A velocity and Q fluctuation equation inversion method based on local domain travel time

Abstract

The application discloses a velocity and Q fluctuation equation inversion method based on local domain travel time, relates to the technical field of oil exploration, and comprises the following steps: obtaining seismic data through viscoacoustic forward modeling; calculating travel time difference and obtaining time difference accompanying source; calculating inverse propagating wave field and gradient; updating velocity model and Q model. The method is based on wave equation travel time inversion, uses travel time information, avoids the problem of cycle skipping of full waveform inversion under the condition of large time difference, and reduces the dependence on the initial model; the local domain travel time difference is calculated by using the DTW algorithm, the corresponding time difference can be accurately calculated, the cross-correlation algorithm tends to large-amplitude in-phase axis under the condition of large time difference is avoided, and the inversion precision is improved; the method uses travel time information to simultaneously update the velocity and Q, avoids a large amount of Fourier transform calculation in the frequency domain method, and greatly improves the inversion efficiency.

Description

Technical Field

[0001] This invention relates to the field of petroleum exploration technology, and in particular to a method for inverting velocity and Q-wave equations based on local domain travel time. Background Technology

[0002] The viscosity of real geological formations affects the propagation of seismic waves, causing amplitude attenuation and phase distortion. This attenuation characteristic is usually quantified by the quality factor Q. A low Q value means that the energy loss or attenuation of each wave cycle is large. If these attenuations are not compensated, it will lead to reduced imaging resolution and inaccurate imaging location. Especially in oil and gas reservoir areas, absorption attenuation compensation must be performed to obtain accurate reservoir information and high-quality imaging results. The prerequisite for high-resolution imaging is to obtain a high-resolution velocity and Q model.

[0003] Current methods for obtaining velocity and Q models are primarily based on full-waveform inversion (FWI), and a series of inversion strategies are developed based on this. However, due to the inaccuracy of the initial velocity, there is a highly nonlinear relationship between the residual objective function and the velocity. When the initial velocity is poor, there is a large travel time difference between the observed seismic record and the simulated seismic record, which can easily lead to cycle skipping problems and cause the inversion to get trapped in local minima. Furthermore, since velocity and Q are a pair of strongly correlated parameters, they significantly influence each other in the inversion process, and any Q-tomography method is highly dependent on the accuracy of the velocity model. The mainstream industrial workflow uses a separate inversion method, but the correlation between velocity and Q can lead to insufficient accuracy in the separate inversion results, posing difficulties for oil and gas exploration.

[0004] Travel time is linearly correlated with long-wavelength velocities, therefore, tomographic inversion using travel time information is often employed to obtain preliminary velocity models, primarily including ray-based methods and wave equation-based methods. Due to limitations such as high-frequency assumptions in ray-based methods, wave equation-based travel time inversion can handle complex wavefield conditions and directly calculates travel time differences from seismic records without requiring additional travel time calculations, greatly improving inversion efficiency. However, to obtain more accurate travel time differences, cross-correlation methods require windowing during calculation. This approach can cause the travel time differences to be biased towards large-amplitude in-phase axes within the time window, leading to a reduction in the resolution of the inversion results.

[0005] Obtaining high-resolution velocity and Q models is one of the urgent problems to be solved in oil exploration. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention discloses a velocity and Q wave equation inversion method based on local domain travel time. This method is based on travel time inversion of the wave equation. By combining the time difference objective function with the SLS-based viscous acoustic wave equation through a connection function, the accompanying source of the time difference is derived, and the gradients with respect to velocity and Q are obtained. The accompanying source of the time difference has the influence of both velocity and Q, enabling the method to update the velocity and Q models simultaneously under the condition of the initial model range. Furthermore, by employing the DTW algorithm, a more accurate travel time difference can be obtained, thus improving the inversion accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for inverting velocity and Q-wave equations based on local domain travel time includes the following steps:

[0009] Step 1: Obtain seismic data through acoustic forward modeling.

[0010] Based on the viscous acoustic wave equation of the standard linear solid attenuation model SLS, Q-display is introduced into the wave equation. The observed seismic records are obtained by forward modeling with the real velocity model and the real Q model using the finite difference method, and the simulated seismic records of the first iteration are obtained by forward modeling with the initial velocity model and the initial Q model, while preserving the forward propagation wave field part in the gradient.

[0011] Step 2: Calculate the travel time difference and obtain the associated sources of the time difference.

[0012] The local travel time difference between observed and simulated seismic records is calculated using the DTW algorithm, and the associated sources of the travel time difference are calculated using the derived formula.

[0013] Step 3: Calculate the backpropagating wavefield and gradient

[0014] Substituting the adjoint source into the adjoint equation yields the reverse propagating wave field, which, combined with the forward propagating wave field, provides the gradient between velocity and Q.

[0015] Step 4: Update the velocity model and Q-model

[0016] The velocity and Q are updated by gradient correspondence, and a new simulated seismic record is obtained by forward modeling using the new velocity and Q model. Steps two to four are repeated to obtain the final velocity and Q model.

[0017] Optionally, in step one, based on the viscous acoustic wave equation of the standard linear solid attenuation model, Q is explicitly introduced into the wave equation, as shown in the following formula:

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, Represents a pressure field. Represents the velocity vector. Represents divergence, Represents density, Represents memory variables related to the quality factor Q. Representative at The source function at that location, , , and These are parameters related to velocity and Q, and their relationship is shown in the following formula:

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] In the formula, Represents frequency.

[0027] Optionally, in step two, based on the adjoint state method, the corresponding adjoint equation is derived, as shown in the following formula:

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula, Represents the source of time difference, , , , With the wave equation , , , One-to-one correspondence.

[0033] Optionally, in step two, the DTW algorithm is used to replace the traditional cross-correlation method to calculate the travel time difference between the observed seismic record and the simulated seismic record, and the travel time difference value is mapped to each point in the seismic record to accurately calculate the local travel time difference.

[0034] Optionally, in step three, the gradients of the time difference objective function with respect to velocity and Q are derived respectively, as shown in the following formulas:

[0035] ;

[0036] ;

[0037] ;

[0038] In the formula, Represents the objective function. The travel time difference between observed and simulated seismic records. represent The gradient, through updating Speed ​​up Q's updates. Represents the velocity gradient. Represents bulk modulus. The divergence representing the velocity vector is the propagating wave field portion obtained and preserved during the forward modeling of the viscous acoustic wave equation in step one. and In step three, the back propagating wave field part is obtained by calculating the adjoint equation, and the gradient is calculated simultaneously during the calculation of the adjoint equation.

[0039] During the derivation of the gradient, the form of the time difference-related source is obtained, as shown in the following formula:

[0040] ;

[0041] In the formula, This represents the derivative of the observed seismic record with respect to time after incorporating the time difference.

[0042] The beneficial effects of this invention are as follows: This invention connects travel time information with the viscous acoustic wave equation through travel time inversion of the wave equation. Based on the linear correlation between velocity and long-wavelength velocity, it simultaneously inverts velocity and Q-model even when the initial model is poor. Furthermore, it uses the DTW algorithm to calculate the travel time difference between observed seismic records and simulated seismic records, which can obtain more accurate travel time difference values ​​compared to cross-correlation algorithms, thus improving inversion accuracy. Finally, simulation experiments using a thrust body model are conducted to demonstrate the accuracy of the method of this invention.

[0043] The method of this invention utilizes travel time information to simultaneously perform tomographic inversion of velocity and Q, avoiding the dependence of full waveform multi-parameter inversion on the initial model. At the same time, it uses travel time information to invert the Q model, avoiding a large number of Fourier calculations in traditional frequency domain methods, thus reducing computational costs. In addition, by using the DTW algorithm to calculate the travel time difference, a more accurate time difference value can be obtained, improving the inversion accuracy. Attached Figure Description

[0044] Figure 1This is a schematic diagram of the process for inverting the velocity and Q-wave equations based on local domain travel time according to the present invention.

[0045] Figure 2A This is a real velocity model shown in one embodiment of the present invention;

[0046] Figure 2B This is a true Q-model shown in an embodiment of the present invention;

[0047] Figure 3A This is an initial inversion velocity model shown in one embodiment of the present invention;

[0048] Figure 3B This is an initial Q-model shown in one embodiment of the present invention;

[0049] Figure 4 This is a forward-modeled seismic record illustrated in one embodiment of the present invention;

[0050] Figure 5A The time difference calculation result is shown in one embodiment of the present invention;

[0051] Figure 5B This is a time difference-related source illustrated in one embodiment of the present invention;

[0052] Figure 6A The final inversion velocity result is shown in one embodiment of the present invention;

[0053] Figure 6B This is the final inversion Q result shown in one embodiment of the present invention;

[0054] Figure 7A This is a comparison of the inverted velocity and the actual velocity shown in an embodiment of the present invention;

[0055] Figure 7B This is a comparison of the inverted Q and the real Q channel shown in an embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 a part of the embodiments of the present invention, not all of them. 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. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. 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.

[0057] A method for inverting velocity and Q-wave equations based on local travel time, such as... Figure 1 As shown, it includes the following steps:

[0058] Step 1: Obtain seismic data through acoustic forward modeling.

[0059] In wave equation inversion, to simulate the viscosity of real strata, the Q parameter needs to be introduced into the wave equation. Different theories have different forms of viscous-acoustic wave equations. This invention, based on the SLS model's viscous-acoustic wave equation, explicitly introduces the quality factor Q into the wave equation, as shown in the following formula:

[0060] ;

[0061] ;

[0062] ;

[0063] In the formula, Represents a pressure field. Represents the velocity vector. Represents divergence, Represents density, Represents memory variables related to the quality factor Q. Representative at The source function at that location, , , and These are parameters related to velocity and Q, and their relationship is shown in the following formula:

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] In the formula, Represents frequency.

[0069] Figure 2A For a realistic thrust velocity model, Figure 2B To correspond with the Q-model, the red area in the figure represents a low Q-value region, which in reality manifests as a gas reservoir region with strong attenuation. Based on this velocity model and the Q-model, the observed seismic records are simulated using the aforementioned viscous acoustic wave equation, as shown below. Figure 4 As shown.

[0070] Figure 3AThe initial velocity model is obtained by smoothing the real model on a large scale. It is linear in the longitudinal direction and simulates the initial velocity model obtained in actual production. Figure 3B The initial Q model is a uniform model, simulating an unknown gas reservoir area in actual production.

[0071] Step 2: Calculate the travel time difference and obtain the associated sources of the time difference.

[0072] The DTW algorithm is used to calculate the local travel time difference between observed and simulated seismic records, and the associated sources of the travel time difference are calculated using the derived formula. The key to wave equation travel time inversion lies in the calculation of travel time difference. In order to obtain accurate travel time difference, windowing is generally used for cross-correlation calculation. However, when the travel time difference is large, the travel time difference value will be biased towards the large amplitude in-phase axis in the time window, resulting in a decrease in inversion accuracy.

[0073] To obtain an accurate time difference, this invention uses the DTW algorithm for calculation, such as... Figure 5A As shown, each point in the data domain corresponds to its time difference value, rather than calculating a time difference for each time window in windowed calculations, while simultaneously obtaining the time difference associated with the source ( Figure 5B Its form is obtained from the gradient derivation process, and the formula is as follows:

[0074] ;

[0075] In the formula, Represents the source of time difference, This represents the derivative of the observed seismic records with respect to time after incorporating time differences. This represents the travel time difference between observed earthquake records and simulated earthquake records.

[0076] Step 3: Calculate the backpropagating wavefield and gradient

[0077] Traditional wave equation travel time inversion methods are only applied to acoustic wave equations. However, both velocity and Q affect travel time. Therefore, this method is applied to viscous acoustic wave equations, and the gradients of the time difference objective function with respect to velocity and Q are derived separately, as shown in the following formulas:

[0078] ;

[0079] ;

[0080] ;

[0081] In the formula, Represents the objective function. The travel time difference between observed and simulated seismic records. represent The gradient, through updating Speed ​​up Q's updates. Represents the velocity gradient. Represents bulk modulus. The divergence representing the velocity vector is the propagating wave field portion obtained and preserved during the forward modeling of the viscous acoustic wave equation in step one. and In step three, the back propagating wave field part is obtained by calculating the adjoint equation, and the gradient is calculated simultaneously during the calculation of the adjoint equation.

[0082] Step 4: Update the velocity model and Q-model

[0083] By updating the velocity and Q through gradient correspondence and repeating the iteration, the final velocity model is obtained. Figure 6A ) and Q model ( Figure 6B Through random sampling comparison () Figure 7A , Figure 7B It is evident that the inverted velocity curve closely matches the true velocity curve, and the inverted Q-model curve accurately reflects the location of the attenuation region. This method of inversion, when the initial model is essentially linear, yields a velocity model that... Figure 3A ) and uniform Q model ( Figure 3B The high-precision velocity model and Q model were obtained, providing an initial model for full waveform inversion applications in actual production.

[0084] This invention is based on the wave equation travel time inversion theory. It develops a velocity and Q wave equation inversion method based on local domain travel time. By using the viscous acoustic wave equation under the SLS model, the gradient of the time difference objective function with respect to velocity and Q is derived, and the time difference adjoint source is obtained. This allows for the simultaneous inversion of velocity and Q models under the condition of initial model range. At the same time, it avoids the large amount of Fourier transform calculations in the frequency domain Q inversion method, reducing the computational cost. Furthermore, the DTW algorithm is used to calculate the local domain travel time difference, which yields more accurate time difference values ​​compared to the traditional cross-correlation algorithm, thus improving the inversion accuracy.

[0085] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for inverting velocity and Q-wave equations based on local domain travel time, characterized in that, Includes the following steps: Step 1: Obtain seismic data through acoustic forward modeling. Based on the viscous acoustic wave equation of the standard linear solid attenuation model, Q is explicitly introduced into the wave equation. The observed seismic records are obtained by forward modeling with the real velocity model and the real Q model using the finite difference method, and the simulated seismic records of the first iteration are obtained by forward modeling with the initial velocity model and the initial Q model, while preserving the forward propagation wave field part in the gradient. Step 2: Calculate the travel time difference and obtain the associated sources of the time difference. The local travel time difference between observed and simulated seismic records is calculated using the DTW algorithm, and the associated sources of the travel time difference are calculated using the derived formula. Step 3: Calculate the backpropagating wavefield and gradient Substituting the time difference-related source into the adjoint equation yields the antipropagating wave field, which, combined with the forward propagating wave field, provides the gradient between velocity and Q. Step 4: Update the velocity model and Q-model The velocity and Q are updated by gradient correspondence, and a new simulated seismic record is obtained by forward modeling using the new velocity model and Q model. Steps two to four are repeated to obtain the final velocity model and Q model. In step one, based on the viscous acoustic wave equation of the standard linear solid attenuation model, Q is explicitly introduced into the wave equation, as shown in the following formula: ； ； ； In the formula, Represents the velocity vector. Represents divergence, Representative at The source function at that location, Represents a pressure field. Represents memory variables related to the quality factor Q. Represents density, Represents bulk modulus. , , and These are parameters related to velocity and Q, and their relationship is shown in the following formula: ； ； ； ； In the formula, Represents frequency; In step two, based on the adjoint state method, the corresponding adjoint equation is derived, as shown in the following formula: ； ； ； ； In the formula, Represents the source of time difference, , , , With the wave equation , , , One-to-one correspondence, and In step three, the back propagating wave field part is obtained by calculating the adjoint equation, and the gradient is calculated simultaneously during the calculation of the adjoint equation. In step three, the gradients of the time difference objective function with respect to velocity and Q are derived, as shown in the following formulas: ； ； ； In the formula, Represents the objective function. The travel time difference between observed and simulated seismic records. represent The gradient, through updating Speed ​​up Q updates. Represents the velocity gradient. The divergence representing the velocity vector is the propagating wave field part obtained and saved in step one through the forward modeling of the viscous acoustic wave equation; During the derivation of the gradient, the form of the time difference-related source is obtained, as shown in the following formula: ； In the formula, This represents the derivative of the observed seismic record with respect to time after incorporating the time difference.

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