CN105678843A - Local quick updating method of mixed voxel geological body model - Google Patents

Local quick updating method of mixed voxel geological body model Download PDF

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CN105678843A
CN105678843A CN201610018808.1A CN201610018808A CN105678843A CN 105678843 A CN105678843 A CN 105678843A CN 201610018808 A CN201610018808 A CN 201610018808A CN 105678843 A CN105678843 A CN 105678843A
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model
volume elements
structure body
local
geological structure
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CN105678843B (en
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田宜平
吴冲龙
刘刚
张志庭
李新川
何珍文
张夏林
翁正平
徐凯
孔春芳
李章林
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Wuhan Dida Kundi Science & Technology Co Ltd
China University of Geosciences
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Wuhan Dida Kundi Science & Technology Co Ltd
China University of Geosciences
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    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00Three dimensional [3D] modelling, e.g. data description of 3D objects
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Abstract

The invention discloses a local quick updating method of a mixed voxel geological body model. Firstly, the method builds an overall mixed voxel geological body model, which is an IHG-TIN model (Irregular Hexahedron Grid and Triangle Irregular Network). When the mixed voxel geological body model needs to be updated because of a local new bore hole or other local exploration data, the method only needs to build a local mixed voxel geological body model on the same local scale. A new voxel is used to replace a voxel at the same position of the original model locally, then a new layer model is extracted from the updated mixed voxel geological body model, and the topological relation and geological properties of the layer model are updated, so that quick local dynamic updating is achieved. The original model does not need to be rebuilt from the beginning, and thus the dynamic updating efficiency and model precision of geological bodies can be improved.

Description

A kind of mixing volume elements model of geological structure body local Rapid Updating
Technical field
The application relates to geological exploration field, particularly relates to a kind of mixing volume elements model of geological structure body local Rapid Updating.
Background technology
External three-dimensional geological modeling originates in 20 century 70s.
Wherein, relatively more influential have:
J.L.Mallet (1989) professor of France Nancy. university proposes " discrete smooth interpolation method " technology, a three-dimensional geological modeling software based on this technological development, and its modeling approach substantially belongs to aspect modeling.
Subsequently, Bezier-NURBS (Bezier-non-uniform rational B-spline) compound curved surface of DeKemp (1999) comes matching three dimensional structure face, Courrioux etc. (2001) propose Voronoi (voronoi she) figure and build geological object etc. and broadly fall into the aspect modeling of same layer homogenizing, all can not express the fine attribute that each point is heterogeneous.
Recently,F. the geologic body the solid unit modeling of (2013) research Aeromagnetic data is waited, TIN model conversion is become the integrated model of geologic process of three-dimensional grid by WatsonCarl etc. (2015) research, and the change of geological property, data type etc. is considered in geological modeling by Hoyer etc. (2015).
This shows that Geologic modeling develops to fine modeling direction.
So far, abroad have been developed for some three-dimensional geological modeling softwares, but these modeling methods and modeling software still have difficulties in complex geologic body fine modeling, dynamic renewal.
The research of domestic three-dimensional geological modeling starts from the nineties in 20th century. Wu Chonglong etc. (1996) rate develops Three-Dimensional Basin modeling software first with IDL, and hereafter three-dimensional modeling research gradually spreads out. Wherein, the representative based on boring modeling method has: Hou Enke (2002), Wu Lixin (2004), Wuqiang County (2004) etc. propose generalized tri-prism (GTP) model, develop correlation modeling software. This modeling approach has the drawback that and cannot process the situation with complicated structure face.
Typical Representative based on aspect modeling method has: the Hydraulic and Hydro-Power Engineering geology 3 d modeling system that Zhong Denghua etc. (2005) develop; Bend the red firm grade (2008) the three-dimensional geological model rapid build based on intersection folded profile;Old build the big medium scale three-dimensional geological modeling method in equality (2014) emphasis metallogenic belt. This modeling approach is beyond expression the anisotropism within same layer. Recently, He Zhenwen etc. (2012), Weng Zhengping (2013) have carried out the research of the aspects such as Dynamic and Multi dimensional modeling, complicated geological body three-dimensional models rapid build and update method respectively. Show that domestic Geologic modeling is developing to fine modeling, dynamic more new direction.
Although three-dimensional geological object model achieves tremendous development, also some research worker has attempted the research that geologic body dynamically updates, these update methods are all based on the thinking from FEM layer model to volume element model, there is topological relation and attribute information during model modification simultaneously and update the problems such as difficult, efficiency is low, sometimes must push over block mold all to rebuild, it is impossible to realize local and quickly dynamically update.
Summary of the invention
Invention provides a kind of mixing volume elements model of geological structure body local Rapid Updating, the technical problem locally quickly dynamically updated to solve existing modeling not realize.
For solving above-mentioned technical problem, the invention provides a kind of mixing volume elements model of geological structure body local Rapid Updating, described method includes:
Utilize former data construct entirety mixing volume elements model of geological structure body;
Utilize the local change data construct in described former data and the local mixing volume elements model of geological structure body of described overall mixing volume elements model of geological structure body same scale;
Utilize the volume elements in described local mixing volume elements model of geological structure body to replace and update the volume elements of relevant position in described overall mixing volume elements model of geological structure body;
Entirety after updating mixes the TIN TIN FEM layer model extracted volume elements model of geological structure body after updating.
Preferably, described utilize former data construct entirety mixing volume elements model of geological structure body before, described method also includes:
Described former data are carried out pretreatment.
Preferably, described utilize former data construct entirety mixing volume elements model of geological structure body, specifically include:
The TIN TIN FEM layer model that described former data carry out former data is utilized to build;
TIN FEM layer model based on described former data builds described overall mixing volume elements model of geological structure body.
Preferably, described based on the described overall mixing volume elements model of geological structure body of described TIN FEM layer model structure, specifically include:
The TIN FEM layer model utilizing described former data construct retrains, and the space that FEM layer model is defined carries out the subdivision of Irregular hexahedron, builds the mixing volume elements model of geological structure body risen and fallen along various FEM layer models;
Utilize model attributes instrument that the described mixing volume elements model of geological structure body risen and fallen along various FEM layer models is carried out assignment, complete the structure of described overall mixing volume elements model of geological structure body.
Preferably, the local mixing volume elements model of geological structure body of the described local change data construct utilized in described former data and described overall mixing volume elements model of geological structure body same scale, specifically include:
Utilize described local change data to carry out local and change the TIN FEM layer model structure of data;
The TIN FEM layer model utilizing described local change data builds described local mixing volume elements model of geological structure body.
Preferably, the described TIN FEM layer model utilizing described local change data builds described local mixing volume elements model of geological structure body, specifically includes:
The TIN FEM layer model utilizing described local change data construct retrains, and the space that local FEM layer model is defined carries out the subdivision of Irregular hexahedron, builds the local mixing volume elements model of geological structure body risen and fallen along various FEM layer models;
Utilize model attributes instrument that the described mixing volume elements model of geological structure body risen and fallen along various FEM layer models is carried out assignment, complete the structure of described local mixing volume elements model of geological structure body.
By one or more technical scheme of the present invention, the invention have the advantages that or advantage:
The invention discloses a kind of mixing volume elements model of geological structure body local Rapid Updating, first complete the structure of overall mixing volume elements model of geological structure body. If local has new boring or other survey data to need to update mixing volume elements model of geological structure body, only need to build the local local mixing volume elements model of geological structure body with yardstick, new volume elements local is utilized to replace the volume elements of master mould same position, the TIN FEM layer model after updating is extracted again from the mixing volume elements model of geological structure body after renewal, complete the topological relation of TIN FEM layer model and the renewal of geological property, update thus realizing quick local dynamic station, reconstruction need not all be shifted onto by original model, it is possible to improves geologic body and dynamically updates efficiency and model of geological structure body precision.
Accompanying drawing explanation
Fig. 1 is IHG-TIN grid plan schematic diagram in the embodiment of the present invention;
Fig. 2 is the implementation process figure mixing volume elements model of geological structure body local Rapid Updating in the embodiment of the present invention;
Fig. 3 is the Organization Chart that the present invention mixes volume elements model of geological structure body local Rapid Updating.
Detailed description of the invention
The method of the present invention, starts with from original geologic information data such as () boring, section, attributes, first in conjunction with Irregular hexahedron volume elements subdivision and geologic body model attributes, completes the structure of geologic body entirety mixing volume elements model of geological structure body. If local has new boring or other survey data to need to update model of geological structure body, only need to build the local mixing volume elements model of geological structure body with yardstick by above-mentioned steps, the volume elements block of master mould same position is replaced in the volume elements local utilizing local mixing volume elements model of geological structure body, the TIN FEM layer model after updating is extracted again from the mixing volume elements model of geological structure body after renewal, completing the renewal of the topological sum geological property of TIN FEM layer model, updating thus realizing quick local dynamic station. The topological relation and the attribute that the method overcome new surface model in conventional update method from face to body update difficulty, it is to avoid surface model and body Model shift reconstruction onto, improve modeling efficiency and precision.
In order to make the application the technical staff in the technical field be more clearly understood that the application, below in conjunction with accompanying drawing, by specific embodiment, technical scheme is described in detail.
Present invention utilizes mixing volume elements model of geological structure body IHG-TIN model (that is: Irregular hexahedron grid (IrregularHexahedronGrid)-TIN (TriangleIrregularNetwork) model), FEM layer model (FEM layer model can Seamless integration-take topological relation, geology into account semantic) and volume element model (volume element model can finely express attribute) can be unified by it. And this model can express the multiple dimensioned geological model of storage further.
In this mixing volume elements model of geological structure body (IHG-TIN model), TIN TIN is used for describing the various stratal surfaces of storage and structure face, Irregular hexahedron grid IHG is different from cube grid, each hexahedral element can be irregular, and four points on hexahedral each can be non-coplanar. What this was just free to the fluctuating along stratum and tomography walks always subdivision geologic body, generates irregular hexahedral mesh.
Stratal surface and fault plane is just represented in the part face of the hexahedral element lattice adjacent with stratal surface and fault plane, just FEM layer model and volume element model are coupled, IGH-TIN as shown in Figure 1 mixes volume elements grid schematic diagram, lines thick in figure are fault lines, and mixing volume elements carries out element subdivision along tomography.Follow-up from mixing volume elements model of geological structure body extract layer surface model become easier to, only need to search for out by the quadrilateral surface of hexahedral element lattice part adjacent to stratal surface and fault plane, convert two trianglees to, constitute TIN, get final product the extraction (comprising stratal surface, structure face, Stratigraphic Time attribute, contact relation etc.) of complete layer surface model.
The tactical rule of the L × M × N of cube grid followed by IHG-TIN model in logical structure, namely L cell is divided in the X direction, divide M cell in the Y direction, divide N number of cell in z-direction, in special places such as borders, Irregular hexahedron can be degenerated to various form by the coincidence of node, but keeps the tactical rule of grid. This mixing volume elements model of geological structure body, due to the FEM layer model with spatial topotaxy and the irregular body meta-model comprising geological property, can express the geologic body refined model of Multi hiberarchy and multi scale, it is also possible to supports follow-up various specialty analysis.
Referring to Fig. 2, the technical solution adopted in the present invention is:
S1, utilizes former data construct entirety mixing volume elements model of geological structure body.
First, from original geologic information data such as () boring, section, attributes, acquisition can be used for the former data modeled, then former data be carried out pretreatment. For borehole data, first input borehole data is selected and projects. When choosing boring, will considering the comprehensive of drill hole information and two principles of uniformity of borehole space distribution, the boring chosen projects according to aperture coordinate and strata division attribute. Then the section of input is selected and projects, note the unified conversion of coordinate and the correct conversion of profile azimuth.
Then, the TIN FEM layer model (TIN FEM layer model) that described former data carry out former data is utilized to build.
Specifically, after former data are carried out pretreatment, utilize knowledge reasoning to judge point set and the lines collection in each section or the upper corresponding same stratal surface of boring or structure face, utilize point set and lines collection to be completed each stratal surface or the TIN model construction in structure face by space interpolation, improve the contact relation modified between each surface model as necessary by interactive editor. Build rear TIN FEM layer model and just inherited the geological property on corresponding boring or section, complete the expression that geology is semantic.
Finally, described overall mixing volume elements model of geological structure body is built based on the TIN FEM layer model of described former data.
After the TIN FEM layer model building former data, complete the structure of overall mixing volume elements model of geological structure body in combinations with Irregular hexahedron volume elements subdivision and model attributes instrument.
Specifically, build entirety mixing volume elements model of geological structure body and be divided into two parts: first, by the subdivision of Irregular hexahedron, the TIN FEM layer model utilizing former data retrains, the space that FEM layer model is defined is carried out the subdivision of Irregular hexahedron, builds the mixing volume elements model of geological structure body risen and fallen along various FEM layer models. Second, utilize model attributes instrument to complete the structure of overall mixing volume elements model of geological structure body. That is: utilize the method such as Krieger or distance power inverse ratio that various attribute informations (such as: grade, pressure etc.) are interpolated, and give corresponding property value by each Irregular hexahedron volume elements, complete the structure of overall mixing volume elements model of geological structure body.
If having the needs of local multi-scale Modeling further, it is possible to entirety is mixed the volume elements in volume elements model of geological structure body and carries out local fine subdivision, it is achieved multi-scale Modeling.
If local only need to build local mixing volume elements model of geological structure body by above-mentioned steps, specifically refer to as explained below after having new boring or other data to enter.
S2, utilizes the local change data construct in described former data and the local mixing volume elements model of geological structure body of described overall mixing volume elements model of geological structure body same scale.
If local has new boring or other survey data to need to update entirety mixing volume elements model of geological structure body, only need to build the local mixing volume elements model of geological structure body with yardstick by above-mentioned steps. Remaining is exactly the fusion problem of new and old IHG-TIN model. Owing to being the volume elements of same yardstick, it is easy to find the new and old volume elements of correspondence position, replace and update.
First introduce the building process of local mixing volume elements model of geological structure body below.
If former data have data to be updated, obtain the local change data after updating. For borehole data, if borehole data has been changed, then obtain the borehole data after change.
First, local change data are carried out pretreatment.
The TIN FEM layer model (FEM layer model of TIN) that local change data carry out local change data is utilized to build.
The building process of the TIN FEM layer model of similar former data, when building the TIN FEM layer model of local change data, knowledge reasoning is utilized to judge point set and the lines collection in each section in local or the upper corresponding same stratal surface of boring or structure face, utilize point set and lines collection to be completed each stratal surface or the TIN model construction in structure face by space interpolation, improve the contact relation modified between each surface model as necessary by interactive editor. Build rear TIN FEM layer model and just inherited the geological property on corresponding boring or section, complete the expression that geology is semantic.
Finally, the TIN FEM layer model described local mixing volume elements model of geological structure body of structure of data is changed based on local.
After building the TIN FEM layer model of local change data, complete the structure of local mixing volume elements model of geological structure body in combinations with Irregular hexahedron volume elements subdivision and model attributes instrument.
Specifically, build local mixing volume elements model of geological structure body and be divided into two parts: first, by the subdivision of Irregular hexahedron, the TIN FEM layer model that data are changed in local is utilized to retrain, the space that local FEM layer model is defined is carried out the subdivision of Irregular hexahedron, builds the local mixing volume elements model of geological structure body risen and fallen along various FEM layer models. Second, utilize model attributes instrument to complete the structure of local mixing volume elements model of geological structure body. That is: utilize the method such as Krieger or distance power inverse ratio that various attribute informations (such as: grade, pressure etc.) are interpolated, and give corresponding property value by each Irregular hexahedron volume elements, complete the structure of local mixing volume elements model of geological structure body.
If having the needs of local multi-scale Modeling further, it is possible to the volume elements in local mixing volume elements model of geological structure body is carried out local fine subdivision, it is achieved multi-scale Modeling.
S3, utilizes the volume elements in described local mixing volume elements model of geological structure body to replace and updates the volume elements of relevant position in described overall mixing volume elements model of geological structure body, complete the local updating of mixing volume elements model of geological structure body.
Utilizing new volume elements local to replace the volume elements of master mould same position, extracting the topological relation of new FEM layer model complete layer surface model and the renewal of geological property, thus realizing quick local dynamic station renewal etc.
In the updated, below step can also be carried out: extract the FEM layer model after updating
Utilize the mixing volume elements model of geological structure body after updating, extract FEM layer model therein, complete the synchronized update of geologic body stratal surface, structure face, topological relation and attribute information.
S4, the entirety after updating mixes the TIN TIN FEM layer model extracted volume elements model of geological structure body after updating, the topological relation of complete layer surface model and the renewal of geological property.
Below in conjunction with specific embodiment, the invention will be further described, but does not limit the present invention.
Embodiment:
1. certain modeling region boring set (n) and cross-sectional data (m bar) of input;
2. boring and section are projected in three-dimensional scenic;
3., by strata division information, select n boring boring point identical with layer attribute in m bar section and stratigraphic boundary lines, utilize triangulation and space interpolation to produce the FEM layer model on each stratum;
4. by constructing distributed intelligence, select structure dew point, face and structure line in n boring and m bar section, utilize triangulation and constraint space interpolation to produce each structure surface model;
5. build the TIN FEM layer model within geologic body;
6. by the subdivision of Irregular hexahedron, utilize TIN FEM layer model to retrain, the space that FEM layer model is defined is carried out the subdivision of Irregular hexahedron, build the entirety mixing volume elements model of geological structure body risen and fallen along various FEM layer models.
7. repeat 1-6 and walk local data's update area local mixing volume elements model of geological structure body with yardstick;
8. relatively overall mixing volume elements model of geological structure body and locally mixture unit model of geological structure body;
9. replace the entirety mixing volume elements model of geological structure body updating relevant position by the volume elements of local mixing volume elements model of geological structure body, complete the renewal of mixing volume elements model of geological structure body;
10. the entirety mixing volume elements model of geological structure body after search renewal, extracts the TIN FEM layer model after updating, it is achieved the synchronized update replacement of new FEM layer model.
It addition, be the adaptability and the practicality that strengthen this method, 1-6 step reserve artificial guided interaction interface, it is possible to increase part man-machine interactively, improved the precision of model.
Referring to Fig. 3, it is a kind of Organization Chart mixing volume elements model of geological structure body local Rapid Updating of the present invention, specific as follows:
The data such as the original whole boring of step 1., section, attribute carry out data prediction.
Step 2. carries out overall TIN FEM layer model and builds. When building, utilize knowledge reasoning to judge point set and the lines collection in each section or the upper corresponding same stratal surface of boring or structure face, utilize point set and lines collection to be completed each stratal surface or the TIN model construction in structure face by space interpolation, improve the contact relation modified between each surface model as necessary by interactive editor. Build rear TIN FEM layer model and just inherited the geological property on corresponding boring or section, complete the expression that geology is semantic.
The overall IHG-TIN of step 3. mixes volume elements and builds, and mainly merges: Irregular hexahedron subdivision, model attributes.
Step 4. builds overall mixing volume elements model of geological structure body.
The data such as the step 5. new boring in local, section, attribute carry out data prediction.
Step 6. local T IN FEM layer model builds. When building, utilize knowledge reasoning to judge point set and the lines collection in corresponding same stratal surface or structure face on localized borehole or section, utilize point set and lines collection to be completed each stratal surface or the TIN model construction in structure face by space interpolation, improve the contact relation modified between each FEM layer model as necessary by interactive editor. Build rear local T IN FEM layer model and just inherited the geological property on corresponding boring or section, complete the expression that geology is semantic.
Step 7. local I HG-TIN mixes volume elements and builds, and mainly merges: Irregular hexahedron subdivision, model attributes.
Step 8. builds local mixing volume elements model of geological structure body.
Step 9. updates the integrally plastid IHG-TIN model merged. Mainly local volume elements is replaced and is updated.
Step 10. update after geologic body aspect, structure face, topological relation and attribute. That is: aspect, structure face, attributes extraction.
Compared with prior art, beneficial effects of the present invention is embodied in the following aspects:
1. owing to taking first replacement to update the FEM layer model reverse thinking that geologic body volume element model updates in geologic body again, the topological relation and the attribute that overcome new surface model in conventional update method from face to body update difficulty, it is to avoid surface model and body Model shift reconstruction onto.
2. owing to adopting geologic body to update replacement with the volume element model of yardstick, it is not necessary to complicated geometric operation, renewal speed is fast, improves the efficiency that geologic body local dynamic station updates.
3., owing to have employed mixing volume elements model of geological structure body IHG-TIN model, spatial topotaxy and the geological property of extracting FEM layer model after updating are simply easy.
4. owing to have employed mixing volume elements model of geological structure body IHG-TIN model, this model energy Seamless integration-takes the semantic FEM layer model of topological relation, geology and the fine volume element model expressing fine attribute into account, multi-scale Modeling can be carried out further, it is possible to meet the follow-up various specialty analysis being respectively directed to volume elements and bin.
In a word, after the thinking first updating volume elements update step surface model again is introduced by the present invention, volume elements is utilized to update the feature of simple and fast, efficiently solve the difficult problem that geologic body local dynamic station updates, it is possible to promote the use of in the softwares such as various three-dimensional geological modeling systems, hydrocarbon information system, mine enterprise information system, geologic survey system or disaster information system.
Although having been described for the preferred embodiment of the application, but one of ordinary skilled in the art is once know basic creative concept, then these embodiments can be made other change and amendment. So, claims are intended to be construed to include preferred embodiment and fall into all changes and the amendment of the application scope.
Obviously, the application can be carried out various change and modification without deviating from spirit and scope by those skilled in the art. So, if these amendments of the application and modification belong within the scope of the application claim and equivalent technologies thereof, then the application is also intended to comprise these change and modification.

Claims (6)

1. a mixing volume elements model of geological structure body local Rapid Updating, it is characterised in that described method includes:
Utilize former data construct entirety mixing volume elements model of geological structure body;
Utilize the local change data construct in described former data and the local mixing volume elements model of geological structure body of described overall mixing volume elements model of geological structure body same scale;
Utilize the volume elements in described local mixing volume elements model of geological structure body to replace and update the volume elements of relevant position in described overall mixing volume elements model of geological structure body;
Entirety after updating mixes the TIN TIN FEM layer model extracted volume elements model of geological structure body after updating.
2. the method for claim 1, it is characterised in that
Described utilize former data construct entirety mixing volume elements model of geological structure body before, described method also includes:
Described former data are carried out pretreatment.
3. the method for claim 1, it is characterised in that
Described utilize former data construct entirety mixing volume elements model of geological structure body, specifically include:
The TIN TIN FEM layer model that described former data carry out former data is utilized to build;
TIN FEM layer model based on described former data builds described overall mixing volume elements model of geological structure body.
4. method as claimed in claim 3, it is characterised in that described based on the described overall mixing volume elements model of geological structure body of described TIN FEM layer model structure, specifically includes:
The TIN FEM layer model utilizing described former data construct retrains, and the space that FEM layer model is defined carries out the subdivision of Irregular hexahedron, builds the mixing volume elements model of geological structure body risen and fallen along various FEM layer models;
Utilize model attributes instrument that the described mixing volume elements model of geological structure body risen and fallen along various FEM layer models is carried out assignment, complete the structure of described overall mixing volume elements model of geological structure body.
5. the method for claim 1, it is characterised in that the local mixing volume elements model of geological structure body of the described local change data construct utilized in described former data and described overall mixing volume elements model of geological structure body same scale, specifically includes:
Utilize described local change data to carry out local and change the TIN FEM layer model structure of data;
The TIN FEM layer model utilizing described local change data builds described local mixing volume elements model of geological structure body.
6. method as claimed in claim 5, it is characterised in that the described TIN FEM layer model utilizing described local change data builds described local mixing volume elements model of geological structure body, specifically includes:
The TIN FEM layer model utilizing described local change data construct retrains, and the space that local FEM layer model is defined carries out the subdivision of Irregular hexahedron, builds the local mixing volume elements model of geological structure body risen and fallen along various FEM layer models;
Utilize model attributes instrument that the described mixing volume elements model of geological structure body risen and fallen along various FEM layer models is carried out assignment, complete the structure of described local mixing volume elements model of geological structure body.
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CN111275819A (en) * 2019-12-18 2020-06-12 自然资源部国土卫星遥感应用中心 Application method of global elevation reference model of remote sensing satellite
CN111459955A (en) * 2020-03-13 2020-07-28 济南轨道交通集团有限公司 Three-dimensional geological structure model automatic updating method and system based on GIS platform
CN111612903A (en) * 2020-04-29 2020-09-01 中冶沈勘工程技术有限公司 Geological data visualization method based on mixed data model
CN113239058A (en) * 2021-05-27 2021-08-10 中国地质大学(武汉) Three-dimensional geological body model local dynamic updating method based on knowledge graph reasoning
CN113421194A (en) * 2021-06-04 2021-09-21 贵州省地质矿产勘查开发局 Method for extracting hidden fault according to Booth gravity anomaly image

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