A viscoacoustic medium characteristic wave and primary wave combined least square reverse time migration method

Abstract

The application discloses a viscoacoustic medium characteristic wave and primary wave combined least square reverse time migration method and belongs to the technical field of oil geophysical exploration. The method constructs a new combined Q least square reverse time migration target function, introduces a viscoacoustic differential equation and an accompanied pseudo-differential equation, describes forward and reverse propagation wave fields of the combined Q least square reverse time migration, deduces Q compensation wave field propagation, Q compensation accompanied operators and Q attenuation migration operators of primary waves, multiple waves, diffracted waves and prism waves, constructs a new gradient formula, and realizes Q least square reverse time migration of combined multiple waves, diffracted waves, prism waves and primary waves in a viscoacoustic medium. The method can accurately image structures under salt, steeply inclined flanks, small faults and rock caves, obtain clearer complex structure information, obtain high-resolution and high-quality imaging diagrams, and solves the problem of unclear imaging of current special complex high-steep structures.

Description

Technical Field

[0001] This invention relates to the field of petroleum geophysical exploration technology, specifically to a method for joint least squares reverse time migration of characteristic waves and primary waves in viscous acoustic media. Background Technology

[0002] Complex subsurface structures, such as subsalt formations, steeply dipping flanks, small faults, and cavities, pose significant challenges to high-resolution imaging. In imaging complex exploration areas, reverse time migration (RTM) based on the two-way wave equation has advantages over migrations based on ray and one-way wave equations. Nevertheless, due to limitations in observation systems, traditional RTM struggles to image these complex subsurface structures. To overcome the limitations of traditional migration methods, least squares RTM, based on least squares inversion and adjoint state theory, has been proposed and rapidly developed. However, least squares RTM requires substantial iterations and computational costs to obtain high-resolution images of subsalt formations, steeply dipping flanks, small faults, and cavities.

[0003] Compared to primary waves, multiples, diffracted waves, and prismatic waves have unique propagation paths, which can be fully utilized to improve imaging obtained from primary waves. The idea of ​​constructing pseudo-primary waves using multiples can be traced back to work in seismic interferometry; the key to this method is constructing pseudo-primary waves. Subsequently, this pseudo-primary wave imaging method has been widely used and rapidly developed because it can flexibly replace multiples in migration imaging. However, imaging noise is introduced during the construction of pseudo-primary waves. Another approach is to use low-order multiples as virtual sources to achieve high-order multiple imaging. A multiple inverse time migration method has been proposed, separating the observation data into primary multiples and multiples of different orders.

[0004] Earth possesses significant inelastic properties, and the attenuation of seismic waves is caused by viscoelasticity. Ignoring subsurface attenuation during imaging will lead to severe amplitude loss and phase distortion in migration imaging. Due to the attenuation effect of the subsurface medium, accurate and effective seismic wave energy compensation is a challenge in imaging. To compensate for attenuation, two main methods can be considered in prism wave imaging. The first method, called the inverse Q-filtering method, is effective and computationally efficient. However, it cannot accurately correct attenuation under complex geological conditions. The other is the Q-compensated migration method. In recent years, some least-squares reverse-time migration methods based on Q-compensation using various viscoelastic pseudo-differential equations have been developed. Summary of the Invention

[0005] This invention aims to solve the problem that conventional reverse time migration is difficult to image complex and steep structures in the prior art. This invention proposes a joint least squares reverse time migration method for characteristic waves and primary waves in viscous acoustic media, which realizes joint imaging of diffraction waves, prism waves, multiple waves and primary waves in viscous acoustic media, and achieves high-precision imaging by using the least squares iterative idea.

[0006] To achieve the above-mentioned objectives, the technical solution of the present invention is as follows:

[0007] A method for combining characteristic waves and primary waves in a viscous acoustic medium with least squares reverse time migration, characterized by the following steps:

[0008] Construct the objective function of least-squares reverse-time migration combining the characteristic wave and the primary wave of the viscous acoustic medium;

[0009] The viscosity-acoustic differential equation and the adjoint quasi-differential equation are introduced into the objective function;

[0010] The forward and reverse propagation wave fields of the joint least squares reverse time migration of characteristic waves and primary waves in a viscous acoustic medium are accurately simulated to obtain wave field values.

[0011] Least-squared reverse time migration imaging of the characteristic wave and primary wave of the viscous acoustic medium is achieved based on the wave field value.

[0012] In one embodiment, the objective function for the combined least-squares reverse-time migration of the characteristic wave and the primary wave in the viscous acoustic medium is:

[0013]

[0014] In the formula, a0, a1, ..., a4 represent coefficients respectively; and These are, respectively, a first-order wave, an i-th-order multiple wave, a diffracted wave, and a prism wave; The inverse offset operator represents the attenuation of the primary wave, where m is the reflection coefficient model; and These represent the inverse offset operators for i-th order multiple waves, diffracted waves, and first-order waves, respectively.

[0015] In one embodiment, the attenuated seismic data comprising multiple waves, diffracted waves, prismatic waves, and primary waves is as follows:

[0016]

[0017] The objective function for conventional least-squares reverse time migration is:

[0018]

[0019] Therefore, the gradient formula obtained from equation (2) is:

[0020]

[0021] In the formula, As a primary wave adjoint operator, the noise increases with the number of iterations of least squares reverse time migration.

[0022] In one embodiment, the gradient formula obtained from the objective function of equation (4) is as follows:

[0023]

[0024] In the formula, and These represent the wave fields of the primary wave, multiple waves, diffracted wave, and prism wave propagating in the backward direction, respectively; δv represents the velocity perturbation, and F... Ci F Cr F Co and F Cp These represent the primary wave, multiple waves, diffracted wave, and prism wave fields, respectively, propagating in the forward direction.

[0025] In one embodiment, the introduced viscosity-acoustic differential equation is expressed as follows:

[0026]

[0027] In the formula, Represents the forward-propagating wave field, where F is the source matrix. Here, σ represents the Laplace operator, v is the wave propagation velocity, t is the wave propagation time, σ represents the stress parameter, and τ represents the strain parameter.

[0028] In one embodiment, with Q compensation, equation (6) can be simplified to

[0029]

[0030] In the formula, x is the coordinate, L S For the forward propagation operator of the wave field.

[0031] In one embodiment, the method for introducing the adjoint quasi-differential equation is as follows:

[0032] Based on the Born approximation theory, the following offset equation can be obtained:

[0033]

[0034] In the formula, F0 represents the source term of the perturbation wavefield, and I represents the migration result term; according to the adjoint state theory, the adjoint equation can be obtained:

[0035]

[0036] In the formula, This represents the wave field operator propagating after Q-compensation. This represents the synthesized data for Q-decay.

[0037] In one embodiment, accurately simulating the forward propagation wave field of the least-squares reverse-time migration of the characteristic wave and the primary wave of the viscous acoustic medium specifically includes:

[0038] The inverse offset equation is shown below.

[0039]

[0040] In the formula F′ represents the wavefield of the compensated source term wave propagation. C The earthquake source indicating compensation;

[0041] The forward propagation wave field is represented as:

[0042]

[0043] In the formula, x s Indicates the coordinates of the earthquake source. It can be calculated using the following formula:

[0044]

[0045] In the formula, The forward operand representing compensation, This represents the positively extended source wave field. Let I(x) represent the offset result of the xth shot, S represent the firing point, and r represent the receiving point.

[0046] In one embodiment, the backpropagation wavefield of the joint least-squares reverse-time offset of the characteristic wave and the primary wave in the viscous acoustic medium is represented as:

[0047]

[0048] In the formula, and yes and The accompanying operator of the compensation, The backpropagation operator represents compensation; and This represents the composite data calculated in the intermediate process compared to the original data. and This represents the final synthesized data and the original data for attenuation compensation; and denoted as the initial backpropagation operator and the receiving wave field in the iteration, respectively; the subscripts 0, 1 and 2 in the formula represent the initial state, intermediate state and final state, respectively.

[0049] In one embodiment, the least-squares reverse-time migration of the characteristic wave and the primary wave of the viscous acoustic medium based on the obtained wavefield value specifically includes:

[0050] The step size for k iterations using the steepest descent method is:

[0051]

[0052] Calculate the conjugate gradient direction and the corresponding step size. The result of the k-th iteration is updated as follows:

[0053] I (k) =I (k-1) -α (k) z (k) (15)

[0054] I (k) Let α represent the result of the k-th least-squares reverse time shift. (k) Let z be the step size of the k-th iteration. (k) This represents the updated gradient.

[0055] In summary, the present invention has the following advantages:

[0056] 1. This invention proposes a joint least squares reverse time migration method for characteristic waves and primary waves in viscous acoustic media. By deriving the Q-compensated wave field propagation, primary wave, multiple wave, diffraction wave and prism wave companion operators, as well as the Q-attenuation migration operator, it improves the imaging effect of subsalt structures, steeply tilted flanks, small faults and pores.

[0057] 2. The method of this invention is based on inversion theory and compensates for the Q attenuation of primary waves, multiple waves, diffracted waves and prism waves on all propagation paths respectively;

[0058] 3. Compared with traditional viscosity least squares reverse time migration and uncompensated joint least squares reverse time migration of characteristic waves and primary waves, the method of the present invention has certain advantages in obtaining clearer complex structural information, stronger deep energy and higher resolution high-quality imaging by combining primary wave, multiple wave, diffraction wave and prism wave imaging. Attached Figure Description

[0059] Figure 1 To decay the Sigsbee2B model, Figure 1 (a) is the velocity model. Figure 1 (b) is the Q-model;

[0060] Figure 2 Sigsbee2B viscosonic reverse time migration imaging after Laplace filtering (a) and uncompensated reverse time migration imaging (b);

[0061] Figure 3For the imaging results of 30 iterations, joint least squares reverse time migration of the characteristic wave and the first wave of the viscous acoustic medium was used (a) and conventional least squares reverse time migration of the viscous acoustic medium was used (b).

[0062] Figure 4 The imaging results for 30 iterations are: joint acoustic least squares reverse time migration using multiple waves, prism waves and first waves (a), joint acoustic least squares reverse time migration using multiple waves, diffraction waves and first waves (b), joint acoustic least squares reverse time migration using diffraction waves, prism waves and first waves (c) and uncompensated joint least squares reverse time migration (d).

[0063] Figure 5 The reflection coefficient model method (a) and the least squares reverse time migration of sound waves (b) are used. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to embodiments, but the implementation of the present invention is not limited thereto.

[0065] Example 1

[0066] This embodiment provides a method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium, including:

[0067] Step 1: Construct the objective function of the least-squares reverse-time migration of the characteristic wave and the primary wave of the viscous acoustic medium;

[0068] Step 2: Introduce the viscosity-acoustic differential equation and the adjoint quasi-differential equation into the objective function;

[0069] Step 3: Accurately simulate the forward and reverse propagation wave fields of the joint least squares reverse time migration of the characteristic wave and the primary wave in the viscous acoustic medium to obtain the wave field values;

[0070] Step 4: Achieve least-squares reverse time migration imaging of the characteristic wave and primary wave of the viscous acoustic medium based on the wave field value.

[0071] Example 2

[0072] This embodiment provides a method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium. Based on Embodiment 1, preferably, step 1 is implemented as follows:

[0073] Attenuated seismic data including multiple waves, diffracted waves, prismatic waves, and primary waves are available.

[0074]

[0075] In the formula, and These are primary waves, i-th order multiple waves, diffracted waves, and prism waves, respectively.

[0076] The objective function for conventional least-squares reverse time migration is:

[0077]

[0078] In the formula, Let m represent the inverse offset operator for attenuating the primary wave, and m be the reflection coefficient model. Therefore, the gradient formula obtained from equation (2) is:

[0079]

[0080] In the formula, This is a primary wave adjoint operator. As the number of iterations of the least squares reverse time migration increases, the noise becomes stronger.

[0081] The objective function for constructing the joint least-squares reverse-time migration of the characteristic wave and the primary wave in a viscous acoustic medium is:

[0082] In the formula, a0, a1, ..., a4 represent coefficients respectively; and These represent the inverse offset operators for the i-th order multiple wave, diffracted wave, and first wave, respectively. The gradient formula obtained from (4) is as follows:

[0083]

[0084] In the formula, and These represent the wave fields of the primary wave, multiple waves, diffracted wave, and prism wave propagating in the backward direction, respectively; δv represents the velocity perturbation, and F... Ci F Cr F Co and F Cp These represent the primary wave, multiple waves, diffracted wave, and prism wave fields, respectively, propagating in the forward direction.

[0085] Step 2 is implemented as follows:

[0086] The viscosity pseudo-differential equation can be used as follows:

[0087]

[0088] In the formula, Represents the forward-propagating wave field, where F is the source matrix. Here, σ represents the Laplace operator, v is the wave propagation velocity, t is the wave propagation time, σ represents the stress parameter, and τ represents the strain parameter.

[0089] In the case of Q compensation, equation (6) can be simplified to

[0090]

[0091] In the formula, x is the coordinate, L S Let be the forward propagation operator for the wave field. Based on the Born approximation theory, we can obtain the following migration equation:

[0092]

[0093] In the formula, F0 represents the source term of the perturbation wave field, and I represents the migration result term.

[0094] According to the adjoint state theory, we can obtain the adjoint equation:

[0095]

[0096] In the formula, This represents the wave field operator propagating after Q-compensation. This represents the synthesized data for Q-decay.

[0097] Step 3 is implemented as follows:

[0098] The inverse offset equation is shown below.

[0099]

[0100] In the formula F′ represents the wavefield of the compensated source term wave propagation. C The earthquake source that indicates compensation.

[0101] The forward propagation wave field is represented as:

[0102]

[0103] In the formula, x s Indicates the coordinates of the earthquake source. It can be calculated using the following formula:

[0104]

[0105] In the formula, The forward operand representing compensation, This represents the positively extended source wave field. Let I(x) represent the offset result of the xth shot, S represent the firing point, and r represent the receiving point.

[0106] The wave field propagating backward is represented as:

[0107]

[0108] In the formula, and yes and The accompanying operator of the compensation, The backpropagation operator represents compensation. and This represents the composite data calculated in the intermediate process compared to the original data. and This represents the final synthesized data and the original data for attenuation compensation; and denoted as the initial backpropagation operator and the receiving wave field in the iteration, respectively; the subscripts 0, 1 and 2 in the formula represent the initial state, intermediate state and final state, respectively.

[0109] Step 4 is implemented as follows:

[0110] The proposed joint least-squares reverse-time migration of characteristic waves and primary waves in viscous acoustic media, using the steepest descent method, has an iterative step size of k iterations as follows:

[0111]

[0112] Calculate the conjugate gradient direction and the corresponding step size. The result of the k-th iteration is updated as follows:

[0113] I (k) =I (k-1) -α (k) z (k) (15)

[0114] I (k) Let α represent the result of the k-th least-squares reverse time shift. (k) Let z be the step size of the k-th iteration. (k) This represents the updated gradient.

[0115] Example 3

[0116] Based on Example 2 above, we provide an example of joint least-squares reverse-time migration of characteristic waves and primary waves in viscous acoustic media using the attenuated Sigsbee2B dataset. The Sigsbee2B model exhibits high-velocity salt layer structures, posing a significant challenge to imaging subsalt deposits. Furthermore, some small-scale caves are also difficult to image accurately. In our example, the standard Sigsbee2B model is modified and resampled to 12000m × 4000m, with a spatial grid spacing of 15m × 10m in the x and z directions. The velocity model and Q-model of the attenuated Sigsbee2B model are as follows: Figure 1 (a) and Figure 1 As shown in (b).

[0117] The following observation system and forward modeling parameters were selected to synthesize the attenuation dataset: a maximum offset of 3000 m, 201 geophones with a geophone spacing of 15 m, 120 shots with a shot interval of 75 m. The source function was a Ricker wavelet with a dominant frequency of 25 Hz. The sampling interval was 0.6 ms, and the recording time was 4.8 s. In this example, the joint least-squares reverse-time migration of the characteristic wave and the primary wave in the viscous acoustic medium was performed 30 times. Figure 2 (a) shows the imaging results of the viscoacoustic reverse time migration. Figure 2 (b) shows the results of conventional uncompensated reverse time migration imaging. Figure 2 After attenuation compensation, (a) has higher resolution and stronger depth.

[0118] Figure 3 The images are the results after 30 iterations. For comparison, we also provide images from conventional viscoacoustic least-squares reverse-time migration, such as... Figure 3 As shown in (b). Compared with viscosonic least squares reverse time migration, Figure 3 The combined imaging results of primary, secondary, diffracted, and prismatic waves in (a) show clearer subsalt structures (indicated by solid arrows), salt dome flanks (indicated by narrow arrows), and small caves (indicated by ellipses). Furthermore, the combined least-squares reverse time migration of the characteristic waves of the viscous acoustic medium and the primary wave yields better resolution, wider illumination, and more balanced amplitude.

[0119] To highlight the contributions of different wave types, after 30 iterations, joint viscosity least squares reverse time migration imaging (VTM) of multiple waves, prism waves, and primary waves, joint viscosity least squares VTM of multiple waves, diffracted waves, and primary waves, and joint viscosity least squares VTM of diffracted waves, prism waves, and primary waves were used, such as... Figure 4 As shown, (a), (b), (c), and (d) are respectively. From these results, we can clearly see that multiple waves, prism waves, and diffraction waves improve the imaging of subsalt structures, salt dome flanks, and small-scale caves, respectively. Figure 4 The uncompensated joint least squares reverse time migration shown in (d) has poor resolution and more artifacts. Figure 5 (a) and (b) in the figure show the reflection coefficient model using acoustic data and the acoustic joint least squares reverse time migration, respectively, for comparison only.

[0120] Numerical examples of this invention show that, compared with traditional viscosonic least squares reverse time migration and uncompensated joint least squares reverse time migration of characteristic waves and primary waves, this method has certain advantages in obtaining clearer complex structural information, stronger deep energy, and higher resolution high-quality imaging by combining primary waves, multiple waves, diffraction waves, and prism waves.

[0121] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Any simple modifications or equivalent changes made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for combining characteristic waves and primary waves in a viscous acoustic medium with least squares reverse time migration, characterized in that, Includes the following steps: Construct the objective function for the joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium: （4） In the formula, , ,..., They represent coefficients respectively; , , and They are respectively the first wave, i Multiple waves, diffraction waves, and prism waves; The inverse offset operator represents the attenuation of the first wave. m For the reflection coefficient model; , and Represent i Inverse offset operators for first-order multiple waves, diffracted waves, and first-order waves; Introducing the viscosity-acoustic differential equation and its adjoint quasi-differential equation into the objective function, the viscosity-acoustic differential equation is expressed as follows: （6） In the formula, Represents a forward propagating wave field. F Let be the source matrix, and ▽ be the Laplace operator. v Let be the speed of wave propagation, and t be the time it takes for the wave to propagate. Indicates stress parameters, Indicates the strain parameter; The forward and reverse propagation wave fields of the joint least squares reverse time migration of characteristic waves and primary waves in a viscous acoustic medium are accurately simulated to obtain wave field values. Least-squared reverse time migration imaging of the characteristic wave and primary wave of the viscous acoustic medium is achieved based on the wave field value.

2. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1, characterized in that, Attenuated seismic data including multiples, diffracted waves, prismatic waves, and primary waves are as follows: （1） Based on the conventional least-squares reverse-time offset objective function: （2） The gradient formula is obtained from equation (2): （3） In the formula, As a primary wave adjoint operator, the noise increases with the number of iterations of least squares reverse time migration.

3. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1, characterized in that, The gradient formula obtained from the objective function of equation (4) is as follows: （5） In the formula, , , and These represent the wave fields of the primary wave, multiple waves, diffracted wave, and prism wave propagating in the backward direction, respectively. Indicates velocity disturbance, and These represent the primary wave, multiple waves, diffracted wave, and prism wave fields, respectively, propagating in the forward direction.

4. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1, characterized in that, exist Q In the case of compensation, equation (6) simplifies to （7） In the formula x As coordinates, For the forward propagation operator of the wave field.

5. A method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1 or 4, characterized in that, The implementation method of introducing the adjoint quasi-differential equation is as follows: Based on the Born approximation theory, the following offset equation is obtained: （8） In the formula, This represents the source term of the perturbation wave field. I This represents the offset result term; according to the adjoint state theory, the adjoint equation is obtained: （9） In the formula, express Q The wave field operator after compensation propagation, express Q Synthetic data of attenuation.

6. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1, characterized in that, The accurate simulation of the forward propagation wave field of the joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium specifically includes: The inverse offset equation is shown below. （10） In the formula This represents the wavefield of the source term wave propagation for compensation. The earthquake source indicating compensation; The forward propagation wave field is represented as: （11） In the formula, Represents the coordinates of the earthquake source, where, The forward operand representing compensation, This represents the positively extended source wave field.

7. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 1, characterized in that, It can be calculated from the following formula: （12） In the formula, The backpropagation operator represents compensation. I(x) Let S represent the offset result of the xth shot, S represent the firing point, and r represent the receiving point.

8. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 6, characterized in that, The back-propagating wave field of the joint least-squares reverse-time migration of the characteristic wave and the primary wave in a viscous acoustic medium is expressed as: （13） In the formula, and yes and The accompanying operator of the compensation, The backpropagation operator represents compensation; and This represents the composite data calculated in the intermediate process compared to the original data. and This represents the final synthesized data and the original data for attenuation compensation; and denoted as the initial backpropagation operator and the receiving wave field in the iteration, respectively; the subscripts 0, 1 and 2 in the formula represent the initial state, intermediate state and final state, respectively.

9. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 8, characterized in that, The least-squares reverse-time migration of the characteristic wave and the primary wave in the viscous acoustic medium, based on the obtained wavefield values, specifically includes: Using the steepest descent method k The step size for the next iteration is: ，（14） Calculate the conjugate gradient direction and the corresponding step size.

10. The method for joint least-squares reverse-time migration of characteristic waves and primary waves in a viscous acoustic medium according to claim 9, characterized in that, No. k The result of the next iteration is updated in the following way: ，（15） This represents the result of the least-squares reverse-time offset in the k-th iteration. Let k be the iteration step size. This represents the updated gradient.

Images