A method for simultaneous inversion of free parameters and Moho surface based on a constant density model

Abstract

This invention provides a method for simultaneous inversion of free parameters and the Moho surface based on a constant density model, comprising: estimating initial values ​​of the free parameters of the constant density model based on the Moho surface gravity anomaly and its constraint depth; the free parameters of the constant density model include constant offset and residual density; inverting the Moho surface depth using a fast inversion method based on the latest calculated values ​​of the free parameters of the constant density model using a dual-interface gravity field model; outputting the free parameters of the constant density model and its inverted Moho surface depth when the stopping iteration condition is met; and updating the iterative values ​​of the free parameters of the constant density model using a linear regression relationship between the constraint depth and the inverted depth of the Moho surface when the stopping iteration condition is not met. This invention, by establishing a linear regression relationship between the constraint depth and the inverted depth of the Moho surface, can accurately estimate the free parameters of the constant density model, achieving simultaneous inversion of the free parameters of the constant density model and the Moho surface depth.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and in particular to a method for simultaneous inversion of free parameters and the Moho surface based on a constant density model. Background Technology

[0002] The undulations of the Moho discontinuity are often associated with the distribution of oil, gas, and metallic mineral resources, but since they are located deep within the Earth, indirect exploration using geophysical methods is necessary. Traditional geophysical exploration encompasses four directions: gravity, magnetism, electromagnetism, and seismicity. Among these, seismic and gravity exploration are the mainstream methods for detecting Moho discontinuities. Deep reflection seismic exploration offers high accuracy but is often conducted in the form of profiles. Gravity exploration is convenient for detecting the Moho discontinuity from a surface perspective, but requires known depth constraints.

[0003] The gravity anomaly constant migration mainly affects the mean depth of the Moho inversion results, while the residual density mainly affects the magnitude of the Moho undulation difference. There are currently two main methods for selecting the residual density. The first method uses the empirical relationship between density and seismic wave velocity to obtain the densities of the crust and mantle separately, and then calculates the Moho residual density; this method is greatly affected by the accuracy of the empirical formula. The second method directly estimates the residual density using an approximate relationship between gravity anomaly and depth; this method is generally affected by the distribution and number of constraint points. Fedi (1997) proposed using the slope of the linear regression of gravity anomaly with unit density forward gravity anomaly as the constant residual density estimate. Florio (2018) developed Fedi's constant residual density estimation method and applied it to basement inversion studies. Li et al. (2022) improved Fedi and Florio's constant residual density estimation method and inverted the Moho depth in the South China Sea. However, the estimation of the constant migration value has not yet been reported. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide a method for simultaneous inversion of free parameters and the Moho surface based on a constant density model.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for simultaneous inversion of free parameters and the Moho surface based on a constant density model includes:

[0007] Step 1: Obtain the Moho gravity anomaly and its Moho constraint depth;

[0008] Step 2: Estimate the initial values ​​of the free parameters of the constant density model based on the Moho gravity anomaly and the Moho constraint depth; the free parameters of the constant density model include constant offset and residual density;

[0009] Step 3: Based on the k-th iteration value of the free parameters of the constant density model, the depth of the Moho surface is inverted using the fast inversion method of the dual-interface gravity field model;

[0010] Step 4: When the stopping iteration condition is met, output the free parameters of the constant density model and its Moho inversion depth;

[0011] Step 5: When the stopping iteration condition is not met, update the free parameter values ​​of the constant density model in the (k+1)th iteration using the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth, set k+1 to k, and return to step 3.

[0012] Preferably, step 2: estimating the iterative initial values ​​of the free parameters of the constant density model based on the Moho gravity anomaly and its Moho constraint depth includes:

[0013] Using the Bouguer plate formula, a linear regression relationship between the Moho surface constraint depth and the Moho surface gravity anomaly is established.

[0014] Based on the Moho surface gravity anomaly and the linear regression relationship between the Moho surface constraint depth, a linear fitting function is obtained.

[0015] The initial values ​​of the free parameters of the constant density model are estimated using the linear fitting function.

[0016] Preferably, the linear regression equation is:

[0017]

[0018] Among them, h i Indicates the constraint depth. This indicates a gravity anomaly at the Mohorovičić discontinuity at the constraint point. Represents the first fitted parameter. This represents the second fitting parameter, and the initial value of the constant offset during iteration is... The initial value for the iteration of the remaining density is G is the gravitational constant.

[0019] Preferably, in step 5, the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth is as follows:

[0020] h i =a k h ki +b k

[0021] Among them, h ki Let a represent the depth of the Moho at the constraint point obtained by inverting the free parameter values ​​using the k-th iteration. k b represents the first regression coefficient. kDenotes the second regression coefficient, and the initial value of the updated residual density in the iteration is... The iterative initial value of the updated constant offset is c. k+1 =c k -2πGσ k+1 b k , σ k c represents the residual density after the k-th iteration. k This represents the constant offset after the k-th iteration.

[0022] The present invention also provides an electronic device, including a bus, a transceiver, a memory, a processor, and a computer program stored in the memory and executable on the processor. The transceiver, the memory, and the processor are connected via the bus. When the computer program is executed by the processor, it implements the steps in the above-mentioned method for simultaneous inversion of free parameters and Moho surface based on a constant density model.

[0023] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps in the above-described method for simultaneous inversion of free parameters and Moho surface based on a constant density model.

[0024] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0025] This invention provides a method for simultaneous inversion of free parameters and Moho surface based on a constant density model. Compared with the prior art, this invention can accurately estimate the free parameters of the constant density model by establishing a linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth, thus achieving simultaneous inversion of the free parameters of the constant density model and the Moho surface depth. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 The flowchart illustrates a method for simultaneously inverting free parameters and the Moho surface based on a constant density model, as provided in this invention.

[0028] Figure 2 The distribution map of Moho gravity anomaly and depth constraint points provided by this invention.

[0029] Figure 3 This is a map showing the true depth distribution of the Moho surface provided by the present invention.

[0030] Figure 4 This is a scatter plot of Moho gravity anomaly and constraint depth provided by the present invention.

[0031] Figure 5 The Moho surface inversion error iterative convergence curve provided by this invention.

[0032] Figure 6 The iterative convergence curve of the free parameter estimate of the constant density model provided by this invention.

[0033] Figure 7 The depth map of the Moho inversion provided by this invention.

[0034] Figure 8 The Moho inversion error diagram provided by this invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] To achieve the above objectives, the present invention provides the following solution:

[0037] A method for simultaneous inversion of free parameters and the Moho surface based on a constant density model includes:

[0038] Step 1: Obtain the Moho gravity anomaly and its Moho constraint depth;

[0039] Step 2: Estimate the initial values ​​of the free parameters of the constant density model based on the Moho gravity anomaly and the Moho constraint depth; the free parameters of the constant density model include constant offset and residual density;

[0040] Furthermore, step 2 includes:

[0041] Using the Bouguer plate formula, a linear regression relationship between the Moho surface constraint depth and the Moho surface gravity anomaly is established; wherein, the linear regression relationship is:

[0042]

[0043] Among them, h i Indicates the constraint depth. This indicates a gravity anomaly at the Mohorovičić discontinuity at the constraint point. Represents the first fitted parameter. This represents the second fitting parameter, and the initial value of the constant offset during iteration is... The initial value for the iteration of the remaining density is G is the gravitational constant.

[0044] Based on the Moho surface gravity anomaly and the linear regression relationship between the Moho surface constraint depth, a linear fitting function is obtained.

[0045] The initial values ​​of the free parameters of the constant density model are estimated using the linear fitting function.

[0046] Step 3: Based on the k-th iteration value of the free parameters of the constant density model, the depth of the Moho surface is inverted using the fast inversion method of the dual-interface gravity field model;

[0047] Step 4: When the stopping iteration condition is met, output the free parameters of the constant density model and its Moho inversion depth;

[0048] Step 5: When the stopping iteration condition is not met, update the free parameter values ​​of the constant density model in the (k+1)th iteration using the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth, set k+1 to k, and return to step 3.

[0049] It should be noted that in step 5, the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth is as follows:

[0050] h i =a k h ki +b k

[0051] Among them, h ki Let a represent the depth of the Moho at the constraint point obtained by inverting the free parameter values ​​using the k-th iteration. k b represents the first regression coefficient. k This represents the second regression coefficient, and the iterative value of the updated residual density is... The iterative value of the updated constant offset is c. k+1 =c k -2πGσ k+1 b k , σ k c represents the residual density after the k-th iteration. k This represents the constant offset after the k-th iteration.

[0052] The present invention will further illustrate the above-mentioned method for simultaneous inversion of free parameters and Moho surface based on constant density model with specific embodiments:

[0053] This invention primarily solves the technical problem of accurately estimating the free parameters (constant offset values ​​of gravity anomalies and residual density) of the constant density model in gravity Moho inversion, achieving simultaneous inversion of the free parameters of the constant density model and the depth of the Moho. It is readily known from the classic Bouguer plate formula that the gravity anomaly caused by a Bouguer plate with residual density σ and thickness h is...

[0054] g=2πGσh, (1)

[0055] Where G is the gravitational constant. If the depth of the upper interface is 0 and the undulation of the Moho is represented by h(x,y), then the gravity anomaly of the region (Moho) can be obtained from equation (1).

[0056] g reg (x,y)≈2πGσh(x,y)+c,(2)

[0057] Where c is the offset value of the gravity anomaly constant. Assume a constant residual density that differs from the true value. Then, the Bougger plate formula can be used to approximately obtain...

[0058]

[0059] Among them, the Moho surface undulates Based on and g reg (x,y) is obtained by inversion. Comparing equations (2) and (3), we can obtain...

[0060]

[0061] Equation (4) demonstrates the approximate invariance of the functional relationship between the interface depth and the free parameters of the constant density model, which is also the core point of this invention. When some base depth constraint points are available, the free parameters of the constant density model and the Moho surface depth can be estimated iteratively using Equation (4). This invention mainly solves the technical problem of accurate estimation of the free parameters of the constant density model in gravity constant density Moho surface inversion, and realizes the simultaneous inversion of the free parameters of the constant density model and the Moho surface depth.

[0062] The following is in conjunction with the appendix Figure 1-8 The method for simultaneous inversion of free parameters and Moho surface based on a constant density model in this invention will be further described in detail below:

[0063] Step 101: Given the maximum number of iterations k max And the inversion error limit ε.

[0064] Step 102: Estimate the initial values ​​of the free parameters for the constant density model. Using the Bourger formula, establish the constraint depth h. i Gravity anomaly at the Mohorovičić discontinuity Linear regression relationship:

[0065]

[0066] Wherein, the initial value of the constant offset is The initial value of the residual density is G is the gravitational constant.

[0067] Mohorovičić discontinuity g gravity anomaly reg ( Figure 2 It has a residual density of -0.4 g / cm³. 3 Moho noodles ( Figure 3 The depth constraint points of the Moho surface are represented by red pentagrams and randomly distributed within the study area. (This is obtained through forward modeling with an artificially added constant offset of 400 mGal.) Figure 2 The constraint depth and the scatter plot of gravity anomalies at the Mohorovičić discontinuity are shown below. Figure 4 As shown, the linear fitting function for both is:

[0068]

[0069] Therefore, the initial value of the constant offset is approximately 283 mGal, and the constant residual density is approximately -0.278 g / cm³. 3 .

[0070] Step 103: Invert the Moho depth. Eliminate constant offset values ​​from the regional (Moho) gravity anomaly:

[0071] g k =g reg -c k (7)

[0072] Based on residual density σ k and gravity anomaly g k The depth h of the Mohorovičić discontinuity was inverted using a fast inversion method based on a dual-interface gravity field model (Wang Wanyin and Pan Zuoshu, 1993). k .

[0073] Step 104: Determine whether to stop the iteration. Invert the Moho surface depth h at N constraint points using interpolation. ki If k≥k max or If the iteration stops, proceed to step 105.

[0074] The Moho inversion error iterative convergence curve is as follows: Figure 5 As shown, the error decreased significantly after only one iteration, indicating that the convergence rate of this method is very high. The root mean square error of the final constraint points is 0.049 km, and the root mean square error of all points (i.e., the entire model) is 0.082 km, which is much smaller than the grid spacing of 2 km.

[0075] Step 105: Update the free parameters of the constant density model. Utilize the constraint depth h i With inversion depth h ki Establish a linear regression relationship:

[0076] h i =a k h ki +b k (8)

[0077] Update residual density using regression coefficients constant offset c k+1 =c k -2πGσ k+1 b k .

[0078] The convergence curve of the free parameter iteration of the constant density model is as follows: Figure 6 As shown, the constant shift and residual density were accurately estimated to be 402 mGal and -0.403 g / cm³, respectively. 3 The values ​​are 400 mGal and -0.4 g / cm³. 3 Very close. The final Mohorovičić discontinuity inversion depth ( Figure 7 ) and true depth ( Figure 3 The results are basically consistent, and the inversion error is ( Figure 8 The range is also very small, not exceeding 0.4km and mostly not exceeding 0.2km.

[0079] This invention achieves the following technical effects: After inputting the Moho gravity anomaly and depth constraint points, accurate estimates of the free parameters of the constant density model are obtained after several iterations. When the iterative convergence condition is met, the free parameters of the constant density model and the inverted depth of the Moho are output. This process is fully automated and requires no manual parameter adjustment.

[0080] This invention also provides an electronic device, including a bus, a transceiver, a memory, a processor, and a computer program stored in the memory and executable on the processor. The transceiver, the memory, and the processor are connected via the bus. When the computer program is executed by the processor, it implements the steps in the aforementioned method for simultaneous inversion of free parameters and the Moho surface based on a constant density model. Compared with the prior art, the beneficial effects of the electronic device provided by this invention are the same as those of the aforementioned method for simultaneous inversion of free parameters and the Moho surface based on a constant density model, and will not be elaborated upon here.

[0081] This invention also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps in the aforementioned method for simultaneous inversion of free parameters and the Moho surface based on a constant density model. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided by this invention are the same as those of the aforementioned method for simultaneous inversion of free parameters and the Moho surface based on a constant density model, and will not be elaborated upon here.

[0082] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for simultaneous inversion of free parameters and Moho surface based on a constant density model, characterized in that, include: Step 1: Obtain the Moho gravity anomaly and its Moho constraint depth; Step 2: Estimate the initial values ​​of the free parameters of the constant density model based on the gravity anomaly of the Moho surface and its constraint depth; the free parameters of the constant density model include constant offset and residual density; Step 3: Based on the k-th iteration value of the free parameters of the constant density model, the depth of the Moho surface is inverted using the fast inversion method of the dual-interface gravity field model; Step 4: When the stopping iteration condition is met, output the free parameters of the constant density model and its Moho inversion depth; Step 5: When the stopping iteration condition is not met, update the k+1th iteration value of the free parameters of the constant density model using the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth, set k+1 to k, and return to step 3.

2. The method for simultaneous inversion of free parameters and Moho surface based on a constant density model according to claim 1, characterized in that, Step 2: Estimating the initial values ​​of the free parameters of the constant density model based on the Moho gravity anomaly and its Moho constraint depth, including: Using the Bouguer plate formula, a linear regression relationship between the Moho surface constraint depth and the Moho surface gravity anomaly is established. Based on the Moho surface gravity anomaly and the linear regression relationship between the Moho surface constraint depth, a linear fitting function is obtained. The initial values ​​of the free parameters of the constant density model are estimated using the linear fitting function.

3. The method for simultaneous inversion of free parameters and Moho surface based on a constant density model according to claim 2, characterized in that, The linear regression equation is as follows: Among them, h i Indicates the constraint depth. This indicates a gravity anomaly at the Mohorovičić discontinuity at the constraint point. Denotes the first fitted parameters. This represents the second fitting parameter, and the initial value of the constant offset iteration is... The initial value for the iteration of the residual density is G is the gravitational constant.

4. The method for simultaneous inversion of free parameters and Moho surface based on a constant density model according to claim 3, characterized in that, In step 5, the linear regression relationship between the Moho surface constraint depth and the Moho surface inversion depth is as follows: h i = a k h ki + b k Among them, h ki Let a represent the depth at the constraint point inverted using the free parameter values ​​from the k-th iteration, where a is the depth inverted from the Moho surface. k b represents the first regression coefficient. k Denotes the second regression coefficient, and the initial value of the updated residual density in the iteration is... The iterative initial value of the updated constant offset is c. k+1 =c k -2πGσ k+1 b k , σ k c represents the residual density after the k-th iteration. k This represents the constant offset after the k-th iteration.

5. An electronic device comprising a bus, a transceiver, a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the transceiver, the memory, and the processor are connected via the bus, characterized in that, When the computer program is executed by the processor, it implements the steps in the method for simultaneous inversion of free parameters and Moho surface based on a constant density model as described in any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps in the method for simultaneous inversion of free parameters and Moho surface based on a constant density model as described in any one of claims 1-4.

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