Gravity and magnetic data variable factor constraint inversion method based on physical property change feedback

Abstract

The invention relates to the field of gravity and magnetic data inversion, in particular to a gravity and magnetic data variable factor constraint inversion method based on physical property change feedback, which comprises the following steps: constructing a constraint inversion objective function by using gravity and magnetic data, gravity and magnetic gradient data and constraint information; iteratively solving the physical property of the constrained inversion objective function; the weight factor is dynamically adjusted according to the size of a model constraint term and a distortion degree calculation formula, then the adjusted weight factor is substituted into a constraint inversion objective function for iterative solution, the physical property distortion degree and a data fitting term are calculated, and when the requirement is met, the physical property obtained through iteration is the result. According to the method, based on a physical characteristic feedback mechanism in the iteration process, the constraint term weight factor which is firstly minimum, then increased and finally zero is established, high-precision constraint inversion of information constraints such as borehole physical properties and seismic interpretation structures is achieved through the constraint term weight factor, the constraint performance can be improved in a self-adaptive mode, and distortion of inversion results is avoided.

Description

Technical Field

[0001] The 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 underground physical property distribution 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 cells that fit 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 larger 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 of seismic interpretation can be added to the inversion as constraint information to form 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 the constrained inversion, which is used to balance the intensity ratio of the constraint information effect 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 large, and the inversion result will be distorted.

[0004] The size of the weight factor is related to many factors such as the segmentation scheme, the location of the observation point, the type of constraint information, the state of the inversion result, etc. Its rules are complex, which makes it difficult to obtain the best weight factor in practice. In addition, high-resolution constraint information will make the effect of the constraint weight factor more obvious, which is easy to cause distortion of the inversion result. Most existing methods are based on optimization methods or trial and error methods to estimate the weight factor, but the scope of application is limited and the effect is not ideal. The existing adaptive adjustment of the weight factor scheme still needs to control the change of the weight with the number of iterations through empirical parameters. It also requires multiple trials and errors to select a more appropriate range of changes and does not consider the state of the inversion results of each iteration. Summary of the invention

[0005] The existing methods for selecting weight factors in constrained inversion have poor effects. The adaptive adjustment scheme still requires manual participation and insufficient consideration factors. Therefore, the present invention establishes a variable-factor constrained inversion method for gravity and magnetic data based on physical property change feedback, establishes a feedback mechanism for physical properties at each time during the iterative solution process, and adaptively controls the weight factors of the constraint terms by evaluating the matching degree between the physical property results of each iteration and the constraint information and the distortion degree of the physical property results, so as to achieve a better constraint effect in constrained inversion. The present invention provides the following technical solutions: A variable-factor constrained inversion method for gravity and magnetic data based on physical property change feedback, comprising the following steps: First step, constructing a constrained inversion objective function by using gravity and magnetic data, gravity and magnetic gradient data, and constraint information; Second step, iteratively solving for physical properties of the constrained inversion objective function; Third step, dynamically adjusting the weight factor according to the size of the model constraint term and the 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 when the requirements are met, the physical property obtained by iteration is the result.

[0006] As a further solution of the present invention: The constraint information includes geological information, borehole information, interface information, etc.

[0007] As a further solution of the present invention: The constrained inversion objective function is: ，A is the kernel function matrix, m is the physical property, d is the geophysical data, W d is the weighting matrix in the weighted constraint term, m 0 is the known physical property constraint, u is used to balance the data fitting term and the model constraint term in the formula, and is the weight factor for balancing the two two-norm terms.

[0008] As a further solution of the present invention: The distortion degree calculation formula is: , where m x , m y , m z are the gradients of the iterative inversion physical property in the x , y , z three directions, are the distortion evaluation weights in different directions.

[0009] 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: During the iterative solution process, substitute the results of two consecutive iterations into the model constraint term. 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; During the iterative solution process, substitute the results of two consecutive iterations into the model constraint term. 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, substitute the results of two consecutive iterations into the distortion degree calculation formula. When the latter distortion degree calculation result is much larger than the previous distortion degree calculation result, the weight factor becomes 0, and the previous iteration result is used to continue the iterative solution.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the physical property feature feedback mechanism during the iterative process, the present invention establishes a constraint term weight factor that first decreases, then increases, and finally becomes 0. Using the constraint term weight factor, high-precision constrained inversion with information constraints such as borehole physical properties and seismic interpretation structures is realized, which can adaptively improve the constraint performance and avoid the distortion of the inversion results. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flowchart of the variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback in an embodiment of the present invention.

[0012] Figure 2 It is an example of magnetic anomalies and a partition effect diagram of two cubes in an embodiment of the present invention. Among them, (a) is the magnetic forward modeling result and model distribution of the prism model; (b) is the slice of the unconstrained inversion result of the prism model; (c) is the slice of the traditional constrained inversion result of the prism model; (d) is the slice of the variable factor constrained inversion result of the prism model of the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0013] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0014] To meet the requirement of accurately interpreting the physical property distribution in 3D physical property inversion with clear structure, and to avoid the problem of inversion result distortion caused by high-resolution constraint information during constraint, the weight factor of the constraint term is dynamically adjusted. In the method of the present invention, the weight factor of the constraint term will be increased from a minimum to a level that can effectively improve the inversion result as the objective function is solved iteratively, remain stable in the subsequent several iterations, and the weight of the constraint term will be reduced back to the minimum before the inversion result is distorted. The process of first increasing and then decreasing the constraint term factor will form an arched weight factor change curve, so it is called the "arch" type constraint inversion method.

[0015] 1. Adaptive constraint term factor increasing mechanism based on model constraint term feedback The objective function of physical property inversion of gravity and magnetic data is shown in formula (1).

[0016] 。

[0017] Among them, A is the kernel function matrix, m is the physical property, d is the geophysical data, W d is the weighting matrix in the weighted constraint term, m 0 is the known physical property constraint, u is used to balance the data fitting term and the model constraint term in the formula. The amplitude of the two two-norm terms directly affects the constraint effect.

[0018] By analyzing the correlation between the characteristics of the inversion result and the amplitude of the constraint term in each iteration process, the weight factor u of the constraint term is adjusted in real time based on this, so as to better play the role of constraint. Specifically, the weight factor is initially selected as 0.001. By comparing the physical properties m calculated before and after two consecutive iterations of the inversion , when increases with iteration, the weight factor u remains unchanged. When decreases with iteration, the weight factor u becomes 10 times the original.

[0019] When it is a structural model constraint, the prior structural model constraint uses whether the difference between the prior structural information interpreted by seismic, borehole, etc. and the structural result of the physical property obtained by inversion is close to the minimum to control the inversion result. Its form is shown in formula (2) 。

[0020] Among them, FA matrix with element values of 0 or 1, which is used to extract known physical property units to control the range of constrained unit bodies. D z A difference matrix in the vertical direction, which is used to calculate the z directional gradient of the physical properties of each unit. v 0 is the known physical property gradient obtained based on seismic or borehole data. By changing the vertical physical property gradient to a cross-gradient, the three-dimensional physical property structure information can be further constrained.

[0021] Similarly, by analyzing the correlation between the characteristics of the inversion results and the amplitudes of the constraint terms during each iteration, the weight factor of the constraint term u is adjusted in real time to better exert the constraint effect. Specifically, the weight factor is initially selected as 0.001. By comparing the physical properties m calculated before and after two consecutive iterations of the inversion , when increases with iteration, the weight factor u remains unchanged; when decreases with iteration, the weight factor u becomes 10 times the original.

[0022] 2. Adaptive constraint term factor reduction mechanism based on the feedback of the distortion evaluation formula When the resolution of the prior information is much higher than the physical property inversion results, due to the excessive local constraint weight, there will be a significant resolution difference between the internal physical properties and the unconstrained physical properties, resulting in distortion of the inversion results. Therefore, a physical property distortion degree evaluation formula D is designed to use it as feedback information to timely improve the distortion of the physical property results caused by the excessive weight of the constraint term during the iterative solution process. The distortion degree evaluation formula is shown in formula (3) .

[0023] Among them, m x , m y , m z are the gradients of the iterative inversion physical properties in the x , y , z three directions to analyze whether there are unexpected physical property mutations in the inversion results. is the distortion evaluation weight in different directions, and its weight value is related to the expected trend of the known constraint information structure to weaken the influence of the physical property mutations that meet the expectations. The present invention establishes the correlation between the inversion iterative physical property results and the action of the constraint term to adaptively adjust the weight factor of the constraint term. When DThe value of u suddenly increases significantly during the iteration process, indicating that distortion occurs. At this time, select the previous iteration result to continue the iterative inversion and set the weight factor of the constraint term

[0024] to 0, so as to achieve the best effect of the constraint term without giving the weight factor of the constraint term.

[0025] Refer to Figure 1 - Figure 2 , Figure 2 Figure (a) shows the position of the prism model and its corresponding abnormal data. Figure 2 Figure (b) shows the slice result display of the unconstrained inversion result at y = 2000 m. Figure 2 Figure (c) shows the slice result display of the traditional constrained inversion result at y = 2000 m; Figure (d) shows the slice result display of the variable factor constrained inversion result of the method of the present invention at y = 2000 m. Figure 2 The white dotted line in Figure 2 indicates the position of the true prism boundary. By comparing Figure 2 the unconstrained inversion shown in Figure (b) and the traditional constrained inversion shown in Figure 2 Figure (c), it can be seen that the traditional constrained inversion will have distortion. By calculating the constrained inversion of the magnetic data of the underground prism based on borehole physical properties by the method of the present invention, the inversion result is as shown in Figure 2 Figure (d). It can be seen from

[0026] 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 there is no distortion compared with the traditional constrained inversion.

Claims

1. A variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback, characterized in that It includes the following steps: In the first step, a constrained inversion objective function is constructed using gravity and magnetic data, gravity and magnetic gradient data, and constraint information; In the second step, the physical properties are iteratively solved for the constrained inversion objective function; In the third step, the weight factor is dynamically adjusted based on the magnitude of the model constraint term and the distortion degree calculation formula, and then the adjusted weight factor is substituted into the constrained inversion objective function for iterative solution to calculate the physical property distortion degree and the data fitting term. When the requirements are met, the physical properties obtained from the iteration are the results.

2. The variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback according to claim 1, wherein The constraint information includes geological information, borehole information, and interface information.

3. The method for constrained inversion of gravity and magnetic data with variable factors 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 is the physical property, d is the geophysical data, W d is the weighting matrix in the weighted constraint term, m 0 is the known physical property constraint, u is used to balance the data fitting term and the model constraint term for the two weight factors of the two - norm terms.

4. The variable factor constrained inversion method for gravity and magnetic data based on physical property change feedback according to claim 1, characterized in that The calculation formula for the distortion degree is as follows: , where m x , m y , m z are the gradients of the iterative inversion physical properties in x , y , z three directions, and are the distortion evaluation weights in different directions.

5. The method for constrained inversion of gravity and magnetic data with variable factors based on physical property change feedback according to claim 1, wherein The dynamic adjustment of the weight factor based on the magnitude of the model constraint term and the distortion degree calculation formula includes the following steps: During the iterative solution process, the results of two consecutive iterations are substituted into the model constraint term. When the model constraint calculated from the result of the latter iteration is not less than the model constraint term calculated from the result of the previous iteration, the weight factor increases; During the iterative solution process, the results of two consecutive iterations are substituted into the model constraint term. When the model constraint calculated from the result of the latter iteration is less than the model constraint term calculated from the result of the previous iteration, 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 calculated result of the distortion degree in the latter iteration is much larger than that in the previous iteration, the weight factor becomes 0, and the iteration continues using the result of the previous iteration.

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