A variable factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes

Abstract

The present invention relates to the field of gravity and magnetic data inversion, and specifically to a variable-factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes, comprising the following steps: constructing a constrained inversion objective function using gravity and magnetic data, gravity and magnetic gradient data, and constraint information; iteratively solving the physical properties of the constrained inversion objective function; dynamically adjusting a weight factor based on the size of a model constraint term and a distortion degree calculation formula, then substituting the adjusted weight factor into the constrained inversion objective function for iterative solution, calculating the physical property distortion degree and the data fitting term, and the physical properties obtained by the iteration when the requirements are met are the results. Based on the feedback mechanism of physical property characteristics during the iteration process, the present invention establishes a constraint term weight factor that first becomes extremely small, then increases, and finally becomes 0. The constraint term weight factor is used to achieve high-precision constrained inversion constrained by information such as borehole physical properties and seismic interpretation structure, and can adaptively improve constraint performance and avoid distortion of inversion results.

Description

Technical Field

[0001] The present invention relates to the field of gravity and magnetic data inversion, and in particular to a gravity and magnetic data variable factor constrained inversion method based on physical property change feedback. Background Art

[0002] Gravity and magnetic potential field data inversion is a method of inverting the distribution of underground physical properties using observed gravity and magnetic data. It requires dividing the underground space to be inverted into closely arranged grid cells, and establishing a kernel function matrix through the forward formula of the grid cell at the surface observation point under unit physical property. Then, a linear equation system is established using the measured gravity and magnetic data at the observation point, the kernel function matrix and the unknown physical properties at each grid cell. By solving the linear equation system, the physical property values ​​at the underground grid cell that fits the gravity and magnetic data are obtained. The commonly used solution method is an iterative solution method such as the conjugate gradient method.

[0003] In the inversion of gravity and magnetic potential field data, since the number of unknowns representing the physical properties of the subdivided units is much greater than the number of observation points, the inversion result is a least squares solution, which has multiple solutions. Prior information such as physical properties obtained through drilling or interfaces from seismic interpretation can be added as constraint information to the inversion, forming a constrained inversion method. Under the premise of meeting the characteristics of gravity and magnetic data, the inversion results are more closely matched with the prior information. There is a weight factor in constrained inversion to balance the intensity of the constraint information and the gravity and magnetic data fitting effect. If the weight factor is too small, the constraint information will not work, and the improvement of the inversion result accuracy will be limited. If the weight factor is too large, the constraint information intensity will be too high, and the inversion result will be distorted.

[0004] The size of the weight factor depends on many factors, including the subdivision scheme, observation point location, type of constraint information, and the state of the inversion results. The complex nature of these factors makes it difficult to obtain the optimal weight factor in practice. Furthermore, high-resolution constraint information can lead to a more pronounced effect of the constraint weight factor, which can easily distort the inversion results. Existing methods for estimating weight factors often rely on optimization or trial-and-error methods, but these methods have limited applicability and yield suboptimal results. Existing adaptive weight factor schemes still rely on empirical parameters to control how the weight changes with the number of iterations. This similarly requires multiple trials and errors to select a suitable range and fails to consider the state of the inversion results at each iteration. Summary of the Invention

[0005] The existing methods for selecting weight factors in constrained inversion are not effective, and the adaptive adjustment scheme still requires manual participation and takes insufficient factors into consideration. To this end, the present invention establishes a variable factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes, establishes a feedback mechanism for each physical property in the iterative solution process, and adaptively controls the weight factors of the constraint items by evaluating the degree of match between the physical property results of each iteration and the constraint information and the degree of distortion of the physical property results, thereby achieving better constraint effects in constrained inversion. The present invention provides the following technical solutions:

[0006] A variable factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes includes the following steps:

[0007] The first step is to construct a constrained inversion objective function using gravity and magnetic data, gravity and magnetic gradient data, and constraint information;

[0008] The second step is to iteratively solve the physical properties of the constrained inversion objective function;

[0009] The third step is to dynamically adjust the weight factor based on the size of the model constraint term and the distortion degree calculation formula, and then substitute the adjusted weight factor into the constrained inversion objective function for iterative solution to calculate the degree of physical property distortion and data fitting terms. When the requirements are met, the physical properties obtained by iteration are the results.

[0010] As a further solution of the present invention: the constraint information includes geological information, drilling information, interface information, etc.

[0011] As a further solution of the present invention: the constrained inversion objective function is:

[0012] ，A is the kernel function matrix, m For physical properties, d For geophysical data, W d is the weighted matrix in the weighted constraint term, m 0 is the known physical property constraint, u It is used to balance the data fitting terms in the formula and model constraints Weight factors for the two 2-norm terms.

[0013] As a further solution of the present invention: the distortion degree calculation formula is: ,in, m x 、 m y 、 m z For iterative inversion of physical properties x 、 y 、 z Gradients in three directions, The weights for evaluating distortion in different directions.

[0014] As a further solution of the present invention, dynamically adjusting the weight factor according to the size of the model constraint term and the distortion degree calculation formula includes the following steps:

[0015] In the iterative solution process, the results of two consecutive iterations are brought into the model constraint terms. When the model constraint calculated by the latter iteration result is not less than the model constraint term calculated by the previous iteration result, the weight factor becomes larger;

[0016] In the iterative solution process, the results of two consecutive iterations are brought into the model constraint terms. When the model constraint calculated by the latter iteration result is less than the model constraint term calculated by the previous iteration result, the weight factor remains unchanged.

[0017] During the iterative solution process, the results of two consecutive iterations are substituted into the distortion degree calculation formula. When the result of the latter distortion degree calculation is much greater than that of the previous distortion degree calculation, the weight factor becomes 0, and the result of the previous iteration is used to continue the iterative solution.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] Based on the feedback mechanism of physical property characteristics during the iterative process, the present invention establishes a constraint item weight factor that first becomes extremely small, then increases, and finally becomes 0. The constraint item weight factor is used to achieve high-precision constrained inversion constrained by information such as borehole physical properties and seismic interpretation structure. It can adaptively improve the constraint performance and avoid distortion of the inversion results. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Flowchart of a variable factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes in an embodiment of the present invention.

[0021] Figure 2 Figure 1 shows two examples of magnetic anomalies and their zoning effects for a cube model, according to an embodiment of the present invention. (a) shows the magnetic forward modeling results and model distribution for the prismatic model; (b) shows a slice of the unconstrained inversion results for the prismatic model; (c) shows a slice of the conventional constrained inversion results for the prismatic model; and (d) shows a slice of the variable-factor constrained inversion results for the prismatic model according to the present invention. DETAILED DESCRIPTION

[0022] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0023] In order to achieve three-dimensional physical property inversion with clear structure to meet the needs of accurately interpreting physical property distribution, and avoid the problem of high-resolution constraint information causing distortion of inversion results when constrained, the constraint item weight factor is dynamically adjusted. The method of the present invention will increase the constraint item weight factor from a very small level to a level that can effectively improve the inversion result as the objective function is solved iteratively, maintain stability in the subsequent iterations, and reduce the constraint item weight back to a very small level before the inversion result is distorted. In this process, the constraint item factor first increases and then decreases, forming an arched weight factor change curve, so it is called an "arched" constrained inversion method.

[0024] 1. Adaptive constraint factor increase mechanism based on model constraint feedback

[0025] The objective function of physical property inversion of gravity and magnetic data is shown in formula (1).

[0026] .

[0027] in, A is the kernel function matrix, m For physical properties, d For geophysical data, W d is the weighted matrix in the weighted constraint term, m 0 is the known physical property constraint, u It is used to balance the data fitting terms in the formula and model constraints The weight factors of the two bi-norm terms directly affect the constraint effect.

[0028] By analyzing the correlation between the characteristics of the inversion results and the amplitude of the constraint items in each iteration, the constraint item weight factor is adjusted based on this. u Real-time adjustments are made to better play the role of constraints. Specifically, the weight factor is initially selected as 0.001, and the physical properties of the two iterations before and after the inversion are compared. m Computed ,when As the iteration increases, the weight factor u Unchanged, when As the iteration decreases, the weight factor u Become 10 times the original.

[0029] When it is a structural model constraint, the prior structural model constraint uses the difference between the prior structural information interpreted by seismic and drilling and the structural results of the physical properties obtained by inversion to control the inversion results. Its form is shown in formula (2):

[0030] .

[0031] in,F It is a matrix with element values ​​of 0 or 1. Its function is to extract the units with known physical properties to control the range of the constrained unit body. D z It is the difference matrix in the vertical direction, which is used to calculate the physical properties of each unit. z Directional gradient, v 0 is the known physical property gradient obtained from seismic or drilling. Replacing the vertical physical property gradient with a cross gradient can further constrain the 3D physical property structure information.

[0032] Similarly, by analyzing the correlation between the characteristics of the inversion results and the amplitude of the constraint items in each iteration, the constraint item weight factor is adjusted based on this. u Real-time adjustments are made to better play the role of constraints. Specifically, the weight factor is initially selected as 0.001, and the physical properties of the two iterations before and after the inversion are compared. m Computed ,when As the iteration increases, the weight factor u Unchanged, when As the iteration decreases, the weight factor u Become 10 times the original.

[0033] 2. Adaptive constraint factor reduction mechanism based on distortion evaluation formula feedback

[0034] When the resolution of the prior information is much higher than the physical property inversion result, the local constraint weight is too large, which will lead to a significant resolution difference between the internal physical properties and the unconstrained physical properties, resulting in distortion of the inversion result. Therefore, the evaluation formula for the degree of physical property distortion is designed. D , which is used as feedback information to timely improve the distortion of physical property results caused by excessive weight of constraint items during the iterative solution process. The distortion degree evaluation formula is shown in formula (3)

[0035] .

[0036] in, m x 、 m y 、 m z For iterative inversion of physical properties x 、 y 、 z The gradients in three directions are used to analyze whether there are unexpected property mutations in the inversion results. The weights for evaluating distortion in different directions are related to the expected trend of the known constraint information structure, thereby reducing the impact of expected physical property mutations. The present invention establishes a correlation between the inversion iterative physical property results and the effects of the constraint terms, thereby adaptively adjusting the constraint term weight factors. DThe value of suddenly increases significantly during the iteration process, indicating that distortion occurs. At this time, select the previous iteration result to continue iterative inversion and set the constraint weight factor u Set it to 0 to achieve the best effect of the constraint item without giving a constraint item weight factor.

[0037] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0038] See Figure 1-Figure 2 , Figure 2 (a) is the position of the prism model and its corresponding abnormal data, Figure 2 (b) is the slice result of the unconstrained inversion result at y=2000 meters. Figure 2 (c) is a slice display of the traditional constrained inversion result at y = 2000 meters; (d) is a slice display of the variable factor constrained inversion result of the method of the present invention at y = 2000 meters, Figure 2 The white dashed line in the middle indicates the actual prism boundary position. Figure 2 (b) and the unconstrained inversion shown in Figure 2 (c) shows the traditional constrained inversion. It can be seen that the traditional constrained inversion will be distorted. The constrained inversion of the underground prism based on the magnetic data of the borehole physical properties is calculated by the method of the present invention. The inversion results are as follows Figure 2 (d) As shown, from Figure 2 It can be seen from the figure that the method of the present invention can accurately obtain the position and boundary of the prism. Compared with the unconstrained inversion result, the inversion result of the present invention is more accurate and has no distortion compared with the traditional constrained inversion.

[0039] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A variable factor constrained inversion method for gravity and magnetic data based on feedback of physical property changes, characterized in that: The following steps are involved: The first step is to construct a constrained inversion objective function using gravity and magnetic data, gravity and magnetic gradient data, and constraint information; The second step is to iteratively solve the physical properties of the constrained inversion objective function; The third step is to dynamically adjust the weight factor according to the size of the model constraint term and the distortion degree calculation formula. Then, the adjusted weight factor is substituted into the constrained inversion objective function for iterative solution. The physical property distortion degree and data fitting term are calculated. When the requirements are met, the physical property obtained by iteration is the result. The distortion degree calculation formula is: ,in, m x 、 m y 、 m z For iterative inversion of physical properties x 、 y 、 z Gradients in three directions, The weights for evaluating distortion in different directions.

2. The variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback according to claim 1 is characterized in that: The constraint information includes geological information, drilling information and interface information.

3. The variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback according to claim 1 or 2, characterized in that: The constrained inversion objective function is: , A is the kernel function matrix, m For physical properties, d For geophysical data, W d is the weighted matrix in the weighted constraint term, m 0 is the known physical property constraint, u It is used to balance the data fitting terms in the formula and model constraints Weight factors for the two 2-norm terms.

4. The variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback according to claim 1 is characterized in that: The dynamic adjustment of the weight factor according to the size of the model constraint term and the distortion degree calculation formula includes the following steps: In the iterative solution process, the results of two consecutive iterations are brought into the model constraint terms. When the model constraint calculated by the latter iteration result is not less than the model constraint term calculated by the previous iteration result, the weight factor becomes larger; In the iterative solution process, the results of two consecutive iterations are brought into the model constraint terms. When the model constraint calculated by the latter iteration result is less than the model constraint term calculated by the previous iteration result, the weight factor remains unchanged. During the iterative solution process, the results of two consecutive iterations are substituted into the distortion degree calculation formula. When the result of the latter distortion degree calculation is much greater than that of the previous distortion degree calculation, the weight factor becomes 0, and the result of the previous iteration is used to continue the iterative solution.

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