Patents
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Abstract
The invention provides a three-dimensional magnetotelluric multi-resolution inversion method, a device, equipment and a medium, which comprise input observation data, frequency parameters and an initial inversion model, and an electric field control equation is constructed according to the frequency parameters and the initial inversion model; solving an electric field by using the constructed electric field control equation, obtaining a magnetic field of the earth surface by using electric field interpolation, and then obtaining a forward response corresponding to the initial inversion model; determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field, solving the pseudo-forward electric field to obtain the objective function of the current inversion model, judging whether inversion is stopped or not, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting a final inversion model. The finally output inversion model of the invention can be very close to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target.
Description
Technical Field
The invention mainly relates to the technical field of magnetotelluric numerical simulation, in particular to a three-dimensional magnetotelluric multi-resolution inversion method, device, equipment and medium.
Background
Magnetotelluric exploration is one of key technologies for geophysical exploration, and based on the difference of electrical properties of underground rock ores, the distribution and change of a natural electromagnetic field in space and time caused by the electrical difference are analyzed, so that the electrical structure distribution characteristics of underground media are revealed. The exploration technology has wide exploration depth, is not influenced by a high-resistance layer, and is widely applied to a plurality of fields such as mineral exploration, engineering geophysical prospecting, earth deep structure research and the like.
In practical field exploration, the area to be researched is a large-scale three-dimensional area, and for economic reasons, measuring stations for exploration are usually placed on the ground surface and the number of measuring stations is very limited, so that when the method is explained, inversion is often needed to be carried out by combining multiple types of electromagnetic data, and underground information resources are fully excavated and utilized. Currently, modEM and WSINV3DMT are two sets of open source codes which are the main stream internationally, and inversion algorithms thereof mostly depend on structured grids, and have proven their excellent performances in many practical applications.
However, when dealing with complex terrain and geologic models, structured grids still face challenges, requiring a large number of grids to finely disperse the investigation region, and unstructured grids are more suitable for differentially dispersing various investigation regions due to their flexibility, and thus are favored and applied by numerous students. However, unstructured grid inversion also faces challenges: such as the complexity of the grid configuration, the pathological coefficient matrix caused by the overstretching of the grid, and the need for extensive post-processing. It is therefore becoming particularly critical to study a multi-resolution based structured grid, to differentially discrete the regions of interest, and to bypass the unstructured grid. The current multi-resolution method is gradually applied to three-dimensional electromagnetic forward modeling, and the research of the multi-resolution method applied to inversion is not seen.
In addition, since the new century, the development of electromagnetic measurement technology has greatly promoted the research of the earth electromagnetic field, and large-scale electromagnetic measurement technology has been vigorously developed, so that the requirement of multi-data type multi-resolution inversion is difficult to be met by the traditional inversion algorithm. Therefore, the research on the method for high-efficiency and high-precision inversion based on the multi-electromagnetic data type multi-resolution grid has practical significance.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a three-dimensional magnetotelluric multi-resolution inversion method, device, equipment and medium.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
in one aspect, the invention provides a three-dimensional magnetotelluric multi-resolution inversion method comprising:
inputting observation data, frequency parameters and an initial inversion model, wherein the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
constructing an electric field control equation according to the frequency parameters and the initial inversion model;
solving an electric field by using the constructed electric field control equation, and obtaining a magnetic field of the earth surface by using electric field interpolation so as to obtain a forward response corresponding to the initial inversion model;
determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field based on the constructed pseudo-forward equation, and further solving to obtain the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>Is initially invertedModel, ->For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and calculating the root mean square fitting difference of the current inversion model obtained by solving, judging whether the inversion is stopped based on the root mean square fitting difference of the objective function or the current iteration times, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting the final inversion model.
The inversion model finally output by the invention is the final conductivity or resistivity structure model of the underground geologic body obtained by inversion at the end of inversion, and the model can be very close to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target.
Further, the three-dimensional cuboid grid model edge corresponding to the magnetotelluric three-dimensional exploration targetx、y、zPerforming meshing in the direction, and meshing into a plurality of three-dimensional cuboid meshing units to obtain meshing parameters of a three-dimensional cuboid meshing model corresponding to the magnetotelluric three-dimensional exploration target, wherein the conductivity of each three-dimensional cuboid meshing unitOr resistivity->The conductivity value or the resistivity value of different three-dimensional cuboid grid units is constant.
In another aspect, the present invention provides a three-dimensional magnetotelluric multi-resolution inversion apparatus comprising:
the system comprises a first module, a second module and a third module, wherein the first module is used for inputting observation data, frequency parameters and an initial inversion model, the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
the second module is used for constructing an electric field control equation according to the frequency parameters and the initial inversion model;
the third module is used for solving an electric field by utilizing the constructed electric field control equation, obtaining a magnetic field of the earth surface by utilizing electric field interpolation, and further obtaining forward modeling response corresponding to the initial inversion model;
a fourth module, configured to determine an objective function of the current inversion model, construct a forward-looking equation based on the objective function of the current inversion model, and solve a forward-looking electric field based on the constructed forward-looking equation, thereby solving the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and a fifth module, configured to calculate a root mean square fitting difference of the current inversion model obtained by solving, determine whether to stop inversion based on the root mean square fitting difference of the objective function or the current iteration number, if the inversion is not finished, update the inversion model in the objective function in the fourth module, adjust an update step length of the inversion model until the inversion is finished, and output a final inversion model.
In another aspect, the present invention provides a computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the following steps when executing the computer program:
inputting observation data, frequency parameters and an initial inversion model, wherein the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
constructing an electric field control equation according to the frequency parameters and the initial inversion model;
solving an electric field by using the constructed electric field control equation, and obtaining a magnetic field of the earth surface by using electric field interpolation so as to obtain a forward response corresponding to the initial inversion model;
determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field based on the constructed pseudo-forward equation, and further solving to obtain the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and calculating the root mean square fitting difference of the current inversion model obtained by solving, judging whether the inversion is stopped based on the root mean square fitting difference of the objective function or the current iteration times, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting the final inversion model.
In another aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of:
inputting observation data, frequency parameters and an initial inversion model, wherein the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
constructing an electric field control equation according to the frequency parameters and the initial inversion model;
solving an electric field by using the constructed electric field control equation, obtaining a magnetic field of the earth surface by using electric field interpolation, and further obtaining forward response corresponding to the initial inversion model by calculation;
determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field based on the constructed pseudo-forward equation, and further solving to obtain the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and calculating the root mean square fitting difference of the current inversion model obtained by solving, judging whether the inversion is stopped based on the root mean square fitting difference of the objective function or the current iteration times, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting the final inversion model.
It can be appreciated that the present invention enables the current inversion model to be obtained through continuous iterative updatingGradually approaching to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target, when the root mean square fitting difference RMS of the calculated objective function is smaller than a preset threshold value or the iteration number of inversion reaches the set highest upper limit, the corresponding inversion model is the optimal final conductivity or resistivity structure model of the underground geologic body obtained by inversion, and can be very close to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target.
The invention provides a three-dimensional magnetotelluric multi-resolution inversion method which can meet the requirements of fine and rapid inversion imaging of large-scale electromagnetic data.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a three-dimensional magnetotelluric multi-resolution inversion method provided in one embodiment;
FIG. 2 is a schematic illustration of a blind low-resistance ore body model in one embodiment;
FIG. 3 is a schematic diagram of a model slice obtained by inversion of the hidden low-resistance ore body model shown in FIG. 2 based on different observation data by using the three-dimensional magnetotelluric multi-resolution inversion method provided by the invention, wherein (a) is an inversion result of using full tensor impedance data on a regular grid, (b) is an inversion result of using full tensor impedance data+dip data on a regular grid, and (c) is an inversion result of using full tensor impedance data+dip data on a multi-resolution grid;
FIG. 4 is a comparison bar chart of inversion times and inversion time of the hidden low-resistance ore body model shown in FIG. 2 based on different observation data by using the three-dimensional magnetotelluric multi-resolution inversion method provided by the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, in an embodiment of the present invention, a three-dimensional magnetotelluric multi-resolution inversion method is provided, which includes the following steps:
inputting observation data, frequency parameters and an initial inversion model;
constructing an electric field control equation according to the frequency parameters and the initial inversion model;
solving an electric field by using the constructed electric field control equation, and obtaining a magnetic field of the earth surface by using electric field interpolation so as to obtain a forward response corresponding to the initial inversion model;
determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field based on the constructed pseudo-forward equation, and further solving to obtain the objective function of the current inversion model;
and calculating the root mean square fitting difference of the current inversion model obtained by solving, judging whether the inversion is stopped based on the root mean square fitting difference of the objective function or the current iteration times, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting the final inversion model.
The invention has wide adaptability, can invert various types of observed data, and the types of the observed data comprise non-diagonal impedance data) Full tensor impedance data (+)>) Data of the inclination (>) Full tensor impedance data + tilt data (+)>) Four inversion data types, one of which may be optionally used for inversion.
The initial inversion model is a priori model and comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model; three-dimensional cuboid grid model edge corresponding to magnetotelluric three-dimensional exploration targetx、y、zPerforming meshing in the direction, and meshing into a plurality of three-dimensional cuboid meshing units to obtain meshing parameters of a three-dimensional cuboid meshing model corresponding to the magnetotelluric three-dimensional exploration target, wherein the conductivity of each three-dimensional cuboid meshing unitOr resistivity->The conductivity value or the resistivity value of different three-dimensional cuboid grid units is constant.
The invention determines the objective function of the current inversion model, expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation.
In one embodiment, for constructing an electric field control equation according to the frequency parameter and the initial inversion model, a specific method is proposed as follows:
according to frequency parametersAnd initial inversion model->Constructing an electric field control equation->Wherein E represents the electric field to be solved, A is the coefficient matrix of the electric field control equation, ++>，/>Representing a rotation operator->Representing a double rotation operator->，/>Represents angular frequency by ∈>Find out->Represents permeability, its value is->，/>Representing an initial inversion model +.>Conductivity or resistivity of each three-dimensional rectangular grid cell; />The right term is composed of a field source and set inversion region boundary conditions.
In particular, the method comprises the steps of,when polarized in the direction, the field source is located at the top of the air layer to make the electric field of the top surface along the x direction +.>1, electric field of the top surface in y direction +.>0, where inversion region edge +.>Lateral boundary field value of direction +.>Control equation by two-dimensional forward modeling>Find out->Representing electric field +.>Second derivative of edge length in x-direction, +.>Representing electric field +.>Edge->Second derivative of the edge length, bottom boundary field value is obtained by interpolating the lowest field value of the two side boundaries, and alongyThe boundary field value of the direction is set to 0;yin the case of directional polarization, the field source is located at the top of the air layer, its value +.>0, at the same time->1, at which time the inversion region is alongyLateral boundary field value of direction +.>Control equation by two-dimensional forward modeling>Find out->Representing electric field +.>Edge of the frameSecond derivative of the directional edge length, while edge +.>The boundary field value of the direction is set to 0, and the bottom boundary field value is obtained by interpolating the field values of the bottommost boundaries on both sides.
In one embodiment, the electric field control equation is constructed based on the aboveSolving an electric field E, obtaining a magnetic field of the earth surface by utilizing E interpolation, and further obtaining forward response corresponding to an initial inversion model, wherein the method specifically comprises the following steps:
dividing the initial inversion model into a plurality of layers of subareas along the Z direction, and respectively constructing interpolation operators with different sparsity for each layer of subareas along the horizontal direction;
(1.2) synthesizing interpolation operators corresponding to all the layer sub-regions to obtain a total sparse sampling operator;
(1.3) multiplying the coefficient matrix A and the right-end term b of the constructed electric field control equation by the total sparse sampling operator to obtain a new sparse matrixAnd modified right-hand term->New sparse matrix ∈>And a corrected right-hand end itemCarrying out solution to obtain a corrected electric field in a constructed electric field control equation>；
(1.4) by the formulaObtaining the magnetic field of the earth's surface->Further utilize electric field->And magnetic field->And obtaining forward response corresponding to the initial inversion model.
Wherein the corrected electric field E is solved in the steps (1.1) to (1.3) new The specific process of the method is a three-dimensional geologic body electromagnetic field numerical simulation method, a device, equipment and a method disclosed in a medium, wherein the specific process is disclosed in an invention patent application with the publication number of CN 113779818A and the publication date of 2021, 12 and 10.
In the step (1.4), the formula is passedObtain magnetic field->Further utilize electric field->And magnetic field->And obtaining forward response corresponding to the initial inversion model. Using the observed data as full tensor impedance data + tilt data (>) For example, first use is made of the electric field +.>And magnetic field->Is of the horizontal component electric field of (2)And magnetic field->Calculating full tensor impedance data, i.e. full tensor impedance response +.>：
；
Wherein the superscript、/>Respectively represent edge->Direction(s) (i.e. the directions of the eyes)>Direction is polarized, is->,/>,And->Respectively represent edgesxA horizontal component of the directionally polarized electric and magnetic fields; />,/>,/>And->Is along the edgeyHorizontal component of the directionally polarized electric and magnetic fields. Full tensor impedance response->Comprising four components, respectively +.>、/>、/>、/>Corresponding to the relationship of electric field and magnetic field in different directions, respectively, i.e. horizontal component electric field +.>And magnetic field->Can be used to define four different impedances:
；
；
then calculate the tilt responseTilt response->Calculated by comparing the surface measured magnetic field components,、/>magnetic fields +.>Magnetic field components in vertical and horizontal directions:
；
similarly, it can be seen that the magnetic fieldVertical magnetic field component->Comprises a representation edge->Direction(s) (i.e. the directions of the eyes)>Vertical magnetic field of directional polarization +.>And->. Tilt response->It comprises two components, respectively +.>、，/>Is usually indicative of the tilt response +.>Component of direction, and->Representing the tilt response->The specific expression of the component of the direction is as follows:
；
in the foregoing embodiment, the determined objective function of the current inversion model is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation.
In one embodiment, constructing a pseudo-forward equation based on an objective function of a current inversion model includes:
(2.1.1) deflecting the current inversion model parameters by an objective function to obtain a gradient expression:
；
wherein the method comprises the steps ofTranspose of the sensitivity matrix;
(2.1.2) sensitivity matrixExpressed in transposed simplified terms as:
；
wherein the method comprises the steps ofIs a coefficient matrix->Matrix obtained by inversion and transposition +.>Is->Transposed matrix of>Expressed as coefficient matrix +.>Deviation of current inversion model parameters and current inversion model +.>Lower electric field response->Product of>Representation->Transposed matrix of>A linear process of interpolating from the field values on the simulated grid to the observation point positions and calculating a forward response;
(2.1.3) solvingVector->The product of (a), i.e
；
(2.1.4) orderCoefficient matrix using electric field control equation>Constructing an equation of pseudo forward>。
Then, based on the constructed pseudo-forward equation, solving the pseudo-forward electric field, and further solving to obtain an objective function of the current inversion model, wherein the method comprises the following steps:
(2.2.1) dividing the initial inversion model into a plurality of layers of subareas along the Z direction, and respectively constructing interpolation operators with different sparsity for each layer of subareas along the horizontal direction;
(2.2.2) synthesizing interpolation operators corresponding to all the layer sub-regions to obtain a total sparse sampling operator;
(2.2.3) multiplying the coefficient matrix and the right term of the forward equation constructed in the step (2.1.4) by the total sparse sampling operator to obtain a new sparse matrix and a corrected right term, introducing the new sparse matrix and the corrected right term of the forward equation into the forward equation constructed in the step (2.1.4), and solving to obtain a corrected forward electric field；
(2.2.4) based on the pseudo-forward electric fieldSolving->Vector->Is multiplied by (2) to obtain the gradient->And the objective function of the current inversion model +.>。
Wherein the corrected quasi-forward electric field is solved in the steps (2.2.1) to (2.2.3)The specific process of the three-dimensional geologic body is disclosed in the invention patent application with publication number of CN 113779818A and publication date of 2021, 12 and 10, and the electromagnetic field numerical simulation method, device, equipment and medium thereof are also adopted.
It will be appreciated that the present invention, through constant iterative updating,so that the obtained current inversion modelGradually approaching to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target, when the root mean square fitting difference RMS of the current model is calculated to be smaller than a preset threshold value or the iteration number of inversion reaches the set highest upper limit, the corresponding inversion model is the optimal final conductivity or resistivity structure model of the underground geologic body obtained by inversion, and the model can be very close to the actual conductivity or resistivity structure of the magnetotelluric three-dimensional exploration target.
In one embodiment, calculating the root mean square fitting difference RMS of the current inversion model includes:
(3.1) calculating an estimation error of the amplitude of the observed data based on the input observed data;
(3.1.1) a preset error percentage a%, wherein the value range of the a% is 1% -10%;
(3.1.2) if the input observed data is off-diagonal impedance data or full tensor impedance data, the estimated error of the observed data amplitude takes the full tensor impedanceImpedance on off-diagonal ∈ ->Multiplying by the error percentage a%; if the input observation data is the inclination data, the estimation error of the amplitude of the observation data is directly a%.
(3.2) calculating the root mean square fitting difference (RMS) of the current inversion model:
；
wherein the method comprises the steps ofNThe total number of observation points is indicated,indicate->Individual observationsPoint (S)>And->Respectively represent +.>Forward-modeling response of observation data at each observation point and current inversion model, +.>Is->Estimation errors of the amplitudes of the individual observations.
Further, whether inversion is finished is judged by calculating the root mean square fitting difference RMS of the current inversion model, and if the root mean square fitting difference RMS of the current inversion model is calculated to be smaller than a preset threshold (for example, 1.01 in an embodiment) or the inversion times are larger than 120 times, the inversion is finished.
If the inversion is not finished, updating an inversion model in the objective function, and adjusting the updating step length of the inversion model, wherein the method comprises the following steps:
(4.1) update step size of the inverse model Using line search；
Through line search formulaSolving the update step length of the inversion model>Wherein->And->The objective function calculated for the current inversion model and the inversion model at the currentStep size +.>Performing an updated inversion model calculated objective function, < ->Regarding +.>The rate of change of (2) is->The value of time (equal to the transpose of the gradient vector of the current iteration model multiplied by its search direction).
(4.2) calculating an update step length of the search direction;
updating step length of search direction,/>Gradient k-1 and transpose thereof, respectively,>the k-th gradient and its transpose;
(4.3) calculating a new search direction，/>,/>The search directions of the kth time and the k-1 time are respectively;
(4.4) updating the inversion modelAdjusting update step length of inversion modelWherein->Respectively the model parameters areIs a target function of (a).
The precision and efficiency of the three-dimensional magnetotelluric multi-resolution inversion method provided by the invention are checked below.
For the blind low-resistance ore body model shown in fig. 2, the model is taken as an initial inversion model, and the inversion region range is as follows:and->Directions are from-28 km to 28 km, and z directions are from-100 km to 62 km; wherein the air layer has a height of-100 km to 0 km and an electrical conductivity of +.>. The high-resistance abnormal body is positioned at the earth surface resistivity of +.>Size 4 km ×4 km ×0.8 km; the blind low-resistance ore body is approximately chair-shaped, and the resistivity is +.>The width of the low resistance body is 5.5 km, the top embedded depth is 1.6 km, and the bottom embedded depth is 4 km; the model area was split into 32×32×30 small cuboid units. Observation point: -5km to 5km, 16 lines, 16 stations per line, 256 stations in total; the number of frequencies is 8 +>The present embodiment performs parallel inversion on the above 8 frequencies.
The three-dimensional magnetotelluric multi-resolution inversion method provided by the invention is realized by MATLAB language programming, and a personal computer used for running a program is configured as follows: AMD Ryzen 7 4800H, main frequency of 2.9GHz, running memory of 16 GB. Fig. 3 is a schematic diagram of model slices obtained by inversion of the hidden low-resistance ore body model shown in fig. 2 based on different observation data by using the three-dimensional magnetotelluric multi-resolution inversion method provided by the invention. Wherein fig. 3 (a) is an inversion result on a regular grid using full tensor impedance data, fig. 3 (b) is an inversion result on a regular grid using full tensor impedance data+dip data, and fig. 3 (c) is an inversion result on a multi-resolution grid using full tensor impedance data+dip data. From fig. 3 (a) and fig. 3 (b), it can be seen that inversion of two data types of full tensor impedance data and full tensor impedance data+tilt data can both well recover the "chair" shaped blind ore body hidden under the high-resistance body, but the latter full tensor impedance data+tilt data can better define the bottom boundary of the "chair", which is more beneficial to our inversion interpretation, and as for the inversion result of fig. 3 (c) and the inversion result of fig. 3 (b), it is explained that the inversion effect of the invention is not affected by adopting the multi-resolution grid, and the inversion result has higher precision.
Fig. 4 is a comparison bar graph of inversion times and inversion time of the three-dimensional magnetotelluric multi-resolution inversion method based on different observation data for the hidden low-resistance ore body model shown in fig. 2, and clearly shows that the inversion times are reduced by adopting full tensor impedance data and inclination data for the hidden low-resistance ore body model researched based on the embodiment, so that the inversion time is shortened, in addition, inversion time of a normal grid can be further reduced by inversion of a multi-resolution grid, and the method for high-efficiency and high-precision inversion of the multi-electromagnetic data type multi-resolution grid has very strong practical significance.
In another embodiment, a three-dimensional magnetotelluric multi-resolution inversion apparatus is provided, comprising:
the system comprises a first module, a second module and a third module, wherein the first module is used for inputting observation data, frequency parameters and an initial inversion model, the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
the second module is used for constructing an electric field control equation according to the frequency parameters and the initial inversion model;
the third module is used for solving an electric field by utilizing the constructed electric field control equation, obtaining a magnetic field of the earth surface by utilizing electric field interpolation, and further obtaining forward modeling response corresponding to the initial inversion model;
a fourth module, configured to determine an objective function of the current inversion model, construct a forward-looking equation based on the objective function of the current inversion model, and solve a forward-looking electric field based on the constructed forward-looking equation, thereby solving the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and a fifth module, configured to calculate a root mean square fitting difference of the current inversion model obtained by solving, determine whether to stop inversion based on the root mean square fitting difference of the objective function or the current iteration number, if the inversion is not finished, update the inversion model in the objective function in the fourth module, adjust an update step length of the inversion model until the inversion is finished, and output a final inversion model.
The implementation method of each module and the construction of the model can be the method described in any of the foregoing embodiments, which is not described herein.
In another aspect, the present invention provides a computer device comprising a memory and a processor, the memory storing a computer program, the processor implementing the steps of the three-dimensional magnetotelluric multi-resolution inversion method provided in any of the embodiments described above when executing the computer program. The computer device may be a server. The computer device includes a processor, a memory, a network interface, and a database connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The database of the computer device is for storing sample data. The network interface of the computer device is used for communicating with an external terminal through a network connection.
In another aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the three-dimensional magnetotelluric multi-resolution inversion method provided in any of the above embodiments.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the various embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The invention is not a matter of the known technology.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (12)
1. The three-dimensional magnetotelluric multi-resolution inversion method is characterized by comprising the following steps of:
inputting observation data, frequency parameters and an initial inversion model, wherein the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
constructing an electric field control equation according to the frequency parameters and the initial inversion model;
solving an electric field by using the constructed electric field control equation, and obtaining a magnetic field of the earth surface by using electric field interpolation so as to obtain a forward response corresponding to the initial inversion model;
determining an objective function of a current inversion model, constructing a pseudo-forward equation based on the objective function of the current inversion model, solving a pseudo-forward electric field based on the constructed pseudo-forward equation, and further solving to obtain the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion model +.>For the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and calculating the root mean square fitting difference of the current inversion model obtained by solving, judging whether the inversion is stopped based on the root mean square fitting difference of the objective function or the current iteration times, if the inversion is not finished, updating the inversion model in the objective function, adjusting the updating step length of the inversion model until the inversion is finished, and outputting the final inversion model.
2. The method for three-dimensional magnetotelluric multi-resolution inversion of claim 1, wherein the three-dimensional cuboid grid model edge corresponding to the magnetotelluric three-dimensional exploration targetx、y、zAnd carrying out grid subdivision in the direction, and subdividing the three-dimensional cuboid grid cells into a plurality of three-dimensional cuboid grid cells to obtain grid subdivision parameters of a three-dimensional cuboid grid model corresponding to the magnetotelluric three-dimensional exploration target, wherein the conductivity or resistivity of each three-dimensional cuboid grid cell is a constant value, and the conductivity values or resistivity values of different three-dimensional cuboid grid cells are different.
3. The three-dimensional magnetotelluric multi-resolution inversion method as defined in claim 1 or 2, wherein the method is based on frequency parametersAnd initial inversion model->Constructing an electric field control equation->Wherein E represents the electric field to be solved, A is the coefficient matrix of the electric field control equation, ++>，/>Representing a rotation operator->Representing a double rotation operator->，/>Represents angular frequency by ∈>The data is obtained by the method,μrepresents permeability of 4π×10 -7 ，/>Representing an initial inversion model +.>Conductivity or resistivity of each three-dimensional rectangular grid cell; />The right term is composed of a field source and set inversion region boundary conditions.
4. The three-dimensional magnetotelluric multi-resolution inversion method as defined in claim 3, wherein the steps of solving the electric field E based on the construction of an electric field control equation, obtaining the magnetic field of the earth surface by utilizing E interpolation, and further obtaining the forward response corresponding to the initial inversion model comprise the following steps:
dividing the initial inversion model into a plurality of layers of subareas along the Z direction, and respectively constructing interpolation operators with different sparsity for each layer of subareas along the horizontal direction;
(1.2) synthesizing interpolation operators corresponding to all the layer sub-regions to obtain a total sparse sampling operator;
(1.3) multiplying the coefficient matrix A and the right-end term b of the constructed electric field control equation by the total sparse sampling operator to obtain a new sparse matrix A new And a corrected right-end term b new New sparse matrix A new And a corrected right-end term b new Carrying out solution to obtain a corrected electric field E in a constructed electric field control equation new ；
(1.4) by the formulaObtaining the magnetic field H of the earth surface new Further utilize electric field E new And magnetic field H new And obtaining forward response corresponding to the initial inversion model.
5. The three-dimensional magnetotelluric multi-resolution inversion method of claim 1, 2 or 4, wherein constructing the pseudo-forward equation based on the objective function of the current inversion model comprises:
(2.1.1) deflecting the current inversion model parameters by an objective function to obtain a gradient expression:
；
wherein the method comprises the steps ofTranspose of the sensitivity matrix;
(2.1.2) sensitivity matrixExpressed in transposed simplified terms as:
；
wherein the method comprises the steps ofIs a coefficient matrix->Matrix obtained by inversion and transposition +.>Is->Transposed matrix of>Expressed as coefficient matrix +.>Deviation of current inversion model parameters and current inversion model +.>Lower electric field response->Product of>Representation->Transposed matrix of>Representing interpolation from field values on a simulated grid toObserving the position of the point and obtaining a linear process of forward response;
(2.1.3) solvingVector->The product of (a), i.e
；
(2.1.4) order，E 0 Representing a quasi-forward electric field, using a coefficient matrix of an electric field control equationConstructing an equation of pseudo forward>。
6. The three-dimensional magnetotelluric multi-resolution inversion method of claim 5, characterized in that solving the quasi-forward electric field based on the constructed quasi-forward equation comprises:
(2.2.1) dividing the initial inversion model into a plurality of layers of subareas along the Z direction, and respectively constructing interpolation operators with different sparsity for each layer of subareas along the horizontal direction;
(2.2.2) synthesizing interpolation operators corresponding to all the layer sub-regions to obtain a total sparse sampling operator;
(2.2.3) multiplying the coefficient matrix and the right term of the forward equation constructed in the step (2.1.4) by the total sparse sampling operator to obtain a new sparse matrix and a corrected right term, introducing the new sparse matrix and the corrected right term of the forward equation into the forward equation constructed in the step (2.1.4), and solving to obtain a corrected forward electric fieldE 0 ；
(2.2.4) based on the pseudo-forward electric field E 0 Solving forVector->And then obtain the gradientAnd objective function->。
7. The three-dimensional magnetotelluric multi-resolution inversion method of claim 6 wherein calculating the root mean square fitting difference RMS of the current inversion model comprises:
(3.1) calculating an estimation error of the amplitude of the observed data based on the input observed data;
(3.1.1) a preset error percentage a%, wherein the value range of the a% is 1% -10%;
(3.1.2) if the input observed data is off-diagonal impedance data or full tensor impedance data, taking the estimated error of the amplitude of the observed data as the element on the off-diagonal of the full tensor impedance multiplied by the error percentage a%; if the input observation data is the inclination data, directly taking a% of the estimation error of the amplitude of the observation data;
(3.2) calculating the root mean square fitting difference (RMS) of the current inversion model:
；
wherein the method comprises the steps ofNThe total number of observation points is indicated,indicate->The observation points are (I)>And->Respectively represent the firstiForward-modeling response of observation data at each observation point and current inversion model, +.>Is->Estimation errors of the amplitudes of the individual observations.
8. The three-dimensional magnetotelluric multi-resolution inversion method of claim 6, characterized in that the method for judging whether the inversion is stopped is: if the calculated root mean square fitting difference RMS of the current inversion model is smaller than a preset threshold value or the current inversion times are larger than 120 times, the inversion is finished.
9. The method of three-dimensional magnetotelluric multi-resolution inversion of claim 6, wherein if the inversion is not finished, updating the inversion model in the objective function, and adjusting the update step size of the inversion model, the method comprising:
(4.1) update step size of the inverse model Using line search；
Through line search formulaSolving the update step length of the inversion model>Wherein->And->The objective function calculated for the current inversion model and the step length +.>Performing an updated inversion model calculated objective function, < ->Regarding +.>The rate of change of (2) is->The value is taken at the time;
(4.2) calculating an update step length of the search direction;
updating step length of search direction, />Gradient k-1 and transpose thereof, respectively,>the k-th gradient and its transpose;
(4.3) calculating a new search direction，/>The search directions of the kth time and the k-1 time are respectively;
(4.4) updating the inversion modelAdjusting update step length of inversion modelWherein->Respectively the model parameters areIs a target function of (a).
10. A three-dimensional magnetotelluric multi-resolution inversion apparatus, comprising:
the system comprises a first module, a second module and a third module, wherein the first module is used for inputting observation data, frequency parameters and an initial inversion model, the observation data are off-diagonal impedance data or full tensor impedance data or inclination data, and the initial inversion model comprises a three-dimensional cuboid grid model corresponding to a magnetotelluric three-dimensional exploration target and conductivity or resistivity of each three-dimensional cuboid grid unit in the three-dimensional cuboid grid model;
the second module is used for constructing an electric field control equation according to the frequency parameters and the initial inversion model;
the third module is used for solving an electric field by utilizing the constructed electric field control equation, obtaining a magnetic field of the earth surface by utilizing electric field interpolation, and further obtaining forward modeling response corresponding to the initial inversion model;
a fourth module, configured to determine an objective function of the current inversion model, construct a forward-looking equation based on the objective function of the current inversion model, and solve a forward-looking electric field based on the constructed forward-looking equation, thereby solving the objective function of the current inversion model; wherein the objective function is expressed as:
；
wherein,the inversion model is a conductivity or resistivity structural model of a magnetotelluric three-dimensional exploration target>For observing data, ++>Forward response for current inversion model, +.>For the initial inversion of the model,for the data covariance matrix,>is a model covariance matrix; />Is a regularization factor; />Is a transpose operation;
and a fifth module, configured to calculate a root mean square fitting difference of the current inversion model obtained by solving, determine whether to stop inversion based on the root mean square fitting difference of the objective function or the current iteration number, if the inversion is not finished, update the inversion model in the objective function in the fourth module, adjust an update step length of the inversion model until the inversion is finished, and output a final inversion model.
11. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the three-dimensional magnetotelluric multi-resolution inversion method of claim 1 when executing the computer program.
12. A computer readable storage medium having stored thereon a computer program, which when executed by a processor performs the steps of the three-dimensional magnetotelluric multi-resolution inversion method as defined in claim 1.
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