CN112242001B - Model parameter disturbance method for wavelet transformation - Google Patents
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Abstract
The invention provides a model parameter disturbance method of wavelet transformation, which specifically comprises the following steps: the method comprises the steps of representing the disturbance of the geophysical model obtained after transformation, which is concentrated on local tree structure sub nodes (with larger depth) as high-frequency detail information of the model, representing tree structure root nodes (with smaller depth), which cover the whole model area, of the disturbance of the geophysical model obtained after transformation as low-frequency approximate information of the model, and converting the tree structure and the geophysical model through wavelet transformation so as to realize the decomposition or reconstruction of the geophysical model. The method provided by the invention can accurately realize the accurate local disturbance of different scales and different areas of the geophysical model by increasing nodes, reducing nodes, disturbing node values and the like. The invention provides necessary technical conditions for development based on wavelet domain geophysical inversion and has wide application prospect.
Description
Technical Field
The invention relates to the technical field of wavelet transform image processing, in particular to a model parameter disturbance method for wavelet transform.
Background
The geophysical method is to utilize the principles and methods of mechanics, electricity, magnetism, heat and other aspects of physics, and to find out the connection and rule between the physical conditions, physical properties and physical states of all parts in the earth from two aspects of time and space by observing and researching the physical conditions, physical properties and physical states of all parts in the earth, so as to realize the understanding of the earth and realize geological exploration and mineral exploration. The geophysical model has wide application range, and mainly comprises oil gas exploration, underground water exploration, mineral exploration, environment monitoring, geothermal exploration, deep structure research and the like.
Wavelet transform is developed on the basis of fourier analysis, and is a rapidly developing field, and compared with fourier transform, wavelet transform is a local transform of space and frequency, and can extract information from signals. The method is widely applied to the fields of voice analysis, image processing, computer vision and the like. The multi-resolution analysis is one of the most important concepts in wavelet transform, and can represent a function as a low-frequency component and a high-frequency component at different resolutions, wherein the low-frequency component has the largest relationship with the function and represents an approximate value thereof, and the high-frequency detail information at different levels represents the local detail component of the function.
The method based on the tree structure is a model parameterization method which is commonly used at present. The method applies multi-resolution analysis of images to a geophysical model, performs wavelet decomposition on the geophysical model to obtain high-detail information and low-frequency approximate information under different resolutions, and stores the high-detail information and the low-frequency approximate information into tree structure nodes according to a certain rule, so as to obtain a corresponding tree structure model; the node operation is carried out on the existing tree structure, such as node addition, node deletion, node value disturbance and the like, so that the overall or local disturbance of the geophysical model is achieved. The tree structure parameterization method provides a universal framework for solving the parameterization problem of one-dimensional or even three-dimensional models, can flexibly use binary trees, quadtrees and octrees to represent the one-dimensional to three-dimensional models, has considerable flexibility in selecting basis functions (such as wavelet transformation, Laplace pyramid transformation and the like), and can select different basis functions according to the characteristics of the problem to be solved.
The geophysical model (such as a one-dimensional layered model) can be represented by a corresponding tree structure model through wavelet transformation into basis functions. The corresponding local area of the geophysical model can be perturbed by manipulating existing tree-structured nodes (adding nodes, subtracting nodes, and changing node values). Therefore, the method can realize that certain disturbance is carried out on the geophysical model by changing the node information in the tree structure. However, if the operation is directly performed on the nodes in the tree structure (especially adding nodes), then the model obtained by performing the direct wavelet reconstruction is wrong. In the wavelet transformation based on the tree structure, how to obtain correct local disturbance is the key for realizing wavelet domain geophysical inversion.
Disclosure of Invention
The invention aims to provide a model parameter perturbation method of wavelet transformation, which can accurately perform local perturbation on different scales and different regions of a geophysical model by increasing nodes, reducing nodes, perturbing node values and the like so as to generate a new model.
In order to achieve the above object, the present invention provides a method for perturbing a model parameter of wavelet transform, which specifically comprises: the method comprises the steps of representing the disturbance of a geophysical model obtained after transformation, which is concentrated on local tree structure sub nodes (with larger depth) as high-frequency detail information of the model, representing tree structure root nodes (with smaller depth), which cover the whole model area, of the disturbance of the geophysical model obtained after transformation as low-frequency approximate information of the model, and converting the tree structure and the geophysical model through wavelet transformation so as to realize the decomposition or reconstruction of the geophysical model;
the high-frequency detail information and the low-frequency approximate information respectively refer to a high-frequency component and a low-frequency component of the image, the low-frequency component describes information in a large range, the high-frequency component describes specific details, and in the gray-scale image, an area with small brightness change is mainly the low-frequency component, and an area with strong brightness change is mainly the high-frequency component.
The perturbation of the transformed geophysical model by the tree-structure child nodes is more concentrated in local parts, and the perturbation area of the transformed geophysical model by the tree-structure root node covers the whole model area, so that the perturbation of different areas and different scales of the geophysical model can be accurately achieved through the operation of different nodes (node increase, node reduction and node value change), and a new model is generated.
As a further scheme of the invention: the method for decomposing the geophysical model comprises the following specific steps:
s1: and performing one-time finest wavelet transform. Performing first wavelet transformation on the geophysical model on the finest grid to obtain the same amount of low-frequency approximate information and high-frequency detail information of the transformed geophysical model;
s2: saving the high-frequency detail information;
s3: and performing wavelet transformation for multiple times aiming at the low-frequency approximate information, storing the high-frequency detail information after each wavelet transformation, and performing wavelet transformation for the low-frequency approximate information until one low-frequency approximate information and one high-frequency detail information are obtained, thereby completing the decomposition of the geophysical model.
Preferably, the relation between the wavelet transformation times of the geophysical model and the number of discrete values contained in the wavelet transformation times is 2NAnd the power, wherein N is the wavelet transformation times of the geophysical model.
As a further scheme of the invention: the method for reconstructing the geophysical model specifically comprises the following steps: under the condition that low-frequency approximate information of the lowest-level resolution and high-frequency detail information under different resolutions are known, the geophysical model is completely restored through inverse wavelet transformation;
preferably, the inverse wavelet transform is as follows: the node values through the tree structure model are finally transformed to the actual geophysical model parameter values (conductivity values σ).
Preferably, before performing the inverse wavelet transform on the tree structure model, the following processing is required:
1) setting a maximum node depth level h aiming at the tree structure, wherein child nodes larger than the depth level cannot be generated;
2) and performing wavelet transformation on the node values of all nodes within the depth level h of the tree structure, wherein the node values which do not exist (namely, empty nodes) are defaulted to be 0.
The technical scheme of the invention has the following beneficial effects:
(1) by the method provided by the invention, when the wavelet transform is used as the basis function of the tree structure model transform, a correct geophysical model can be obtained, namely, only the corresponding model area can be disturbed when the information of the corresponding model in the tree structure is changed, and the method completely conforms to the multi-resolution principle in the wavelet transform.
(2) According to the method provided by the invention, the root node comprises the whole information of the geophysical model, the child nodes with different depth levels correspond to the high-frequency detail information of the model with corresponding levels, the higher the level is, the smaller the disturbance range of the converted geophysical model is, and the more local the model is, and the different scales and different areas of the geophysical model can be accurately disturbed by carrying out node operation (increasing nodes, reducing nodes and disturbing node values) on the existing tree structure.
(3) The tree structure model parameterization method of the invention uses multi-resolution analysis thought in image processing as a reference, and can store the low-frequency and high-frequency detail information of the model through the tree structure, thereby realizing the tree structure-based model parameterization. By changing the node information of the tree structure, the accurate disturbance of the whole or part of the geophysical model can be achieved.
(4) According to the method and the device, after corresponding processing is carried out before inverse wavelet transformation is carried out on the tree structure model, no matter what kind of operation for changing node information is carried out, the number of the node values participating in the wavelet transformation at each time is a fixed value, and the phenomenon that wavelet reconstruction obtains wrong disturbed geophysical model due to change of (node adding, node deleting and node disturbing values) of operation on the tree structure node is avoided.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of the conversion process of the tree structure to the geophysical model of the present invention;
FIG. 2 is a schematic diagram of the conversion process of the geophysical model of the present invention into a tree structure;
FIG. 3 is a diagram illustrating a wavelet transformation process of a one-dimensional model according to the present invention;
FIG. 4(a) is a non-uniform full binary tree representation of a one-dimensional model of the present invention, wherein the black filled nodes represent the existence of the node;
FIG. 4(b) is a model corresponding to a non-uniform full binary tree of the one-dimensional model of the present invention;
FIG. 5(a) is a non-uniform non-perfect binary tree representation of a one-dimensional model of the present invention, wherein a black solid node indicates the existence of the node;
FIG. 5(b) is a model corresponding to a non-uniform non-perfect binary tree of the one-dimensional model of the present invention;
FIG. 6(a) is a schematic diagram of a tree structure model in which only a root node exists in the present invention;
FIG. 6(b) is a schematic diagram of a model of the tree structure of the present invention with 2 levels;
FIG. 6(c) is a schematic diagram of a tree structure with 3 layers according to the present invention;
FIG. 6(d) is a schematic diagram of a tree structure with 4 layers according to the present invention;
FIG. 6(e) is a schematic diagram of a tree structure with 5 levels according to the present invention;
FIG. 7(a1) is a schematic diagram of a layer conductivity model after wavelet transform in accordance with the present invention;
FIG. 7(a2) is the result of the direct wavelet transform of FIG. 7(a1) of the present invention;
FIG. 7(b1) is a diagram of a two-layer conductivity model after wavelet transform in which darkened italic regions represent perturbation regions in accordance with the present invention;
FIG. 7(b2) is the result of the direct wavelet transform of FIG. 7(b1) of the present invention;
FIG. 7(c1) is a diagram of a three-layer conductivity model after wavelet transform in which the darkened italicized font areas represent disturbance areas in accordance with the present invention;
FIG. 7(c2) is the direct wavelet transform result of FIG. 7(c1) of the present invention;
FIG. 7(d1) is a diagram of a four-layer conductivity model after wavelet transform in accordance with the present invention, wherein the darkened italicized font areas represent perturbation regions;
FIG. 7(d2) is the direct wavelet transform result of FIG. 7(d1) of the present invention;
FIG. 7(e1) is a schematic diagram of a five-layer conductivity model after wavelet transform of the present invention, wherein the darkened, slanted font areas represent the perturbation regions;
fig. 7(e2) is the direct wavelet transform result of fig. 7(e1) of the present invention.
Wherein: sigma1、σ2、σ3、σ4、σ5、σ6、σ7And σ8Respectively represent discrete values;
s1、s2、s3and s4Respectively representing low-frequency approximate information of the geophysical model;
d1、d2、d3and d4Respectively representing third-level high-resolution high-frequency detail information of the geophysical model;
D1and D2High-frequency detail information respectively representing the second level resolution;
S1respectively representing the final low-frequency approximate information;
Ɗ1high frequency detail information representing the lowest level of resolution.
Detailed Description
Embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways, which are defined and covered by the claims.
Referring to fig. 1 and 2, in the method for perturbing model parameters through wavelet transformation provided by the present invention, perturbation of a geophysical model obtained through transformation is concentrated on a local tree structure sub-node and is represented as high-frequency detail information of the model, a tree structure root node covering the entire model region with perturbation of the geophysical model obtained through transformation is represented as low-frequency approximate information of the model, and the tree structure and the geophysical model are transformed through wavelet transformation, so as to realize decomposition or reconstruction of the geophysical model.
Preferably, the wavelet transform is a multi-resolution wavelet transform capable of representing a function as low frequency near information and high frequency detail information at different resolutions.
As a further embodiment of the invention: the decomposition method of the geophysical model comprises the following specific steps:
is provided with
Is a length of
Is a discrete sequence of
Then the sequence may
Is represented by the following function:
wherein the content of the first and second substances,
to obtain a set of functions for saving low frequency approximation information,
as a scale function, a function
Performing wavelet decomposition once to obtain
Wherein，
Being wavelet basis functions, coefficients of wavelet basis functions
Constitute half of the coefficients of the wavelet transform, and therefore it is necessary to preserve the high frequency part, while the low frequency part
Continuing to perform wavelet transform, repeating the process for a limited number of times to obtain final product
Is performed.
Equations (1) - (3) show the process of single wavelet decomposition,
obtained by single wavelet decomposition
And
in which the low frequency part
Can continuously execute wavelet transformation for limited times to finally obtain
Is performed.
The geophysical model can be represented by a series of discrete values, and the implementation of the method is illustrated below by a one-dimensional model with discrete values of 8.
The one-dimensional layered earth-electricity model can be represented by a one-dimensional array (see part (a) in fig. 3), for the decomposition of the geophysical model, a first-level wavelet transform is performed on the geophysical model to obtain a transformed model, and for the result of the first-level wavelet transform shown in part (b) in fig. 3, the same amount of low-frequency approximation information and high-frequency detail information can be obtained, and further, for the low-frequency approximation information, a plurality of wavelet transforms are performed until the decomposition cannot be performed again (see part (c) in fig. 3), so as to obtain final low-frequency approximation information S1And high frequency detail information at different resolutions (see section (d) in fig. 3): high frequency detail information Ɗ of lowest resolution1The high-frequency detail information of the second-level resolution and the high-frequency detail information of the third-level high resolution.
For the reconstruction of the geophysical model, the specific implementation steps are opposite to the decomposition of the geophysical model, and the model is completely reduced through inverse wavelet transformation under the condition that the low-frequency approximate information of the lowest resolution and the high-frequency detail information at different resolutions are known.
Preferably, the inverse wavelet transform is as follows: by the final transformation of the node values to the actual discrete values (σ), i.e. given the s, D and D values in fig. 4(a), fig. 4(b), fig. 5(a) and fig. 5(b), σ 1- σ 8 are solved back, which is embodied as follows: the third-stage inverse transform in section (c) of fig. 3 is based on the third-stage low-frequency approximation information S1High frequency detail information Ɗ with lowest resolution1Transforming to obtain s1, s2, and performing wavelet inverse transformation at the second level on the high-frequency detail information D of the second level resolution and the low-frequency approximation information s1, s2 at the second level1、D2Transforming to obtain first-stage low-frequency approximate information s1, s2, s3 and s4, wherein the first-stage inverse wavelet transform is composed of first-stage low-frequency approximate information s1, s2, s3 and s4 and third-stage high-resolution high-frequency detail information d1、d2、d3、d4And transforming to obtain final discrete values of the original model, namely a1, a2, a3, a4, a5, a6, a7 and a 8.
As a further embodiment of the invention: the non-uniform tree structure is suitable for wavelet transformation, wherein non-uniform means that the upper limits of the number of child nodes of a node are different, the complete and non-complete naming standard is whether the number of the nodes of the current tree structure reaches the maximum number of the nodes under the current depth level, and the complete tree structure is shown when the number of the nodes is the maximum, such as fig. 4(a) and fig. 4 (b); when the number of nodes is less than the maximum, the tree structure is not complete, as shown in FIG. 5(a) and FIG. 5 (b). The root node of the binary tree has only one child node, the rest nodes have two child nodes, the structure of the binary tree can be suitable for one-dimensional wavelet transformation, and the specific implementation steps are as follows: stored at the root node of the binary tree is low-frequency approximation information S similar to the model after the multiple wavelet transform in fig. 4(a) and 4(b)1（S1Representing an overall approximation of the model), the second level nodes (i.e., the children nodes under the root node) store the lowest level of resolution high frequency detail information Ɗ1And by analogy, the nodes of the following layers store high-frequency detail information on the resolution of each level.
Preferably, the low-frequency approximate information and the high-frequency detail information can be changed by changing the information thereof so as to achieve the disturbance to different areas of the model thereof.
As a further embodiment of the invention: in order to avoid the problem that in the process of converting the tree structure model into the geophysical model, the wavelet transformation is directly carried out on the current tree structure without setting any parameter, so that the obtained geophysical model cannot obtain a model which is locally disturbed theoretically when a new depth level child node (high-frequency detail information of the model with a higher resolution level) is added. Before wavelet transformation, the tree structure model needs to be processed as follows:
the method comprises the following steps: setting a maximum node depth level h aiming at the tree structure, wherein child nodes larger than the depth level cannot be generated;
step two: performing wavelet transformation on node values of all nodes within the depth level h of the tree structure, and defaulting the node values of empty nodes to be 0;
after the processing of the steps, no matter what kind of operation for changing node information is executed, the number of the node values participating in the wavelet transformation each time is a fixed value, and the phenomenon that the wavelet reconstruction obtains an incorrect disturbed geophysical model due to the change of the operation (node adding, node deleting and node disturbing values) on the nodes of the tree structure is avoided.
Taking the one-dimensional model as an example, when we set the maximum depth level of the tree structure nodes as h, the total number of the tree structure nodes is at most
Subdivision of geophysical model
And (5) dividing into equal parts. Referring to FIGS. 5(a) and 5(b), we set the maximum node depth level to 4 and the model is split into 8 equal parts, since the high frequency detail information d is saved3、d4The corresponding node does not exist (the node value is zero), the conductivity of the corresponding region cannot be disturbed after wavelet transformation, and the actually corresponding model is a five-layer model (the conductivity of the region models of the fourth layer to the eighth layer is equal).
As a further embodiment of the invention: the method for reconstructing the geophysical model comprises the following specific steps:
the method comprises the following steps: initializing a tree structure model: setting the initial model as a root node, and storing the low-frequency approximate information S of the model1=4.0；
Step two: setting the depth level h of the tree structure node: setting the maximum depth level h of the node as 5;
step three: adding model high-frequency detail information of different node depth levels: sequentially adding one sub-node at different depths, wherein the value of each sub-node is set to be 0.2;
step four: and (3) model conversion result: two schemes are used for carrying out conversion operation on the tree structure model, and a haar wavelet transform is taken as an example: (a) performing wavelet transformation on all node values within the node depth level 5 by using the method described herein, wherein the assignment of a nonexistent node is 0; (b) and (4) not setting the depth level of the node, and performing wavelet transformation on all node information of the current tree structure, wherein the value of the nonexistent node is 0.
Fig. 6(a) is a tree structure model in which only root nodes exist, when the maximum depth level is set, nodes that do not exist within the depth level are substituted into the calculation of the wavelet inverse transformation in the form of node values of 0, so that the one-layer conductivity model of fig. 7(a1) can be obtained, and when the maximum depth level is not set, the wavelet inverse transformation is directly performed, so that the one-layer conductivity model of fig. 7(a2) is obtained; fig. 6(b) adds a new depth child node on the basis of fig. 6(a), when the maximum depth level is set, the node that does not exist within the depth level is substituted into the calculation of the wavelet inverse transformation in the form of the node value being 0, so that the two-layer conductivity model of fig. 7(b1) can be obtained, the two-layer conductivity model of fig. 7(b2) can be obtained by directly performing the wavelet inverse transformation without setting the maximum depth level, and it can be seen from fig. 7(b1) that after the maximum depth level is set, when node information is added at a depth greater than the current depth, more local disturbance is generated, which completely conforms to the rule of wavelet transformation and the characteristic of local disturbance of high-frequency detail information at different depth levels; fig. 6(c) adds a new child node to the third depth based on fig. 6(b), when the maximum depth level is set, the node that does not exist within the depth level is substituted into the calculation of inverse wavelet transform in the form of node value 0, so as to obtain the three-layer conductivity model of fig. 7(c1), the three-layer conductivity model of fig. 7(c2) is obtained by directly performing inverse wavelet transform without setting the maximum depth level, and it can be seen from fig. 7(c1) that after the maximum depth level is set, when node information is added to a depth greater than the current depth, more local disturbance is generated, which completely conforms to the rule of wavelet transform and the characteristic of local disturbance of high-frequency detail information of different depth levels; fig. 6(d) adds a new child node to the fourth depth level based on fig. 6(c), when the maximum depth level is set, the node that does not exist within the depth level is substituted into the calculation of the inverse wavelet transform in the form of node value 0, so as to obtain the four-layer conductivity model of fig. 7(d1), the inverse wavelet transform is directly performed without setting the maximum depth level, so as to obtain the four-layer conductivity model of fig. 7(d2), and it can be seen from fig. 7(d1) that after the maximum depth level is set, when node information is added to a depth greater than the current depth, more local disturbance is generated, which completely conforms to the rule of wavelet transform and the characteristic of local disturbance of high-frequency detail information of different depth levels; fig. 6(e) adds a new sub-node to the fifth depth level on the basis of fig. 6(d), when the maximum depth level is set, the node that does not exist within the depth level is substituted into the calculation of the inverse wavelet transform in the form of node value 0, so that the five-layer conductivity model of fig. 7(e1) can be obtained, and when the inverse wavelet transform is directly performed without setting the maximum depth level, the five-layer conductivity model of fig. 7(e2) can be obtained, and it can be seen from fig. 7(e1) that after the maximum depth level is set, when node information is added at a depth greater than the current depth, more local disturbance is generated, which completely conforms to the law of the wavelet transform and the characteristics of local disturbance of high-frequency detail information at different depth levels, and it can be seen from fig. 7(a1), fig. 7(b1), fig. 7(c1), fig. 7(d1) and fig. 7(e1), because the added nodes are the first sub-nodes of each layer, the fixed disturbance area corresponds to the local surface area of the layer model.
The geophysical models (the models shown in fig. 7(a2), fig. 7(b2), fig. 7(c2), fig. 7(d2) and fig. 7(e 2)) obtained by directly performing wavelet transform on the tree structure are wrong, because node values of sub-nodes with different depth levels (high-frequency detail information of the models with different resolution levels) are added, because the depth level of the current node is changed continuously, the subdivision scale of the obtained geophysical model is changed constantly, so that the purpose of theoretically disturbing a more local region of the model cannot be achieved, and the concept of wavelet transform multi-resolution analysis is violated;
and the geophysical model (the models shown in fig. 7(a1), fig. 7(b1), fig. 7(c1), fig. 7(d1) and fig. 7(e 1)) obtained by setting the depth levels of the nodes of the tree structure and then performing wavelet transformation can be seen from the graph, when child nodes (high-frequency detail information of different resolution levels of the model) with larger depth levels appear, the model disturbance region is more local, the wavelet transformation multi-resolution analysis idea is completely embodied, and the tree structure parameterization for correctly obtaining the geophysical model and the correct local region disturbance of the child nodes corresponding to the model are realized.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (4)
1. A method for disturbing model parameters of wavelet transform is characterized in that: representing the disturbance of the geophysical model obtained after transformation, which is concentrated on local tree-shaped structure sub-nodes, as high-frequency detail information of the model, representing the tree-shaped structure root node covering the whole model area with the disturbance of the geophysical model obtained after transformation as low-frequency approximate information of the model, and accurately achieving the disturbance of different areas and different scales of the geophysical model by adopting the operations of increasing the sub-nodes or the root nodes, reducing the sub-nodes or the root nodes and changing the values of the sub-nodes or the root nodes to generate a new model; converting the tree structure and the geophysical model through wavelet transformation to realize the decomposition or reconstruction of the geophysical model;
the disturbance of the transformed geophysical model by the tree-structure child nodes is more concentrated in local parts, the disturbance area of the transformed geophysical model by the tree-structure root node covers the whole model area, and operation is performed in a mode of increasing nodes, reducing nodes or changing node values through different nodes, so that the disturbance of different areas and different scales of the geophysical model is accurately achieved, and a new model is generated;
the method for decomposing the geophysical model adopts a tree structure to represent the geophysical model and comprises the following specific steps:
s1: setting the maximum tree structure layer number, converting the geophysical model into the deepest tree structure at one time, and then performing wavelet transformation on the finest grid to obtain low-frequency approximate information with the same quantity and high-frequency detail information under the corresponding resolution;
s2: saving high-frequency detail information under corresponding resolution;
s3: performing wavelet transformation on the low-frequency approximate information obtained after the wavelet transformation again to obtain the same amount of low-frequency approximate information and high-frequency detail information under the corresponding resolution;
s4: repeating the steps S2 and S3 until low-frequency approximate information of the lowest resolution and high-frequency detail information under the lowest resolution are obtained, and completing the decomposition of the geophysical model;
the method for reconstructing the geophysical model specifically comprises the following steps: under the condition that low-frequency approximate information of the lowest-level resolution ratio and high-frequency detail information under different resolution ratios are known, reconstruction of the geophysical model is achieved through inverse wavelet transformation;
wherein: the high-frequency detail information and the low-frequency approximate information respectively refer to a high-frequency component and a low-frequency component of the image, the low-frequency component describes information in a large range, the high-frequency component describes specific details, and in the gray-scale image, an area with small brightness change is mainly the low-frequency component, and an area with strong brightness change is mainly the high-frequency component.
2. The model parameter perturbation method of claim 1, wherein: if the number of discrete values included in the geophysical model is M, the number N of wavelet transforms of the geophysical model is, correspondingly: m2N。
3. The model parameter perturbation method of claim 1, wherein: the specific inverse wavelet transform mode is as follows: the node values through the tree structure model are finally transformed to the actual geophysical model parameter values.
4. The model parameter perturbation method of claim 3, wherein: before performing inverse wavelet transform on the tree structure model, the following processing is required:
1) setting a maximum node depth level h aiming at the tree structure, wherein child nodes larger than the depth level cannot be generated;
2) and performing wavelet transformation on node values of all nodes within the depth level h of the tree structure, wherein the node values of null nodes which are not existed are defaulted to be 0.
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