CN110941021B - Forward modeling method for gravity anomaly and gradient anomaly based on grid point grid function - Google Patents
Forward modeling method for gravity anomaly and gradient anomaly based on grid point grid function Download PDFInfo
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Abstract
The invention discloses a forward modeling method for gravity anomaly and gradient anomaly based on a grid point grid function, which comprises the following steps: step 1: starting; and 2, step: dividing a model space, and assigning value to the residual density of the abnormal body; and 3, step 3: respectively calculating a trellis function of the gravity anomaly and the gradient anomaly; and 4, step 4: judging the relative position of the observation point and the cuboid unit; and 5: utilizing symmetric interchangeability and translational equivalence; step 6: calling a trellis function of the gravity anomaly and the gradient anomaly; and 7: algebraic summation is carried out to obtain gravity anomaly and gradient anomaly of the observation point by the cuboid; and 8: obtaining the gravity anomaly and the gradient anomaly of the whole model body to the observation point; and step 9: the circulation in the calculation plane is completely finished; step 10: and obtaining a result. The invention solves the problem of low calculation efficiency of the existing calculation method.
Description
Technical Field
The invention relates to the technical field of gravity exploration, in particular to a forward modeling method for gravity anomaly and gradient anomaly based on a grid point grid function.
Background
In the existing gravity exploration forward modeling calculation, a model is divided into a plurality of cuboid units by using common equidistant grid lines, then the abnormity of each cuboid unit to an observation point is calculated, and then the abnormity of all cuboid units to the observation points is summed, namely the abnormity of the whole model body to the observation points is obtained. There are a large number of repeated calculations, resulting in a significant reduction in numerical simulation and inversion efficiency.
The geophysical science newspaper 2003, the Yao Changli and other 'heavy magnetic genetic algorithm three-dimensional inversion medium-high speed calculation and effective storage method technologies' is disclosed in the 02 th phase, forward evolution conditions of a subdivision model are explained by a forward evolution formula of a three-dimensional density model, and calculation of abnormal values of observation points by a grid point is simplified by using symmetrical interchangeability and translation equivalence, so that the calculation efficiency is greatly improved, and the experimental result has a good effect.
The geophysical progress 2012 discloses the progress of a gravity-magnetic data three-dimensional physical property inversion method, such as Chenxi, introduces an equivalent storage geometric grid technology, deduces a formula based on the symmetric interchangeability and translation equivalence of grid point grids, and combines the two formulas to simplify the operation. By utilizing the technology, the geometric grid values of the first grid unit of each layer are calculated, and the geometric grid values of all the grid units can be obtained through a combined formula, so that a large amount of calculated amount and storage amount can be saved, a foundation is laid for inversion, and an experimental result has a good effect.
The existing calculation method can improve the forward speed of the model to a certain extent, but the calculation efficiency is still not high enough, and the space for continuous improvement is provided.
Disclosure of Invention
The invention mainly aims to provide a forward modeling method for gravity anomaly and gradient anomaly based on a grid point grid function, so as to solve the problem of low calculation efficiency of the conventional calculation method.
In order to achieve the above object, the present invention provides a forward modeling method for gravity anomaly and gradient anomaly based on grid point lattice function,
the method comprises the following steps:
step 1: starting;
step 2: dividing a model space, and assigning a value to the residual density of the abnormal body;
and step 3: respectively calculating a trellis function of the gravity anomaly and the gradient anomaly;
and 4, step 4: judging the relative position of the observation point and the cuboid unit;
and 5: utilizing symmetric interchangeability and translational equivalence;
step 6: invoking trellis functions for gravity and gradient anomalies
And 7: algebraic summation is carried out to obtain gravity anomaly and gradient anomaly of the observation point by the cuboid;
and 8: obtaining the gravity anomaly and the gradient anomaly of the whole model body to the observation point;
and step 9: the circulation in the calculation plane is completely finished;
step 10: and obtaining a result.
Further, the step 2 specifically includes: dividing the calculation space into grids, determining the space of the grids and the position of the abnormal body in the grids, converting the unit of the calculation area plane of the calculation space into actual mileage, and assigning a value to the residual density of the abnormal body;
further, step 3 specifically comprises: determining coordinates of observation points in a plane of a calculation area, determining coordinates of a cuboid model unit obtained by subdivision in a calculation space, wherein the observation points circulate in the plane of the calculation area, the cuboid unit circulates in the whole calculation space, grid functions of gravity anomaly and gradient anomaly of all grid points to a first observation point in the model space are respectively calculated, and then the grid functions are stored to be called by later-stage calculation;
further, step 4 specifically includes: in the calculation space, each time the observation point circulates to one position, the cuboid model unit traverses and circulates once in the calculation space, and each time the cuboid model unit circulates to one position, the observation point has a relative position relation with the cuboid model unit.
Further, the steps 5 to 9 are specifically: substituting the position parameters of the observation points and the cuboid units into a gravity anomaly lattice function, calling out 8 stored lattice point pair observation point lattice functions by utilizing symmetrical interchangeability and translation equivalence, then algebraically summing to obtain the gravity anomaly and gradient anomaly of the cuboid units to the observation points, summing the gravity anomaly and gradient anomaly of the cuboid units to the observation points to obtain the gravity anomaly and gradient anomaly of the whole model body to the observation points, and obtaining the gravity anomaly and all gradient anomaly of a calculation area when circulation in a calculation space is completely finished.
The gravity anomaly and the gradient anomaly of each cuboid unit to the observation point in the calculation space are respectively equal to the linear algebraic sum of the gravity anomaly and the gradient anomaly of the grid point where 8 vertexes of the cuboid unit are located to the observation point, the lattice function of the gravity anomaly and the gradient anomaly of the cuboid unit to other observation points in the calculation space can be equivalent to the lattice function of the gravity anomaly and the gradient anomaly of the cuboid unit to P through symmetrical interchangeability and translation equivalence, and therefore the five-dimensional calculation problem is changed into a three-dimensional calculation problem, and the calculation efficiency is greatly improved.
The invention simplifies the five-dimensional calculation problem into a three-dimensional calculation problem by adopting symmetrical interchangeability and translation equivalence, solves the problem of low calculation efficiency caused by a large amount of repeated calculation in the original calculation method by storing and calling the grid function result of the grid point to the observation point abnormity first, improves the calculation speed by nearly 8 times, and achieves the effect of rapid forward modeling.
The invention is further described with reference to the following figures and detailed description. Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to assist in understanding the invention, and are included to explain the invention and their equivalents and not limit it unduly. In the drawings:
fig. 1 is a flowchart of a forward modeling method for gravity anomaly and gradient anomaly based on a grid point lattice function.
Fig. 2 is a schematic diagram of a subsurface subdivision unit.
Fig. 3 is a schematic diagram of a mesh generation unit and an observation point.
Fig. 4 is a schematic diagram of translational equivalence.
FIG. 5 is a schematic diagram of symmetric interchangeability.
FIG. 6 is a g diagram of gravity anomaly obtained by an original alignment algorithm for an underground grid cell model.
FIG. 7 is a gradient anomaly graph obtained by using the original correction algorithm for the underground grid cell model (g for each of graphs a, b, c, d, e, f, g, h, and i)xx、gxy、gxz、gyx、gyy、gyz、gzx、gzy、gzzGradient anomaly map).
FIG. 8 is a g-graph of gravity anomaly obtained by a fast-forward algorithm for an underground grid cell model.
FIG. 9 is a gradient anomaly graph obtained by a fast positive algorithm for the underground grid cell model (the gradient anomalies in graphs a, b, c, d, e, f, g, h, i are gxx, gxy, gxz, gyx, gyy, gyz, gzx, gzy, gzz, respectively)
Detailed Description
The invention will be described more fully hereinafter with reference to the accompanying drawings. Those skilled in the art will be able to implement the invention based on these teachings. Before the present invention is described in detail with reference to the accompanying drawings, it is to be noted that:
the technical solutions and features provided in the present invention in the respective sections including the following description may be combined with each other without conflict.
Moreover, the embodiments of the present invention described in the following description are generally only examples of a part of the present invention, and not all examples. Therefore, all other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative effort shall fall within the protection scope of the present invention.
With respect to terms and units in the present invention. The terms "comprising," "having," and any variations thereof in the description and claims of this invention and the related sections are intended to cover non-exclusive inclusions.
The invention relates to a forward modeling method for gravity anomaly and gradient anomaly based on a grid point grid function, which comprises the following steps of:
step 1: starting;
step 2: dividing a model space, and assigning a value to the residual density of the abnormal body;
and step 3: respectively calculating a trellis function of the gravity anomaly and the gradient anomaly;
and 4, step 4: judging the relative position of the observation point and the cuboid unit;
and 5: utilizing symmetric interchangeability and translational equivalence;
step 6: invoking trellis functions for gravity and gradient anomalies
And 7: algebraic summation is carried out to obtain gravity anomaly and gradient anomaly of the observation point by the cuboid;
and 8: obtaining the gravity anomaly and the gradient anomaly of the whole model body to the observation point;
and step 9: the circulation in the calculation plane is completely finished;
step 10: and obtaining a result.
The step 2 specifically comprises the following steps: dividing the calculation space into grids, determining the space of the grids and the position of the abnormal body in the grids, converting the unit of the calculation area plane of the calculation space into actual mileage, and assigning a value to the residual density of the abnormal body;
the step 3 specifically comprises the following steps: determining coordinates of observation points in a plane of a calculation area, determining coordinates of cuboid model units obtained by subdivision in a calculation space, circulating the observation points in the plane of the calculation area, circulating the cuboid units in the whole calculation space, respectively calculating a lattice function of gravity anomaly and gradient anomaly of all grid points to a first observation point in the model space, and then storing and calling for later-stage calculation;
the step 4 specifically comprises the following steps: in the calculation space, each time the observation point circulates to one position, the cuboid model unit traverses and circulates once in the calculation space, and each time the cuboid model unit circulates to one position, the observation point has a relative position relation with the cuboid model unit.
The steps 5-9 are specifically: substituting the position parameters of the observation points and the cuboid units into a gravity anomaly lattice function, calling out 8 stored lattice point pair observation point lattice functions by utilizing symmetrical interchangeability and translation equivalence, then algebraically summing to obtain the gravity anomaly and gradient anomaly of the cuboid units to the observation points, summing the gravity anomaly and gradient anomaly of the cuboid units to the observation points to obtain the gravity anomaly and gradient anomaly of the whole model body to the observation points, and obtaining the gravity anomaly and all gradient anomaly of a calculation area when circulation in a calculation space is completely finished.
The invention is further illustrated by the following specific embodiments:
dividing the calculation space into grids, determining the space of the grids and the position of the abnormal body in the grids, converting the unit of the upper surface of the calculation space, namely the plane of the calculation area, into the actual mileage, and assigning a value to the residual density of the abnormal body.
The coordinates of the observation points in the plane of the calculation region are (IX, IY), and the coordinates of the cuboid unit in the space are (i, j, k). The observation points circulate in the plane of the calculation area, and the cuboid units circulate in the whole calculation space.
And respectively calculating the grid functions (marked as GravityP) of the gravity anomaly and the gradient anomaly of all grid points to the first observation point (marked as P) in the model space, and then storing the grid functions to be called for later-stage calculation. And calculating the gravity anomaly and the gradient anomaly of each cuboid unit to the observation point P in the space, wherein the gravity anomaly and the gradient anomaly of each cuboid unit to the observation point P are respectively equal to the linear algebraic sum of the gravity anomaly and the gradient anomaly of the grid point where 8 vertexes of the cuboid unit are located to the observation point P. The lattice functions of the cuboid units in the space for gravity anomaly and gradient anomaly of other observation points can be calculated, and the lattice functions for gravity anomaly and gradient anomaly of the cuboid units in the space can be equivalent to those for P through symmetrical interchangeability and translation equivalence, so that the five-dimensional calculation problem is changed into a three-dimensional calculation problem, and the calculation efficiency is greatly improved.
In the calculation space, each time the observation point circulates to one position, the cuboid model unit traverses and circulates once in the calculation space. Every time the cuboid unit arrives at a position in the circulation, the observation point has a relative position relation with the cuboid unit, the position parameters of the observation point and the cuboid unit are substituted into the gravity anomaly lattice function GravityP, 8 stored lattice point pair lattice functions of the observation point can be called out by utilizing the symmetry interchangeability and the translation equivalence, and then the algebraic summation is carried out to obtain the gravity anomaly and the gradient anomaly of the cuboid unit to the observation point. And summing the gravity anomaly and the gradient anomaly of the observation point by all the cuboid units to obtain the gravity anomaly and the gradient anomaly of the observation point by the whole model body.
When the circulation in the calculation space is completely finished, the gravity anomaly g and the gradient anomaly g in the calculation area can be obtainedxx、gxy、gxz、gyx、gyy、gyz、gzx、gzy、gzz。
Fig. 1 is a flow chart of a space domain fast alignment algorithm based on the gravity anomaly and the gradient anomaly of the grid point lattice function, and the flow chart shows the implementation flow of the method of the present invention:
s1: starting;
s2: dividing a model space, and assigning a value to the residual density of the abnormal body;
s3: respectively calculating a trellis function of the gravity anomaly and the gradient anomaly;
s4: judging the relative position of the observation point and the cuboid unit;
s5: utilizing symmetric interchangeability and translational equivalence;
s6: invoking trellis functions for gravity and gradient anomalies
S7: algebraic summation is carried out to obtain gravity anomaly and gradient anomaly of the observation point by the cuboid;
s8: obtaining the gravity anomaly and the gradient anomaly of the whole model body to the observation point;
s9: the circulation in the calculation plane is completely finished;
s10: and obtaining a result.
The method comprises the following specific steps:
1) as shown in fig. 2, the computation space is divided into grids, the distance between the grids and the position of the abnormal body in the grids are determined, the unit of the upper surface of the computation space, i.e. the plane of the computation area, is converted into the actual mileage, and the remaining density of the abnormal body is assigned.
2) As shown in fig. 3, the coordinates of the observation point in the calculation region plane are (IX, IY), and the coordinates of the cuboid unit in the calculation space are (i, j, k). The observation points circulate in the plane of the calculation area, and the cuboid units circulate in the whole calculation space.
3) And respectively calculating the grid functions GravityP of the gravity anomaly and the gradient anomaly of all grid points to the first observation point P in the model space, and then storing the grid functions GravityP to be called by later-stage calculation. And calculating the algebraic sum of the gravity anomaly and the gradient anomaly of each rectangular unit to the observation point P in the space and the algebraic sum of the gravity anomaly and the gradient anomaly of the grid point where 8 vertexes of the rectangular unit are located to the observation point P. The lattice function of the cuboid units in the space for gravity anomaly and gradient anomaly of other observation points can be calculated, and the lattice function of the cuboid units for gravity anomaly and gradient anomaly of P can be equivalent to the lattice function of the cuboid units for gravity anomaly and gradient anomaly through symmetrical interchangeability and translation equivalence, so that the five-dimensional calculation problem is changed into a three-dimensional calculation problem, and the calculation efficiency is greatly improved. As shown in fig. 4, the lattice function of the gravity anomaly and the gradient anomaly of the observation points (3, 4) by the grid points (1, 1, 5) is the same as the lattice function of the gravity anomaly and the gradient anomaly of the observation points (3, 5) by the grid points (1, 2, 5), which is the translation equivalence. As shown in fig. 5, the grid function of gravity anomaly and gradient anomaly of grid points (1, 1, 5) for observation points (3, 4) is the same as the grid function of gravity anomaly and gradient anomaly of grid points (3, 4, 5) for observation points (1, 1), which is symmetric interchangeability.
4) In the calculation space, each time the observation point circulates to one position, the cuboid model unit traverses and circulates once in the calculation space. Every time the cuboid unit arrives at one position in the circulation, the observation point has a relative position relation with the cuboid unit, the position parameters of the observation point and the cuboid unit are substituted into the gravity anomaly lattice function GravityP, 8 stored lattice point pair lattice functions of the observation point can be called out by utilizing the symmetry interchangeability and the translation equivalence, and then the algebraic summation is carried out to obtain the gravity anomaly and the gradient anomaly of the cuboid unit to the observation point. And summing the gravity anomaly and the gradient anomaly of the observation point by all the cuboid units to obtain the gravity anomaly and the gradient anomaly of the observation point by the whole model body.
5) When the loop in the computation space is completed, the gravity anomaly g in the computation region as shown in fig. 8 and the gradient anomalies gxx, gxy, gxz, gyx, gyy, gyz, gzx, gzy, and gzz as shown in fig. 9 can be obtained.
The scheme and the beneficial effects of the invention are verified by an underground grid cell model. FIG. 2 is a schematic diagram of an underground subdivision unit, 21 grid nodes are arranged in the transverse direction of the model, 21 grid nodes are arranged in the longitudinal direction of the model, 16 grid nodes are arranged in the vertical direction of the model, and abnormal bodies are distributed in the whole space. Fig. 6 is a gravity anomaly g map obtained by an original correction algorithm for the underground grid unit model, fig. 7 is a gradient anomaly map obtained by an original correction algorithm for the underground grid unit model (gradient anomaly maps of gxx, gxy, gxz, gyx, gyy, gyz, gzx, gzy and gzz are shown in fig. a, b, c, d, e, f, g, h and i respectively), fig. 8 is a gravity anomaly g map obtained by a fast correction algorithm for the underground grid unit model, and fig. 9 is a gradient anomaly map obtained by a fast correction algorithm for the underground grid unit model (gradient anomaly maps of gxx, gxz, gxx, gyx, gyy, gyz, gzz and gzz are shown in fig. a, b, c, d, e, f, g, h and i respectively). The computer processor used to implement the correction algorithm was Intel (R) core (TM) i5-8265U CPU @1.60GHz 1.80GHz, and the programming software was Matlab2018 a. The calculation time for the model using the prior art was 10.0524s, and the calculation time for the model using the present invention was 1.3125 s. From the calculation results, it can be seen that: the calculation result obtained by the method of the invention is completely the same as the calculation result obtained by the original correction algorithm. Therefore, the method has higher calculation speed and higher efficiency, and compared with the original correction algorithm, the calculation speed is improved by 7.7 times.
The method is an important space domain fast forward algorithm aiming at the gravity anomaly and the gradient anomaly of the underground grid unit model, aims at the problem that the calculation efficiency is not high enough due to a large amount of repeated calculation in the original calculation method, solves the problem that the calculation efficiency is not high enough due to the large amount of repeated calculation in the original calculation method by calculating the grid points to the grid functions of the gravity anomaly and the gradient anomaly of the observation points and storing the grid functions for later calculation and calling, improves the calculation speed by nearly 8 times, and achieves the effect of fast forward.
The contents of the present invention have been explained above. Those skilled in the art will be able to implement the invention based on these teachings. All other embodiments, which can be derived by a person skilled in the art from the above description without inventive step, shall fall within the scope of protection of the present invention.
Claims (1)
1. The forward modeling method for gravity anomaly and gradient anomaly based on grid point grid function is characterized by comprising the following steps:
step 1: starting;
step 2: dividing a model space, and assigning a value to the residual density of the abnormal body;
and step 3: respectively calculating a trellis function of the gravity anomaly and the gradient anomaly;
and 4, step 4: judging the relative position of the observation point and the cuboid unit;
and 5: utilizing symmetric interchangeability and translational equivalence;
step 6: calling a trellis function of the gravity anomaly and the gradient anomaly;
and 7: algebraic summation is carried out to obtain gravity anomaly and gradient anomaly of the observation point by the cuboid;
and 8: obtaining the gravity anomaly and the gradient anomaly of the whole model body to the observation point;
and step 9: the circulation in the calculation plane is completely finished;
step 10: obtaining a result;
the step 2 specifically comprises the following steps: dividing the calculation space into grids, determining the space of the grids and the position of the abnormal body in the grids, converting the unit of the calculation area plane of the calculation space into actual mileage, and assigning a value to the residual density of the abnormal body;
the step 3 specifically comprises the following steps: determining coordinates of observation points in a plane of a calculation area, determining coordinates of a cuboid model unit obtained by subdivision in a calculation space, wherein the observation points circulate in the plane of the calculation area, the cuboid unit circulates in the whole calculation space, grid functions of gravity anomaly and gradient anomaly of all grid points to a first observation point in the model space are respectively calculated, and then the grid functions are stored to be called by later-stage calculation;
the step 4 specifically comprises the following steps: in the calculation space, each time the observation point circulates to one place, the cuboid model unit traverses and circulates once in the calculation space, and each time the cuboid model unit circulates to one place, the observation point has a relative position relation with the cuboid model unit;
the steps 5-9 are specifically: substituting the position parameters of the observation points and the cuboid units into a gravity anomaly lattice function, calling out 8 stored lattice point pair observation point lattice functions by utilizing symmetrical interchangeability and translation equivalence, then algebraically summing to obtain the gravity anomaly and gradient anomaly of the cuboid units to the observation points, summing the gravity anomaly and gradient anomaly of the cuboid units to the observation points to obtain the gravity anomaly and gradient anomaly of the whole model body to the observation points, and obtaining the gravity anomaly and all gradient anomaly of a calculation area when circulation in a calculation space is completely finished.
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