Imaging method and system for high and steep structure

Abstract

The invention provides an imaging method for a high and steep structure, and the method comprises the steps: inputting a velocity field, and building an observation system; constructing an optimal nine-point difference format of the frequency domain acoustic wave equation; prism waves are constructed according to the bon theory; separating uplink and downlink waves; and outputting an imaging result. A novel frequency domain prismatic wave reverse time migration imaging method is provided, and a frequency sound wave prismatic wave reverse time migration algorithm is realized. The prismatic wave reverse time migration performs high-resolution imaging on underground high and steep structures, and provides more reliable data support for geological exploration.

Description

Technical Field

[0001] The present invention relates to the field of petroleum exploration, and in particular to an imaging method and system for high-steep structures. Background Art

[0002] Complex and steep underground structures have always been a difficult problem for migration imaging. Traditional primary wave reverse time migration has difficulty in directly imaging steep underground structures. Studies have found that prism waves, as a characteristic wave, contain effective information about steep underground structures, unlike primary waves. Traditional prism wave reverse time migration processing is performed in the time domain, but the computational efficiency in the time domain is extremely low. The existing frequency domain forward equations are obtained through LU decomposition. Considering the computational accuracy and efficiency, the optimized nine-point difference format is generally used to solve large sparse matrices. According to the born modeling theory, the forward propagation incident wave field of the source and the backward propagation reflected wave field of the receiver are constructed. Because the computational efficiency of the frequency domain is high and the computational cost of the prism wave itself is high, it is meaningful to implement prism wave reverse time migration in the frequency domain. Summary of the Invention

[0003] In view of the above problems, the present invention is proposed to provide an imaging method and system for high-steep structures that overcome the above problems or at least partially solve the above problems.

[0004] According to one aspect of the present invention, a method for imaging high and steep structures is provided, the method comprising:

[0005] Input velocity field and establish observation system;

[0006] Construct the optimal nine-point difference scheme for the frequency domain acoustic wave equation;

[0007] Construct prismatic waves based on born theory;

[0008] Separate the up and down waves;

[0009] Output imaging results.

[0010] Optionally, the inputting of the velocity field and establishing the observation system specifically includes:

[0011] Prism wave reverse time migration imaging processing is realized in the frequency domain, and different observation systems are reasonably constructed according to different models.

[0012] Optionally, the optimal nine-point difference format for constructing the frequency domain acoustic wave equation specifically includes:

[0013] Two-dimensional wave equation in the frequency domain:

[0014]

[0015] Where P0 represents the wave field, f s represents the source function, v represents the propagation velocity of seismic waves, ω represents the angular frequency, and x and z represent the spatial coordinates;

[0016] The discretization method of the two-dimensional frequency domain acoustic wave equation adopts the five-point difference method. The wave field value of a numerical point is determined at five surrounding points. The coordinate axis is rotated 45 degrees to obtain another form of the five-point difference method and the rotated five-point difference format. The two difference methods are combined to obtain the optimal nine-point difference format.

[0017] Optionally, combining the two difference methods to obtain the optimal nine-point difference format specifically includes:

[0018] The weighted sum of the positive five-point difference format and the rotation five-point difference format is as follows:

[0019]

[0020] Where a and b are weight factors, which conform to the relationship a+b=1; and They are the Laplace operator in the positive five-point difference format and the Laplace operator in the difference format after rotating 45 degrees; they satisfy the following relationship:

[0021]

[0022] x′y′ refers to the rectangular coordinate system, and x″y″ refers to the rotated coordinate system;

[0023] The finite difference method is used to replace the solution of the partial differential equation by interpolating polynomials and differentials using a common numerical calculation method, namely:

[0024]

[0025] Where, Refers to the grid spacing in the x-axis direction in two different coordinate systems. Refers to the grid spacing in the z-axis direction in two different coordinate systems;

[0026] In formula (1), Differencing through the grid yields:

[0027]

[0028] Where c, d, and e are weight factors, which conform to the relationship c+4d+4e=1;

[0029] Substituting equation (4) into equation (2) yields the following equation:

[0030]

[0031] Substituting equations (4) and (6) into equation (1) yields the following equation:

[0032]

[0033] After simplification and adding the source function, we get:

[0034]

[0035] Where x s and z s Refers to the gun point location; A, B, C, D, E are:

[0036]

[0037] Construct the coefficient matrix M:

[0038]

[0039] For each frequency component, construct a matrix equation:

[0040] A(v,ω)P(ω)=-B(ω) (11)

[0041] A is the impedance matrix.

[0042] Optionally, constructing a matrix equation specifically includes:

[0043] Use direct and indirect methods;

[0044] Indirect methods are usually iterative;

[0045] The basic idea of ​​the direct method is to convert the original problem into solving the product of two triangular matrices by performing LU decomposition on the coefficient matrix to obtain the solution of the linear equation system;

[0046] In two dimensions, parallel multi-shot calculations using one frequency are implemented together.

[0047] Optionally, the iterative method includes Gauss-Siedel iteration and Jacobi iteration.

[0048] Optionally, constructing a prismatic wave according to Born's theory specifically includes:

[0049] Using formula (1), we can get the source wave field and the receiver wave field P V (x, ω), in the frequency domain, the full wavefield can be quickly and conveniently separated into the incident wavefield and the reflected wavefield by using the model parameter perturbation, as shown in the following formula:

[0050]

[0051] Where, and They represent the incident wavefield propagating forward from the source and the incident wavefield propagating backward from the receiver, respectively, and are calculated by equations (8), (9), (10), and (11), respectively. and They represent the forward-propagating incident wavefield at the source and the backward-propagating reflected wavefield at the receiver, respectively, reflecting the prismatic wave information in reverse time migration;

[0052] According to Born modeling theory, perturbations of model parameters based on Born approximation theory will cause perturbations in the wave field:

[0053]

[0054] Where, I0 represents the conventional reverse time migration imaging result;

[0055] The new source wave field and receiver wave field are calculated by formula (13): and

[0056] Optionally, separating the uplink and downlink waves specifically includes:

[0057] When the energy of the prismatic wave increases relatively, the energy of other interfering waves also increases;

[0058] The wave field separation method is used to extract the upgoing and downgoing waves of reverse time migration;

[0059] The up and down wave fields of the source wave field and the up and down wave fields of the receiving point wave field:

[0060]

[0061] Where S represents the source wavefield, R represents the receiving point wavefield, U represents the upgoing wave, and D represents the downgoing wave.

[0062] Optionally, the output imaging result specifically includes:

[0063] Using the cross-correlation imaging condition, the frequency domain prism wave reverse time migration imaging results are obtained:

[0064]

[0065] The present invention further provides an imaging system for high-steep structures, applying the above-mentioned imaging method for high-steep structures, the imaging system comprising:

[0066] Observation system establishment module, used to input velocity field and establish observation system;

[0067] Acoustic wave equation construction module, used to construct the optimal nine-point difference format of the frequency domain acoustic wave equation;

[0068] Prism wave construction module, used to construct prismatic waves according to Born theory;

[0069] Traveling wave separation module, used to separate uplink and downlink traveling waves;

[0070] The imaging result output module is used to output the imaging results.

[0071] The present invention provides an imaging method for high-steep structures. The method comprises: inputting a velocity field to establish an observation system; constructing an optimal nine-point difference format for the frequency-domain acoustic wave equation; constructing prism waves based on Born theory; separating the upgoing and downgoing waves; and outputting the imaging results. A new frequency-domain prism wave reverse time migration imaging method is proposed, implementing a frequency-domain acoustic prism wave reverse time migration algorithm. Prism wave reverse time migration enables high-resolution imaging of high-steep underground structures, providing more reliable data support for geological exploration.

[0072] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are specifically listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0074] Figure 1 Schematic diagram of the optimized nine-point difference format provided by an embodiment of the present invention, (a) traditional five-point second-order finite difference; (b) 45-degree rotated five-point second-order finite difference; (c) optimal nine-point finite difference;

[0075] Figure 2 A flowchart of frequency domain prismatic wave reverse time migration provided by an embodiment of the present invention;

[0076] Figure 3 The inverted T speed model provided by the embodiment of the present invention;

[0077] Figure 4 The frequency domain single shot record of the inverted T velocity model provided by the embodiment of the present invention;

[0078] Figure 5 A 420ms wavefield snapshot of the inverted T velocity model provided in an embodiment of the present invention;

[0079] Figure 6The conventional reverse time migration in the frequency domain of the inverted T velocity model provided by the embodiment of the present invention;

[0080] Figure 7 The inverted-T velocity model provided by the embodiment of the present invention is a frequency-domain prismatic wave reverse time migration;

[0081] Figure 8 A high-steep salt dome velocity model provided in an embodiment of the present invention;

[0082] Figure 9 Frequency domain single shot record of high steep salt dome velocity model;

[0083] Figure 10 Conventional reverse time migration of steep salt dome velocity model in frequency domain;

[0084] Figure 11 Frequency domain prismatic wave reverse time migration of steep salt dome velocity models. DETAILED DESCRIPTION

[0085] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0086] The terms "comprises" and "comprising" and any variations thereof in the description, embodiments, claims and drawings of the present invention are intended to cover non-exclusive inclusions, for example, including a series of steps or units.

[0087] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0088] Example 1:

[0089] The present invention proposes an efficient imaging method for high-steep structures, which specifically includes the following steps:

[0090] Step 1: Input velocity field and establish observation system;

[0091] The goal of this patent is to realize the reverse time migration imaging processing of prismatic waves in the frequency domain and to rationally construct different observation systems based on different models.

[0092] Step 2: Construct the optimal nine-point difference format of the frequency domain acoustic wave equation;

[0093] The two-dimensional wave equation in the frequency domain is shown as follows:

[0094]

[0095] Where P0 represents the wave field, f s represents the source function, v represents the propagation velocity of seismic waves, ω represents the angular frequency, and x and z represent the spatial coordinates.

[0096] The simplest discretization method for the two-dimensional frequency domain acoustic wave equation is the five-point difference method, which determines the wave field value of a numerical point at five surrounding points, such as Figure 1 (a) As shown. This patent rotates the coordinate axis 45 degrees to obtain another form of five-point difference method, such as Figure 1 (b) shows the five-point difference format after rotation. Combining the two difference methods, we get the optimal nine-point difference format, as shown in Figure 1 (c) shown.

[0097] The weighted summation of the positive five-point difference format and the rotated five-point difference format is as follows:

[0098]

[0099] In the formula, a and b are weight factors, which conform to the relationship a+b=1. and They are the Laplace operator in the positive five-point difference format and the Laplace operator in the difference format after rotating 45 degrees. They satisfy the following relationship:

[0100]

[0101] x′y′ refers to Figure 1 (a) shows the rectangular coordinate system, x″y″ refers to Figure 1 (b) The rotated coordinate system. Using the finite difference method, a common numerical calculation method is used to interpolate the polynomial and its differential to replace the solution of the partial differential equation. That is,

[0102]

[0103] Where, Refers to the grid spacing in the x-axis direction in two different coordinate systems. Refers to the grid spacing along the z-axis in two different coordinate systems. The smaller the grid spacing, the more approximate the values ​​on both sides of the equal sign, that is, the smaller the grid step size, the more accurate the forward modeling results.

[0104] Then, the formula (1) Differencing through the grid yields:

[0105]

[0106] Wherein, c, d, and e are weight factors, which conform to the relationship of c+4d+4e=1.

[0107] Substituting formula (4) into formula (2) yields the following formula:

[0108]

[0109] Substituting equations (4) and (6) into equation (1) yields the following equation:

[0110]

[0111] After simplification and adding the source function, we get:

[0112]

[0113] Where x s and z s Refers to the gun point location. A, B, C, D, and E are:

[0114]

[0115] The coefficient matrix M can be constructed:

[0116]

[0117] For each frequency component, a matrix equation is constructed as follows:

[0118] A(v,ω)P(ω)=-B(ω) (11)

[0119] A is the impedance matrix. There are two methods to solve equation (11): direct method and indirect method. The indirect method is usually an iterative method, such as Gauss-Siedel iteration, Jacobi iteration method, etc. This type of method has low computational efficiency and is not conducive to multi-shot parallelism. The basic idea of ​​the direct method is to perform LU decomposition on the coefficient matrix and transform the original problem into solving the product of two triangular matrices to obtain the solution of the linear equation system. In two dimensions, the parallel multi-shot calculation with one frequency is realized together, and the computational efficiency is greatly improved. This patent chooses the direct method for solution.

[0120] Step 3: Construct prismatic waves according to Born theory:

[0121] Using formula (1), we can get the source wave field and the receiver wave field P V (x, ω), in the frequency domain, the full wavefield is quickly and conveniently separated into the incident wavefield and the reflected wavefield by using the model parameter perturbation, as shown in the following formula:

[0122]

[0123] Where, and They represent the incident wavefield propagating forward from the source and the incident wavefield propagating backward from the receiver, respectively, and are calculated by equations (8), (9), (10), and (11), respectively. and They represent the incident wavefield propagating forward from the source and the reflected wavefield propagating backward from the receiver, respectively, reflecting the prismatic wave information in reverse time migration. According to Born modeling theory, perturbations in the model parameters based on Born approximation theory will cause perturbations in the wavefield, which can be calculated using the following formula:

[0124]

[0125] Where I0 represents the conventional reverse time migration imaging result. The new source wave field and receiver wave field are calculated by equation (13): and

[0126] Step 4: Separation of up and down waves:

[0127] When the energy of the prismatic wave increases relatively, the energy of other interfering waves also increases. To reduce the low-frequency noise in the imaging results, the wavefield separation method is used to extract the upgoing and downgoing waves of the reverse time migration. The upgoing and downgoing wave fields of the source wavefield and the upgoing and downgoing wave fields of the receiving point wavefield are shown in the following formula:

[0128]

[0129] Where S represents the source wavefield, R represents the receiving point wavefield, U represents the upgoing wave, and D represents the downgoing wave.

[0130] Step 5: Output imaging results:

[0131] Using the cross-correlation imaging condition, the frequency domain prism wave reverse time migration imaging result is obtained as shown in the following formula:

[0132]

[0133] The process of calculating frequency domain prismatic wave reverse time migration is summarized as follows: Figure 2 shown.

[0134] Application Experiment

[0135] The invention provides an efficient imaging method for high-steep structures, which is applied to two models and achieves ideal imaging effects.

[0136] First, test the simple model. Figure 3 This paper demonstrates an inverted T velocity model with vertical structure, using which conventional and prismatic RTM are performed. The model has 301 horizontal and 101 vertical grid points, with a spacing of 10 m between grid points. The source excitation location is 1500 m. Figure 4The frequency domain single-shot record of the inverted T velocity model is displayed. There is no dispersion phenomenon in the simulated record, and the reflected wave phase axis is clear and continuous. Figure 5 A 420ms wavefield snapshot of the inverted T velocity model is shown. Figure 6 and Figure 7 The imaging results of conventional RTM and prismatic RTM in the frequency domain are shown. The arrow indicates the area with the best imaging effect for steep structures. The imaging results have higher resolution than conventional primary RTM, demonstrating that prismatic waves significantly improve the imaging of steep structures.

[0137] Then test the complex model. Figure 8 This figure shows a velocity model for a steep salt dome. The model has 601 horizontal and 401 vertical grid points, with a 10-meter spacing between grid points. The earthquake source excitation location is 3,000 meters. Figure 9 A frequency-domain single-shot recording of a high-steep salt dome velocity model is shown. The simulated recording shows no dispersion and clear reflection wave events. Figure 10 and Figure 11 The imaging results of conventional frequency domain reverse time migration and prism wave reverse time migration are shown in Figure 2. Figure 10 and Figure 11 As shown in the box, prismatic wave reverse time migration restores the contours of steep underground structures, resulting in higher resolution and superior imaging to conventional primary wave reverse time migration. For layered structures, prismatic wave imaging does not improve performance; in fact, the energy is not as strong as that of primary wave imaging. This is because the prismatic wave field carries only minimal flat-layer reflection information. In practical applications, a combination of these two methods is necessary to accurately analyze the actual subsurface structural contours and achieve optimal interpretation results.

[0138] Beneficial effects: The present invention proposes an efficient imaging method for high-steep structures, which overcomes the problem of low efficiency in constructing traditional prism waves, breaks through the constraints of constructing prism waves in the traditional time domain, and further improves computing efficiency.

[0139] The above specific implementation methods further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific implementation methods of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An imaging method for high and steep structures, characterized in that: The imaging method comprises: Input velocity field and establish observation system; Construct the optimal nine-point difference scheme for the frequency domain acoustic wave equation; Construct prismatic waves based on born theory; Separate the up and down waves; Output imaging results.

2. The imaging method for high and steep structures according to claim 1, characterized in that: The input velocity field and establishment of the observation system specifically include: Prism wave reverse time migration imaging processing is realized in the frequency domain, and different observation systems are reasonably constructed according to different models.

3. The imaging method for high and steep structures according to claim 1, characterized in that: The optimal nine-point difference format for constructing the frequency domain acoustic wave equation specifically includes: Two-dimensional wave equation in the frequency domain: Where P0 represents the wave field, f s represents the source function, v represents the propagation velocity of seismic waves, ω represents the angular frequency, and x and z represent the spatial coordinates; The discretization method of the two-dimensional frequency domain acoustic wave equation adopts the five-point difference method. The wave field value of a numerical point is determined at five surrounding points. The coordinate axis is rotated 45 degrees to obtain another form of the five-point difference method and the rotated five-point difference format. The two difference methods are combined to obtain the optimal nine-point difference format.

4. The imaging method for high and steep structures according to claim 1, characterized in that: The above-mentioned combination of the two difference methods to obtain the optimal nine-point difference format specifically includes: The weighted sum of the positive five-point difference format and the rotation five-point difference format is as follows: Where a and b are weight factors, which conform to the relationship a+b=1; and They are the Laplace operator in the positive five-point difference format and the Laplace operator in the difference format after rotating 45 degrees; they satisfy the following relationship: x′y′ refers to the rectangular coordinate system, and x″y″ refers to the rotated coordinate system; The finite difference method is used to replace the solution of the partial differential equation by interpolating polynomials and differentials using a common numerical calculation method, namely: Where, Refers to the grid spacing in the x-axis direction in two different coordinate systems. Refers to the grid spacing in the z-axis direction in two different coordinate systems; In formula (1), Differencing through the grid yields: Where c, d, and e are weight factors, which conform to the relationship c+4d+4e=1; Substituting equation (4) into equation (2) yields the following equation: Substituting equations (4) and (6) into equation (1) yields the following equation: After simplification and adding the source function, we get: Where x s and z s Refers to the gun point location; A, B, C, D, E are: Construct the coefficient matrix M: For each frequency component, construct a matrix equation: A(v,ω)P(ω)=-B(ω) (11) A is the impedance matrix.

5. The imaging method for high and steep structures according to claim 4, characterized in that: The construction of a matrix equation specifically includes: Use direct and indirect methods; Indirect methods are usually iterative; The basic idea of ​​the direct method is to convert the original problem into solving the product of two triangular matrices by performing LU decomposition on the coefficient matrix to obtain the solution of the linear equation system; In two dimensions, parallel multi-shot calculations using one frequency are implemented together.

6. The imaging method for high and steep structures according to claim 5, characterized in that: The iterative method includes Gauss-Siedel iteration and Jacobi iteration.

7. The imaging method for high and steep structures according to claim 1, characterized in that: The construction of prismatic waves according to Born's theory specifically includes: Using formula (1), we can get the source wave field and the receiver wave field P V (x, ω), in the frequency domain, the full wavefield can be quickly and conveniently separated into the incident wavefield and the reflected wavefield by using the model parameter perturbation, as shown in the following formula: Where, and They represent the incident wavefield propagating forward from the source and the incident wavefield propagating backward from the receiver, respectively, and are calculated by equations (8), (9), (10), and (11), respectively. and They represent the forward-propagating incident wavefield at the source and the backward-propagating reflected wavefield at the receiver, respectively, reflecting the prismatic wave information in reverse time migration; According to Born modeling theory, perturbations of model parameters based on Born approximation theory will cause perturbations in the wave field: Where, I0 represents the conventional reverse time migration imaging result; The new source wave field and receiver wave field are calculated by formula (13): and 8. The imaging method for high and steep structures according to claim 1, characterized in that: The separation of uplink and downlink specifically includes: When the energy of the prismatic wave increases relatively, the energy of other interfering waves also increases; The wave field separation method is used to extract the upgoing and downgoing waves of reverse time migration; The up and down wave fields of the source wave field and the up and down wave fields of the receiving point wave field: Where S represents the source wavefield, R represents the receiving point wavefield, U represents the upgoing wave, and D represents the downgoing wave.

9. The imaging method for high and steep structures according to claim 1, characterized in that: The output imaging results specifically include: Using the cross-correlation imaging condition, the frequency domain prism wave reverse time migration imaging results are obtained:

10. An imaging system for high-steep structures, using the imaging method for high-steep structures according to any one of claims 1 to 9, characterized in that: The imaging system comprises: Observation system establishment module, used to input velocity field and establish observation system; Acoustic wave equation construction module, used to construct the optimal nine-point difference format of the frequency domain acoustic wave equation; Prism wave construction module, used to construct prismatic waves according to Born theory; Traveling wave separation module, used to separate uplink and downlink traveling waves; The imaging result output module is used to output the imaging results.

Images