CN113514899A - Self-adaptive subdivision inversion method for gravity gradient - Google Patents
Self-adaptive subdivision inversion method for gravity gradient Download PDFInfo
- Publication number
- CN113514899A CN113514899A CN202110786032.9A CN202110786032A CN113514899A CN 113514899 A CN113514899 A CN 113514899A CN 202110786032 A CN202110786032 A CN 202110786032A CN 113514899 A CN113514899 A CN 113514899A
- Authority
- CN
- China
- Prior art keywords
- subdivision
- inversion
- gravity gradient
- tetrahedron
- global
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 230000005484 gravity Effects 0.000 title claims abstract description 38
- 238000000034 method Methods 0.000 title claims abstract description 37
- 239000011159 matrix material Substances 0.000 claims abstract description 12
- 230000002159 abnormal effect Effects 0.000 claims abstract description 8
- 230000003044 adaptive effect Effects 0.000 claims description 5
- 230000002500 effect on skin Effects 0.000 claims description 4
- 238000013461 design Methods 0.000 claims description 3
- 230000001788 irregular Effects 0.000 abstract description 4
- 230000000704 physical effect Effects 0.000 abstract description 4
- 230000006870 function Effects 0.000 description 17
- 238000011161 development Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 229910052500 inorganic mineral Inorganic materials 0.000 description 3
- 239000011707 mineral Substances 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
Abstract
The invention discloses a gravity gradient self-adaptive subdivision inversion method, which comprises the following processes: acquiring gravity gradient abnormal data or gravity gradient abnormal data of the performing model; adopting an inclination angle boundary identification method to divide a tetrahedron within the range that the result is more than or equal to 0; and constructing a non-global kernel function matrix, and realizing non-global tetrahedral subdivision inversion calculation to obtain a spatial density distribution map. The method comprises the steps of delineating the range of a target ore body through boundary identification, and carrying out mesh generation in the range; non-global tetrahedron subdivision is adopted to fit the undulating terrain and irregular geologic bodies, so that the terrain shape is more fit; compared with the traditional physical property inversion method, the method can reduce the subdivision grids by reducing the subdivision range in the same region so as to achieve the purposes of accelerating the inversion speed and improving the inversion precision, and simultaneously reduce the requirements on the performance of a computer.
Description
Technical Field
The invention belongs to the technical field of geophysics, and particularly relates to a gravity gradient self-adaptive subdivision inversion method.
Background
In recent years, with the development of modern technology level, geophysical instruments and testing technology, the gravity gradient measurement method is widely applied. Compared with the traditional gravity anomaly data, the gravity gradient data is more sensitive to anomalies caused by shallow layer anomalies and micro density differences, has higher precision, contains more geological information, and has better application effect on boundary and shape identification of the geological body.
The mineral exploitation depth of China is about 500m, the current situation of mineral resources is in short, in order to realize the sustainable development of the mineral resources and meet the requirements of social and economic development, the inversion efficiency and precision are improved, and the ore finding speed is accelerated.
The underground contains a large amount of geological information, in order to make the inversion information more accurate, the subdivision grid can be reduced, but the inversion efficiency is reduced, and the CPU memory is increased.
Disclosure of Invention
The invention provides a gravity gradient self-adaptive subdivision inversion method, which is characterized in that mesh subdivision is carried out in a boundary identification range, so that the number of subdivision meshes can be reduced, and subdivision areas are divided in ore body boundaries; and in consideration of the actual geological condition, the invention adopts the tetrahedron subdivision to fit the undulating terrain and irregular geologic bodies.
Specifically, the invention is realized by the following technical scheme:
the self-adaptive subdivision inversion method of the gravity gradient is provided, and comprises the following steps:
step 1: acquiring gravity gradient abnormal data or gravity gradient abnormal data of the performing model;
step 2: adopting an inclination angle boundary identification method to divide a tetrahedron within the range that the result is more than or equal to 0;
and step 3: and constructing a non-global kernel function matrix, and realizing non-global tetrahedral subdivision inversion calculation to obtain a spatial density distribution map.
As a further explanation of the present invention, the tilt angle boundary identification method has the following formula:
in the formula:
wherein g iszIs a gravity gradient anomaly.
As a further explanation of the present invention, the process of constructing the non-global kernel function matrix specifically includes:
applying an arbitrary polyhedral gravity anomaly expression to the tetrahedron, arbitrary observation points (x)n,yn,zn) The formula of the gravity anomaly calculation is as follows:
the gravity gradient is the first vertical derivative of gravity anomaly:
wherein: g is a kernel function matrix; gamma is universal gravitation constant 6.672 x 10-11m3/(kg·s2) (ii) a ρ is the tetrahedral density; phi is aiThe included angle between the ith triangle of the tetrahedron and the z axis is shown; j. the design is a squarej,iThe following formula is obtained:
wherein: i is the serial number of the triangle, and j is the serial number of the edge in the ith triangle;
θiis the included angle between the projection of the ith surface normal of the tetrahedron in the horizontal direction and the x direction, wherein theta is more than or equal to 0i≤2π，0≤φi≤π。
As a further explanation of the present invention, when non-global tetrahedron subdivision inversion calculation is implemented, the solved equation solution is the solution of the underdetermined equation, and when the underdetermined equation is solved, the following objective function is constructed:
m is a vector of density parameters; m isrefIs a reference model, generally having a value of 0; lambda is a regularization parameter and plays a role in balancing a data fitting function and a weight function; wdIs a data weighting matrix;
the method is depth weight and is used for constraining an inversion result to enable the result to be more consistent with the fact that the skin effect is overcome, and weight related to the volume is added in the tetrahedral subdivision inversion:
v represents the volume of a tetrahedron, z0The depth weight function is matched with the kernel function under the observation point, alpha is an empirical value, usually 0.5, and beta is an empirical value.
Compared with the prior art, the invention has the following beneficial technical effects:
the method comprises the steps of delineating the range of a target ore body through boundary identification, and carrying out mesh generation in the range; non-global tetrahedron subdivision is adopted to fit the undulating terrain and irregular geologic bodies, so that the terrain shape is more fit; compared with the traditional physical property inversion method, the method can reduce the subdivision grids by reducing the subdivision range in the same region so as to achieve the purposes of accelerating the inversion speed and improving the inversion precision, and simultaneously reduce the requirements on the performance of a computer.
Drawings
FIG. 1 is a flow chart of an adaptive subdivision inversion method of gravity gradient provided by the present invention;
FIG. 2 is a schematic diagram of a three-dimensional tetrahedral subdivision;
FIG. 3 is a graph of the result of a conventional global tetrahedron subdivision inversion;
FIG. 4 is a non-global tetrahedral subdivision inversion result diagram provided by the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a detailed description of the present invention will be given below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
Fig. 1 is a flowchart of an adaptive subdivision inversion method for gravity gradient, which includes the following steps:
step 1: acquiring gravity gradient abnormal data or gravity gradient abnormal data of the performing model;
in the actual measurement process, the measured data is larger than the underground geologic body range, so that during inversion, the geologic body subdivision range is defined by boundary identification, and grid subdivision is performed in the range of the boundary identification result being more than or equal to 0, so that the inversion efficiency and the inversion accuracy can be effectively improved.
Step 2: and (3) performing tetrahedron subdivision in a range that the result is more than or equal to 0 by adopting an inclination angle boundary identification method:
the boundary identification method adopts a tilt angle method, and the formula is as follows:
in the formula:
wherein g iszIs a gravity gradient anomaly.
And step 3: constructing a non-global kernel function matrix, and realizing non-global tetrahedron subdivision inversion calculation to obtain a spatial density distribution diagram:
aiming at the non-regularity of the actual geologic body, better fitting is achieved by using a tetrahedron subdivision; okabe (1979) derived an arbitrary polyhedral gravity anomaly expression, which was applied to tetrahedrons, arbitrary observation points (x)n,yn,zn) The formula of the gravity anomaly calculation is as follows:
the gravity gradient is the first vertical derivative of gravity anomaly:
wherein: g is a kernel function matrix; gamma is universal gravitation constant 6.672 x 10-11m3/(kg·s2) (ii) a ρ is the tetrahedral density; phi is aiThe included angle between the ith triangle of the tetrahedron and the z axis is shown; j. the design is a squarej,iThe following formula is obtained:
wherein: i is the triangle sequence number and j is the edge sequence number in the ith triangle.
θiThe included angle between the projection of the ith plane normal direction of the tetrahedron in the horizontal direction and the x direction is noted: in the formula, theta is more than or equal to 0i≤2π，0≤φi≤π；
The inversion is carried out on the density distribution of the underground space, and the equation solution is the solution of an underdetermined equation because the number of observation points is far less than the number of underground subdivision blocks. To solve the underdetermined equation, the following objective function is constructed:
m is a vector of density parameters; m isrefIs a reference model, generally having a value of 0; lambda is a regularization parameter and plays a role in balancing a data fitting function and a weight function; wdIs a data weighting matrix;
for depth weight, the method is used for constraining the inversion result to make the result more consistent with the actual skin effect to overcome the skin effect, and because the volume of each tetrahedron is different in size, and the size of the volume can influence the function of the depth weight, the weight related to the volume is added in the tetrahedron subdivision inversion:
v represents the volume of a tetrahedron, z0The depth weight function is matched with the kernel function under the observation point, alpha is an empirical value, usually 0.5, and beta is an empirical value.
The following table shows the running time and the memory occupied by the same software of the same computer for inversion when the same data is inverted by adopting the same inversion accuracy (the same sampling point distance, the same mapping accuracy and the same weighting function) compared with the traditional physical property inversion method.
| Run time | Occupying memory | |
| The invention | 270.56s | 62978KB |
| Conventional methods | 747.45s | 165539KB |
The method comprises the steps of delineating the range of a target ore body through boundary identification, and carrying out mesh generation in the range; non-global tetrahedron subdivision is adopted to fit the undulating terrain and irregular geologic bodies, so that the terrain shape is more fit; compared with the traditional physical property inversion method, the method can reduce the subdivision grids by reducing the subdivision range in the same region so as to achieve the purposes of accelerating the inversion speed and improving the inversion precision, and simultaneously reduce the requirements on the performance of a computer.
Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention is described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims (4)
1. A gravity gradient self-adaptive subdivision inversion method is characterized by comprising the following steps:
step 1: acquiring gravity gradient abnormal data or gravity gradient abnormal data of the performing model;
step 2: adopting an inclination angle boundary identification method to divide a tetrahedron within the range that the result is more than or equal to 0;
and step 3: and constructing a non-global kernel function matrix, and realizing non-global tetrahedral subdivision inversion calculation to obtain a spatial density distribution map.
2. The adaptive subdivision inversion method of gravity gradients of claim 1,
the formula of the inclination angle boundary identification method is as follows:
in the formula:
wherein g iszIs a gravity gradient anomaly.
3. The gravity gradient adaptive subdivision inversion method according to claim 1, wherein the process of constructing the non-global kernel function matrix specifically includes:
applying an arbitrary polyhedral gravity anomaly expression to the tetrahedron, arbitrary observation points (x)n,yn,zn) The formula of the gravity anomaly calculation is as follows:
the gravity gradient is the first vertical derivative of gravity anomaly:
wherein: g is a kernel function matrix; gamma is universal gravitation constant 6.672 x 10-11m3/(kg·s2) (ii) a ρ is the tetrahedral density; phi is aiThe included angle between the ith triangle of the tetrahedron and the z axis is shown; j. the design is a squarej,iThe following formula is obtained:
wherein: i is the serial number of the triangle, and j is the serial number of the edge in the ith triangle;
θiis the included angle between the projection of the ith surface normal of the tetrahedron in the horizontal direction and the x direction, wherein theta is more than or equal to 0i≤2π，0≤φi≤π。
4. The gravity gradient adaptive subdivision inversion method of claim 1, wherein in the implementation of the non-global tetrahedral subdivision inversion calculation, the solved equation is solved as a solution of underdetermined equations, and in the solving of the underdetermined equations, the following objective function is constructed:
m is a vector of density parameters; m isrefIs a reference model, generally having a value of 0; lambda is a regularization parameter and plays a role in balancing a data fitting function and a weight function; wdIs a data weighting matrix;
the method is depth weight and is used for constraining an inversion result to enable the result to be more consistent with the fact that the skin effect is overcome, and weight related to the volume is added in the tetrahedral subdivision inversion:
v represents the volume of a tetrahedron, z0The depth weight function is matched with the kernel function under the observation point, alpha is an empirical value, usually 0.5, and beta is an empirical value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110786032.9A CN113514899A (en) | 2021-07-12 | 2021-07-12 | Self-adaptive subdivision inversion method for gravity gradient |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110786032.9A CN113514899A (en) | 2021-07-12 | 2021-07-12 | Self-adaptive subdivision inversion method for gravity gradient |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN113514899A true CN113514899A (en) | 2021-10-19 |
Family
ID=78067523
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110786032.9A Pending CN113514899A (en) | 2021-07-12 | 2021-07-12 | Self-adaptive subdivision inversion method for gravity gradient |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113514899A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113806686A (en) * | 2021-11-19 | 2021-12-17 | 中南大学 | Method, device and equipment for rapidly calculating gravity gradient of large-scale complex geologic body |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017025801A1 (en) * | 2015-08-13 | 2017-02-16 | Cgg Services Sa | System and method for gravity and/or gravity gradient terrain corrections |
| CN110286416A (en) * | 2019-05-13 | 2019-09-27 | 吉林大学 | A kind of fast two-dimensional inversion of Density method based on physical property function |
| CN110333548A (en) * | 2019-07-27 | 2019-10-15 | 吉林大学 | A kind of high-resolution inversion of Density method based on the abnormal weight function of normalization |
-
2021
- 2021-07-12 CN CN202110786032.9A patent/CN113514899A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2017025801A1 (en) * | 2015-08-13 | 2017-02-16 | Cgg Services Sa | System and method for gravity and/or gravity gradient terrain corrections |
| CN110286416A (en) * | 2019-05-13 | 2019-09-27 | 吉林大学 | A kind of fast two-dimensional inversion of Density method based on physical property function |
| CN110333548A (en) * | 2019-07-27 | 2019-10-15 | 吉林大学 | A kind of high-resolution inversion of Density method based on the abnormal weight function of normalization |
Non-Patent Citations (3)
| Title |
|---|
| SIYUAN SUN,ET AL.: "3D Gravity Inversion on Unstructured Grids", 《APPLIED SCIENCES》 * |
| 曾思红: "重力梯度张量正演研究及边界提取", 《中国优秀博硕士学位论文全文数据库(硕士)基础科学辑》 * |
| 黄天统等: "基于非结构化网格的重力梯度张量反演", 《物探与化探》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113806686A (en) * | 2021-11-19 | 2021-12-17 | 中南大学 | Method, device and equipment for rapidly calculating gravity gradient of large-scale complex geologic body |
| CN113806686B (en) * | 2021-11-19 | 2022-02-08 | 中南大学 | Method, device and equipment for rapidly calculating gravity gradient of large-scale complex geologic body |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106777598B (en) | Numerical simulation method for magnetic field gradient tensor of complex magnetic body with arbitrary magnetic susceptibility distribution | |
| CN106646645B (en) | A kind of gravity forward modeling accelerated method | |
| CN112147709B (en) | Gravity gradient data three-dimensional inversion method based on partial smoothness constraint | |
| CN110045432A (en) | Gravitational field forward modeling method and 3-d inversion method under spherical coordinate system based on 3D-GLQ | |
| CN103256914B (en) | A kind of method and system calculating silt arrester inundated area based on DEM | |
| CN109254327B (en) | Exploration method and exploration system of three-dimensional ferromagnetic body | |
| CN111856598B (en) | Magnetic measurement data multilayer equivalent source upper extension and lower extension method | |
| CN113504575B (en) | Joint inversion method based on weight intersection and multiple intersection gradient constraints | |
| CN108984939A (en) | Three-dimensional Gravity field of force forward modeling method based on 3D Gauss-FFT | |
| CN113514899A (en) | Self-adaptive subdivision inversion method for gravity gradient | |
| Wang et al. | Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data | |
| CN109902315B (en) | Method for delineating deep boundary of hidden granite rock mass | |
| CN107748834B (en) | A kind of quick, high resolution numerical simulation method calculating fluctuating inspection surface magnetic field | |
| CN108416082B (en) | Singularity-free calculation method for external disturbance gravity horizontal component of sea area flow point | |
| CN114740540A (en) | Method and system for constructing magnetic anomaly map of ridge region in ocean based on direction constraint | |
| CN108508479B (en) | Method for inverting three-dimensional gravity-magnetic data of open-ground well in cooperation with target position | |
| CN107239559B (en) | Method for calculating position of space moving target based on vector grid | |
| CN115437782A (en) | Bellhop3D parallel implementation method of underwater three-dimensional sound field model based on domestic many-core supercomputing | |
| CN112748471B (en) | Gravity-magnetic data continuation and conversion method of unstructured equivalent source | |
| CN110287620B (en) | Spherical coordinate system density interface forward modeling method and system suitable for earth surface observation surface | |
| CN106611281A (en) | Algorithm based on two-dimensional plane domain distance for solving job shop scheduling problem | |
| CN117688785B (en) | Full tensor gravity gradient data inversion method based on planting thought | |
| CN116184507B (en) | Calculation method and device for thickness of hidden volcanic rock and readable storage medium | |
| CN116794735B (en) | Aviation magnetic vector gradient data equivalent source multi-component joint denoising method and device | |
| Huang | An improved voxel filtering method based on octree structure and point density |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20211019 |
|
| RJ01 | Rejection of invention patent application after publication |