A method for iteratively optimizing extraction of a deep domain seismic wavelet

Abstract

The application discloses a method for iteratively optimizing extraction of a deep domain seismic wavelet, and directly uses deep domain data and original logging data to quickly and efficiently extract a deep domain seismic wavelet. A deep domain seismic wavelet base is established, a target function for deep domain seismic wavelet extraction is constructed, control parameters of the deep domain seismic wavelet base are obtained through optimization iteration, and finally, the deep domain seismic wavelet is obtained, so that the parameter adjustment process is simplified, and the operation difficulty and subjectivity are reduced. In practical application, the deep domain seismic wavelet can be accurately and reliably extracted through a limited number of iterations, and high robustness and accuracy can be maintained under complex geological conditions.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas seismic exploration, specifically relating to an iterative optimization method for extracting depth-domain seismic wavelets. Background Technology

[0002] Extracting seismic wavelets from depth-domain seismic data is an indispensable cornerstone for depth-domain seismic inversion. With the widespread application of depth-domain seismic migration data in Earth exploration and oil and gas resource exploration, inversion using depth-domain seismic data is a crucial foundational method for achieving detailed imaging of subsurface stratigraphic structure and important structural information, characterizing reservoir distribution, and identifying oil and gas resources. However, because depth-domain seismic data does not satisfy the "linear depth invariance" condition of traditional convolution models, existing time-domain seismic wavelet extraction methods cannot be directly applied to the depth domain, posing significant challenges to directly extracting seismic wavelets in the depth domain.

[0003] Currently, the extraction of seismic wavelets in the depth domain mainly relies on two technical approaches: one approach involves converting the depth-domain seismic data to the time domain or constant velocity depth domain, extracting the seismic wavelet using existing time-domain methods, and then converting the extracted seismic wavelet back to the depth domain (Zhang et al., 2018; 2019; 2020; 2022). However, this domain conversion inevitably leads to information loss and error accumulation in both the depth-domain seismic data and depth-domain well logging data, affecting the accuracy of seismic wavelet extraction and reducing computational efficiency. The other approach utilizes depth-wavenumber spectral analysis to extract the seismic wavelet separately for each seismic trace (Zhang and Deng, 2018; 2023; Andreas et al., 2019; Sengupta et al., 2021; Cai et al., 2022; 2024; Sun et al.). As discussed in al. (2024), the lack of depth-domain logging data constraints leads to multiple solutions in seismic wavelet extraction, and the computational overhead and inefficiency are high due to the need to process seismic data channel by channel. This invention aims to address the limitations and problems of these two methods by directly achieving higher efficiency and accuracy seismic wavelet extraction in the depth domain. Summary of the Invention

[0004] The purpose of this invention is to provide a method for rapidly and efficiently extracting depth-domain seismic wavelets directly from depth-domain data and raw well logging data. The method includes the following main steps:

[0005] (1) Input the depth domain logging data of the well, and calculate the depth domain logging reflection coefficient r using the depth domain logging P-wave velocity and V density ρ; input the actual depth domain seismic record S near the well, the length of the seismic record is N, and the depth sampling interval of the seismic record is Δh; set the depth domain seismic wavelet velocity V to be extracted according to the P-wave velocity V. c ;

[0006] (2) Using the characteristics of the actual depth-domain seismic record S near the well and the depth logging reflection coefficient r of the well, a depth-domain seismic wavelet basis ψ(h|k) is established. m Construct the objective function for deep-domain seismic wavelet extraction, σ,φ,a).

[0007]

[0008] Where h represents depth, Let Rs represent the L2 norm. j Let Rs represent the residual of the j-th iteration. 1 =S, (k m ,σ,φ,a) is the set of control parameters for the depth-domain seismic wavelet basis, which represent the mean wave number, scale factor, phase, and amplitude, respectively;

[0009] In the above formula, the wavenumber domain seismic wavelet basis calculated using the depth domain seismic wavelet basis is used to synthesize the depth domain seismic record S′, as shown in the following formula:

[0010] S′(k m ,σ,φ,a)=real{B[A⊙Φ(k|k m ,σ,φ,a)]}·r,

[0011] Where ⊙ denotes the Hadamard product operation of vectors, real{·} denotes the operation of taking the real part, k is the wave number, Φ is the wave number domain seismic sub-wave basis, and A and B are the established phase extension matrix and its corresponding conjugate matrix, respectively.

[0012] (3) Pre-set the number of iterations and the minimum residual E, and use the objective function from the previous step to iteratively solve the control parameter set of the j-th depth domain seismic wavelet basis. The specific process is as follows:

[0013] ① Calculate the mean wavenumber and scale factor of the depth-domain seismic wavelet basis:

[0014]

[0015] Where H(·) represents the Hilbert transform operation, and <·,·> represents the vector dot product operation;

[0016] ② Calculate the amplitude coefficient P in the complex domain. j :

[0017]

[0018] in, The superscript T indicates the matrix transpose operation;

[0019] ③ Calculate the phase and amplitude of the depth-domain seismic wavelet basis:

[0020]

[0021] Where Angle(·) is the argument operation for complex numbers, and |·| is the modulus operation for complex numbers;

[0022] ④ Calculate the residuals using the following formula:

[0023]

[0024] ⑤ Repeat steps ① to ④ until the preset number of iterations is reached or the following formula is satisfied, then exit the iteration process:

[0025]

[0026] (4) Based on the depth-domain seismic wavelet basis extracted in each iteration of the previous calculation, the final depth-domain seismic wavelet is obtained by superimposing the data:

[0027]

[0028] in, This is the final depth-domain seismic wavelet. Attached Figure Description

[0029] Figure 1 These are depth-domain logging data and well-side seismic data used in this embodiment of the invention. The logging data has a depth range of 2914m-3133m, a logging depth sampling interval of 0.15m, and 1461 sampling points. Figure 1 (a) represents the P-wave velocity in well logging. The vertical axis represents depth in meters, and the horizontal axis represents velocity in meters per second (m / s). Figure 1 (b) The logging density is shown on the vertical axis, with depth in meters and density on the horizontal axis, in grams per cubic centimeter (g / cm³). 3 ). Figure 1 (c) represents the well logging reflection coefficient, with the vertical axis representing depth in meters. Figure 1 (d) shows the seismic record near the well in the depth domain. The vertical axis represents the depth in meters, and the horizontal axis represents the trace number. This well is located in trace number 6 (marked with an inverted triangle).

[0030] Figure 2 This describes the depth-domain seismic wavelet extraction process and results in an embodiment of the present invention. Figure 2(a) Comparison between actual well-side depth domain seismic data (black waveform) and depth domain seismic data reconstructed using the depth domain seismic wavelet extracted by this invention (gray waveform). Note: For ease of direct observation and comparison, the depth domain seismic data reconstructed using the depth domain seismic wavelet extracted by this invention (gray waveform) is superimposed on the actual well-side depth domain seismic data (black waveform) profile. The vertical axis represents depth in meters, and the horizontal axis represents the trace number. Figure 2 (b) represents the final extracted depth-domain seismic wavelet, with the vertical axis representing amplitude and the horizontal axis representing length, in meters. Figure 2 (c) represents the amplitude of the depth-domain seismic wavelet basis extracted in each iteration, with the vertical axis representing the amplitude and the horizontal axis representing the iteration number. Figure 2 (d) represents the depth-domain seismic wavelet basis extracted in each iteration, with the vertical axis representing the length in meters and the horizontal axis representing the iteration number. Detailed Implementation

[0031] Figure 1 and Figure 2 The depth-domain seismic wavelet extraction method of the present invention is demonstrated, and its specific implementation includes the following steps:

[0032] (1) Input well depth domain logging data (e.g.) Figure 1 (a) and Figure 1 (b)) Utilizing depth-domain logging P-wave velocity ( Figure 1 (a)) and V density ρ( Figure 1 (b) Calculate the depth domain logging reflection coefficient r( Figure 1 (c)); Input the actual depth domain seismic record S( ) near the well. Figure 1 (d) The well is located in the 6th channel (inverted triangle label), the length of the seismic record is 1461, and the depth sampling interval of the seismic record is 0.15m; based on the P-wave velocity V, the depth domain seismic wavelet velocity V to be extracted is set. c =3000m / s;

[0033] (2) Using the characteristics of the actual depth-domain seismic record S near the well and the depth logging reflection coefficient r of the well, a depth-domain seismic wavelet basis ψ(h|k) is established. m Construct the objective function for deep-domain seismic wavelet extraction, σ,φ,a).

[0034]

[0035] Where h represents depth, Let Rs represent the L2 norm. j Let Rs represent the residual of the j-th iteration. 1 =S, (k m,σ,φ,a) is the set of control parameters for the depth-domain seismic wavelet basis, which represent the mean wave number, scale factor, phase, and amplitude, respectively;

[0036] In the above formula, the wavenumber domain seismic wavelet basis calculated using the depth domain seismic wavelet basis is used to synthesize the depth domain seismic record S′, as shown in the following formula:

[0037] S′(k m ,σ,φ,a)=real{B[A⊙Φ(k|k m ,σ,φ,a)]}·r,

[0038] Where ⊙ denotes the Hadamard product operation of vectors, real{·} denotes the operation of taking the real part, k is the wave number, Φ is the wave number domain seismic sub-wave basis, and A and B are the established phase extension matrix and its corresponding conjugate matrix, respectively.

[0039] (3) Set the number of iterations to 5 and the minimum residual E = 0.001 in advance. Using the objective function from the previous step, iteratively solve the control parameter set of the j-th depth domain seismic wavelet basis. The specific process is as follows:

[0040] ① Calculate the mean wavenumber and scale factor of the depth-domain seismic wavelet basis:

[0041]

[0042] Where H(·) represents the Hilbert transform operation, and <·,·> represents the vector dot product operation;

[0043] ② Calculate the amplitude coefficient P in the complex domain. j :

[0044]

[0045] in, The superscript T indicates the matrix transpose operation;

[0046] ③ Calculate the phase and amplitude of the depth-domain seismic wavelet basis:

[0047]

[0048] Where Angle(·) is the argument operation for complex numbers, and |·| is the modulus operation for complex numbers;

[0049] ④ Calculate the residuals using the following formula:

[0050]

[0051] ⑤ Repeat steps ① to ④ until the preset number of iterations is reached or the following formula is satisfied, then exit the iteration process:

[0052]

[0053] (6) Based on the calculation in the previous step, the actual iteration was completed in 2 steps. Figure 2 (c), i.e., j=2), the depth-domain seismic wavelet basis extracted in the two iterations ( Figure 2 (d) are superimposed to obtain the final depth-domain seismic wavelet. ( Figure 2 (b)):

[0054]

[0055] exist Figure 2 In (a), the reconstructed depth domain seismic data (gray waveform) using the final depth domain seismic wavelet extracted in the embodiment of the present invention is highly consistent with the actual depth domain seismic data (black waveform) near the well, with a correlation coefficient of 0.96, indicating that the method of the present invention is efficient and reliable.

[0056] The advantages of the method of the present invention are as follows: (1) The method of the present invention directly uses the original well logging data to extract the seismic wavelet in the depth domain without resampling the data, thus avoiding the problem of missing detailed information caused by resampling and ensuring that the effective information of the well logging data is fully utilized; (2) In the process of extracting the seismic wavelet in the depth domain, the method of the present invention only requires four control parameters: average wave number, scale factor, phase and amplitude. Compared with the traditional seismic wavelet extraction method, the parameter adjustment process is greatly simplified, and the operation difficulty and subjectivity are reduced; (3) In practical applications, the method of the present invention only needs to perform 2-3 iterations of calculation to accurately and reliably extract the seismic wavelet in the depth domain, showing strong robustness and high computational efficiency.

[0057] The above embodiments are only used to illustrate the present invention. The implementation steps of the method can be varied. Any equivalent transformations and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A method for iteratively optimizing the extraction of depth-domain seismic wavelets, comprising the following steps: (1) Input the depth domain logging data of the well and use the depth domain logging P-wave velocity and density Calculate the depth domain logging reflection coefficient ; Input well-side actual depth domain seismic records The length of the earthquake record is The depth sampling interval of the seismic records is According to the longitudinal wave velocity Set the depth-domain seismic wavelet velocity to be extracted. ; (2) Using actual depth domain seismic records near the well Deep-domain logging reflection coefficient of the well Based on the characteristics, establish a deep-domain seismic wavelet basis. Construct the objective function for deep-domain seismic wavelet extraction: ， Where h represents depth, Describing the L2 norm, Indicates the first The residual of the next iteration, and set , It is the set of control parameters for the depth-domain seismic wavelet basis, which represent the mean wave number, scale factor, phase, and amplitude, respectively. In the above equation, the wavenumber domain seismic wavelet basis calculated using the depth domain seismic wavelet basis is used to synthesize the depth domain seismic record. The formula is as follows: ， in, This represents the Hadamard product operation of vectors. This indicates the operation of taking the real part. For wave number, For wavenumber domain seismic sub-wave bases, and These are the established phase extension matrix and its corresponding conjugate matrix, respectively. (3) Pre-set the number of iterations and the minimum residual. Using the objective function from the previous step, the control parameter set of the j-th depth domain seismic wavelet basis is iteratively solved. The specific process is as follows: ① Calculate the mean wavenumber and scale factor of the depth-domain seismic wavelet basis: ， in, This represents the Hilbert transform operation. This represents the vector dot product operation; Calculate the amplitude coefficient in the complex domain : ， in, The superscript T indicates the matrix transpose operation; ③ Calculate the phase and amplitude of the depth-domain seismic wavelet basis: ， in, For the argument operation of complex numbers, Modular operation for complex numbers; ④ Calculate the residual using the following formula: ， ⑤ Repeat steps ① to ④ until the preset number of iterations is reached or the following formula is satisfied, then exit the iteration process: ； (4) Based on the depth-domain seismic wavelet basis extracted in each iteration of the previous calculation, the final depth-domain seismic wavelet is obtained by superimposing the data: ， in, This is the final depth-domain seismic wavelet.

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