A method and system for extracting attenuated travel times based on optimal wavelets

Abstract

The present invention provides a method and system for extracting attenuated travel time based on the optimal wavelet, belonging to the technical field of geophysical exploration. The method for extracting attenuated travel time based on the optimal wavelet extracts the first arrival waveform signal at the first arrival time, converts the first arrival waveform signal to the complex cepstrum domain, extracts the optimal wavelet in the complex cepstrum domain, and then obtains the attenuated travel time by using the optimal wavelet. In addition to using the time information of the first arrival, the present invention also uses the waveform information of the first arrival, extracts the optimal wavelet through the first arrival waveform, and effectively utilizes the redundant information in the prestack seismic data. During the process of extracting the wavelet, part of the noise interference can be filtered out, providing a more accurate and reliable attenuated travel time for Q-value tomography.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical exploration, and particularly relates to a method and system for extracting attenuated travel time based on the optimal wavelet, which can be applied to the Q-value inversion technology in seismic exploration. Background Technique

[0002] The viscoelastic effect in the earth medium objectively exists and will cause the absorption and attenuation of seismic wave energy, which has a great impact on the imaging quality. Q-value tomography is a reliable Q-value modeling technology. In Q-value modeling, the attenuated travel time is one of the key parameters, and its importance is equivalent to that of the first arrival in velocity tomography. Accurate attenuated travel time is the premise for accurate Q-value modeling.

[0003] The Q-value tomography technology was first applied to the study of natural earthquakes and achieved good results in the study of the attenuation structure in the shallow crust. In recent years, the Q-value tomography technology has also been well developed in oil seismic exploration. This method is based on ray tomography theory, can effectively adapt to the lateral variation of underground Q-value, and does not depend on the absolute amplitude, and can obtain a reliable Q-value distribution. In the Q-value first arrival wave tomography, the attenuated travel time is a very critical parameter. The traditional spectral ratio method can obtain relatively accurate attenuated travel time in the case of simple formation structure. However, as the offset increases, the first arrival not only contains direct waves, but also may contain reflected waves and refracted waves. These waveforms are mixed together, which will cause the disorder of the frequency spectrum, and finally lead to very inaccurate results obtained by the spectral ratio method. In the Q-value reflected wave tomography, if there are relatively thin underlying layers, there will also be overlapping parts in the reflected waves at the top and bottom interfaces, which will also cause the disorder of the frequency spectrum, and then lead to inaccurate extraction of the attenuated travel time and unreliable inversion results.

[0004] Aiming at the above problems, the present invention proposes a technology for extracting attenuated travel time based on the optimal wavelet, which can effectively solve the problem of incorrect extraction of attenuated travel time caused by the mixing of different wave field components, and provides strong technical support for Q-value tomography. No corresponding literature materials have been found for this method. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems existing in the above-mentioned prior art, and provide a method and system for extracting attenuated travel time based on the optimal wavelet, which uses pre-stack shot records to extract accurate attenuated travel time and provides reliable attenuated travel time for the Q-value tomography technology. An accurate Q-value model can help effectively improve the resolution of the seismic migration profile, and accurate attenuated travel time is the premise for accurate Q-value tomography modeling. By using the method for extracting attenuated travel time based on the optimal wavelet of the present invention, the data information of the pre-stack shot records can be fully utilized to provide accurate and reliable attenuated travel time for Q-value tomography, and provide strong technical guarantee for the stability and reliability of Q-value tomography.

[0006] The present invention is achieved through the following technical solutions:

[0007] The first aspect of the present invention provides an attenuation traveltime extraction method based on an optimal wavelet, wherein the method extracts a first-arrival waveform signal at the first-arrival time, converts the first-arrival waveform signal into a reciprocal spectrum domain, extracts an optimal wavelet in the reciprocal spectrum domain, and then uses the optimal wavelet to obtain the attenuation traveltime.

[0008] A further improvement of the present invention is that the method comprises:

[0009] (1) Extracting the first arrival waveform signal at the first arrival position of the pre-stack shot record;

[0010] (2) converting the initial arrival waveform signal into a complex spectrum domain;

[0011] (3) Extracting the best wavelet;

[0012] (4) converting the optimal wavelet into the time domain to obtain the optimal wavelet time domain signal;

[0013] (5) sequentially performing steps (1) to (4) on each seismic trace in each shot record to obtain the best wavelet for each seismic trace; then establishing a relationship between the best wavelet at the minimum offset and the best wavelet at any position;

[0014] (6) Obtain the attenuation slope and then obtain the attenuation travel time.

[0015] A further improvement of the present invention is that the operation of step (1) comprises:

[0016] Pick up the first arrival information on the pre-stack shot record;

[0017] The first arrival waveform signal at the first arrival position of the pre-stack shot record is extracted through the Hamming window.

[0018] A further improvement of the present invention is that the operation of step (2) comprises:

[0019] The first arrival waveform signal is converted into the complex spectrum domain using the following formula to obtain the complex spectrum time series of the first arrival waveform signal:

[0020]

[0021] in, That is, the time series of the complex spectrum of the first arrival waveform signal, s(t) is the first arrival waveform signal, F is the Fourier transform, F -1 is the inverse Fourier transform.

[0022] A further improvement of the present invention is that the operation of step (3) comprises:

[0023] Use the following optimal wavelet filtering formula to perform low-pass filtering on the complex spectrum time series of the first arrival waveform signal to obtain the optimal wavelet:

[0024]

[0025] where x0 is the minimum offset, x i is the offset of the i-th seismic trace, f c is the main frequency of the first arrival waveform signal at the minimum offset, and h(f) is the optimal wavelet.

[0026] A further improvement of the present invention is that the operation of establishing the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position in step (5) includes:

[0027] According to the principle of spectral ratio method, establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position as follows:

[0028]

[0029] where f refers to frequency, w i (f) refers to the spectrum obtained by Fourier transform of the optimal wavelet corresponding to the i-th seismic data, w min-offset (f) refers to the spectrum obtained by Fourier transform of the optimal wavelet at the minimum offset, C is a constant, and t * is the attenuation travel time.

[0030] A further improvement of the present invention is that the operation of step (6) includes:

[0031] Determine the attenuation slope of the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position by least squares linear fitting:

[0032] k * =-πt *

[0033] where k * is the attenuation slope, π is the pi, and t * is the attenuation travel time;

[0034] Calculate the attenuation travel time using the following formula:

[0035]

[0036] A further improvement of the present invention is that the empirical frequency band range used for the least squares linear fitting is: 1Hz~3·f c .

[0037] A further improvement of the present invention is that the method further includes:

[0038] (7) Calculate the ray Q value using the following formula:

[0039]

[0040] Where Q ray is the ray Q value, t is the first arrival time, and t * is the attenuated travel time corresponding to the path.

[0041] In the second aspect of the present invention, a system for extracting attenuated travel time based on the optimal wavelet is provided. The system includes: a memory, a processor, and a computer program stored on the memory. When the computer program is run by the processor, the following steps are executed:

[0042] (1) Extract the first arrival waveform signal at the first arrival position of the pre-stack shot record;

[0043] (2) Convert the first arrival waveform signal to the complex spectrum domain;

[0044] (3) Extract the optimal wavelet, including:

[0045] Perform low-pass filtering on the complex spectrum time series of the first arrival waveform signal using the following optimal wavelet filtering formula to obtain the optimal wavelet:

[0046]

[0047] Where x0 is the minimum offset, x i is the offset of the i-th seismic trace, f c is the main frequency of the first arrival waveform signal at the minimum offset, and h(f) is the optimal wavelet;

[0048] (4) Convert the optimal wavelet to the time domain to obtain the optimal wavelet time domain signal;

[0049] (5) Process each seismic trace in each shot record sequentially according to steps (1) to (4) to obtain the optimal wavelet of each seismic trace; then establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position;

[0050] (6) Obtain the attenuation slope, and then obtain the attenuated travel time.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention solves the problem that the attenuated travel time cannot be accurately obtained when different types of waves such as the first arrival wave, reflection wave, and refraction wave are aliased. In practical problems, in addition to using the time information of the first arrival, the present invention also uses the waveform information of the first arrival, extracts the optimal wavelet through the first arrival waveform, and effectively utilizes the redundant information in the pre-stack seismic data. During the process of wavelet extraction, part of the noise interference can be filtered out, providing a more accurate and reliable attenuated travel time for Q-value tomography. Description of the Drawings

[0052] Figure 1-1 is the velocity gradient model;

[0053] Figure 1-2 is the Q-value model;

[0054] Figure 2 is the shot record obtained by forward modeling of the model through the viscoacoustic wave equation. The vertical axis is time (s), and the horizontal axis is the number of receiving channels;

[0055] Figure 3 is Figure 2 the display of the first arrival waveform thinning in Figure 2 It can be seen from that as the offset increases, the aliasing phenomenon of the first arrival waveform becomes more and more obvious;

[0056] Figure 4 is the display of the wavelet waveform thinning extracted from different seismic channels in the present invention;

[0057] Figure 5 is the ray Q-value extracted by numerical simulation in Embodiment 1. The horizontal direction represents the number of seismic channels, and the vertical direction represents the Q-value;

[0058] Figure 6 is the first arrival attenuation travel time extracted by numerical simulation in Embodiment 1. The horizontal direction represents the number of seismic channels, and the vertical direction represents the attenuation travel time;

[0059] Figure 7 is the seismic shot record in actual production used in Embodiment 2. The horizontal axis represents the number of seismic channels, and the vertical axis represents time;

[0060] Figure 8 is the ray Q-value extracted from actual data in Embodiment 2. The vertical axis represents the Q-value, and the horizontal axis represents the number of seismic channels;

[0061] Figure 9 is the first arrival attenuation travel time extracted from actual data in Embodiment 2. The vertical axis represents the attenuation travel time, and the horizontal axis represents the number of seismic channels;

[0062] Figure 10 Flow chart of the steps of the method of the present invention. Detailed Description of the Embodiments

[0063] The present invention will be further described in detail below with reference to the drawings:

[0064] The present invention can provide accurate attenuation travel times for Q - value tomography. The specific method is as follows: pick up the first - arrival time information on the pre - stack shot records, extract the seismic wave signals at the first - arrival time through a Hamming window, then convert the seismic wave signals to the complex - spectrum domain, and extract the optimal wavelet through optimal wavelet filtering in the complex - spectrum domain. Using the above - mentioned method, the seismic wavelets in the first - arrival waveforms of each seismic data trace are extracted, and the attenuation travel times of the corresponding seismic traces are extracted according to the spectral ratio method.

[0065] Specifically, as Figure 10 shown, an embodiment of the method of the present invention is as follows:

[0066]

Embodiment 1

[0067] The method includes:

[0068] (1) Pick up the first - arrival information on the pre - stack shot records, and extract the first - arrival waveform signals at the first - arrival positions of the pre - stack shot records through a Hamming window; the length of the time window is 1.5 times the primary response duration of the seismic signal, and the primary response duration of the seismic signal can be identified from the seismic shot records. This step can be realized by using conventional data - intercepting operations and will not be elaborated here.

[0069] (2) Convert the first - arrival waveform signals intercepted by the Hamming window in step (1) to the complex - spectrum domain, and the conversion formula is as follows:

[0070]

[0071] Where, is the complex - spectrum time series of the first - arrival waveform signals. s(t) is the first - arrival waveform signal;

[0072] (3) Determine the optimal wavelet using the optimal wavelet filtering formula:

[0073]

[0074] Where, x0 is the minimum offset, x i is the offset of the i - th seismic trace, f c is the main frequency of the first - arrival waveform signal at the minimum offset, and h(f) is the optimal wavelet filtering function.

[0075] Use the above optimal wavelet filtering formula to perform low - pass filtering on the complex - spectrum time series of the first - arrival waveform signals to obtain the filtered complex - spectrum domain signal, that is, the complex - spectrum domain signal of the optimal wavelet;

[0076] (4) Convert the filtered complex - spectrum domain signal in step (3) to the time domain, and the conversion formula is as follows:

[0077]

[0078] where \(w(t)\) is the wavelet time-domain signal, \(F\) is the Fourier transform, and \(F^{-1}\) -1 is the inverse Fourier transform.

[0079] Steps (1) to (4) are all processes of extracting the wavelet. The signal obtained in step (4) is the optimal wavelet corresponding to a seismic trace.

[0080] First, each seismic trace in each shot record is processed from (1) to (4) to extract the optimal wavelet of each seismic trace; then, (5) and (6) are used to perform spectral ratio on the optimal wavelets of each seismic trace in the shot record and the optimal wavelet at the minimum offset to obtain the attenuation travel time.

[0081] (5) In the same shot gather, according to the principle of spectral ratio method, there is the following relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position:

[0082]

[0083] where \(f\) refers to the frequency, \(w_i(f)\) i refers to the spectrum obtained by Fourier-transforming the optimal wavelet corresponding to the \(i\)-th seismic data trace (i.e., \(w(t)\) obtained in step (4)), \(w_0(f)\) min-offset refers to the spectrum obtained by Fourier-transforming the optimal wavelet corresponding to the minimum offset, \(C\) is a constant, and \(t\) * is the attenuation travel time.

[0084] (6) In step (5), the logarithmic spectrum presents as a linear function of frequency. The attenuation slope is determined by least-squares linear fitting, and the empirical frequency band range used for linear fitting is: 1 Hz to \(3\cdot f_0\), where \(f_0\) c refers to the dominant frequency of the optimal wavelet at the minimum offset. c According to the formula in step (5), the attenuation slope is:

[0085] \(k = -\pi t\)

[0086] where \(k\) * is the attenuation slope, \(\pi\) is the circumference ratio, and \(t\) *

[0087] is the attenuation travel time. From the above formula, the expression for the attenuation travel time is: * where \(k\) * is the attenuation slope, \(\pi\) is the circumference ratio, and \(t\)

[0088]

[0089] * is the attenuation slope, \(\pi\) is the circumference ratio, and \(t\) * is the attenuation travel time.

[0090] Define the ray \(Q\)-value:

[0091] ​

[0092] Among them, Q ray is the ray Q value, t is the first arrival time, and t * is the attenuated travel time corresponding to the path. The ray Q value has a clear physical meaning and can evaluate the results more intuitively.

[0093] The present invention also provides a system for extracting attenuated travel time based on the optimal wavelet. Embodiments of the system are as follows:

[0094]

Embodiment 2

[0095] The system includes: a memory, a processor, and a computer program stored on the memory. When the computer program is run by the processor, the following steps are executed:

[0096] (1) Extract the first arrival waveform signal at the first arrival position of the prestack shot record;

[0097] (2) Convert the first arrival waveform signal to the complex spectrum domain;

[0098] (3) Extract the optimal wavelet;

[0099] (4) Convert the optimal wavelet to the time domain to obtain the optimal wavelet time domain signal;

[0100] (5) Process each seismic trace in each shot record sequentially through steps (1) to (4) to obtain the optimal wavelet of each seismic trace; then establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position;

[0101] (6) Obtain the attenuation slope, and further obtain the attenuated travel time.

[0102] The operation of step (1) includes:

[0103] Pick up the first arrival information on the prestack shot record;

[0104] Extract the first arrival waveform signal at the first arrival position of the prestack shot record through a Hamming window.

[0105] The operation of step (2) includes:

[0106] Use the following formula to convert the first arrival waveform signal to the complex spectrum domain to obtain the complex spectrum time series of the first arrival waveform signal:

[0107]

[0108] Among them, is the complex spectrum time series of the first arrival waveform signal, and s(t) is the first arrival waveform signal.

[0109] The operation of step (3) includes:

[0110] The optimal wavelet filter formula below is used to filter the complex spectrum time series of the first arrival waveform signal Perform low-pass filtering to obtain the optimal wavelet:

[0111]

[0112] Among them, x0 is the minimum offset, x i is the offset distance of the ith seismic trace, f c is the main frequency of the first arrival waveform signal at the minimum offset, and h(f) is the optimal sub-wave.

[0113] The operation of establishing the relationship between the best wavelet at the minimum offset and the best wavelet at any position in step (5) includes:

[0114] According to the principle of spectral ratio method, the relationship between the best wavelet at the minimum offset and the best wavelet at any position is established as follows:

[0115]

[0116] Where f is the frequency, w is the i (f) refers to the spectrum obtained by Fourier transform of the best wavelet corresponding to the i-th seismic data, w min-offset (f) refers to the spectrum obtained by Fourier transform of the best wavelet at the minimum offset, C is a constant, t * For attenuation when traveling.

[0117] The operation of step (6) includes:

[0118] The attenuation slope of the relationship between the best wavelet at the minimum offset and the best wavelet at any position is determined by least squares linear fitting:

[0119] k * =-πt *

[0120] Among them, k * is the attenuation slope, π is the circumference, t * For attenuation when traveling;

[0121] The attenuation travel time is calculated using the following formula:

[0122]

[0123] The least square linear fitting uses an empirical frequency band range of 1 Hz to 3 f c .

[0124] The embodiments of the present invention are as follows:

[0125] [Example 3]: Model test

[0126] To prove the correctness and effectiveness of the described method and demonstrate that the method has higher precision, a numerical simulation is designed for verification as follows.

[0127] As Figure 1-1 and Figure 1-2 shown, a geological model is designed where the velocity shows a gradient change from top to bottom, gradually increasing, and the Q value shows a layered distribution, gradually increasing from top to bottom. There are 601 grid points horizontally and 301 grid points vertically, with a grid size of 10 m.

[0128] As Figure 2 , using the designed velocity model and Q value model, forward modeling is performed using the visco - acoustic wave equation to obtain the visco - acoustic shot records. Since there are no obvious horizons in the velocity, there are no obvious reflection event axes.

[0129] As Figure 3 , the first - arrival waveforms of different seismic traces are extracted, and it is found that as the offset increases, the first - arrival waveforms gradually show aliasing and clutter.

[0130] As Figure 4 shown, the optimal wavelet is extracted from the first - arrival waveforms of each seismic trace. For a more intuitive display, Figure 4 partial seismic trace wavelets are extracted for display.

[0131] As Figure 5 shown, using the optimal wavelets extracted from each seismic trace data, the spectral ratio method is used with the wavelet at the minimum offset to obtain the ray Q value of the corresponding ray path of the first - arrival wave as a quality control measure.

[0132] As Figure 6 shown, using the optimal wavelets extracted from each seismic trace data, the spectral ratio method is used to obtain the first - arrival attenuation travel time corresponding to each seismic trace data.

[0133]

Example 4

[0134] As Figure 7 , it is the actual data of a certain block in a certain oilfield. The structure of this block is relatively simple, the signal - to - noise ratio is average, and it is representative.

[0135] As Figure 8 shown, using the method of the present invention, the optimal wavelets of the first - arrival waveforms of each trace data are extracted, and the ray Q value is obtained by the spectral ratio method.

[0136] As Figure 9 shown, using the method of the present invention, the optimal wavelets extracted from the first - arrival waveforms of each trace are used, and the first - arrival attenuation travel time is obtained by spectral ratio.

[0137] The absorption attenuation characteristics of the earth's medium objectively exist. Especially near the surface, it will cause severe attenuation of seismic waves, which deeply affects the quality of seismic wave imaging. Q-value tomography is a good method for near-surface Q-value modeling. However, it is difficult to accurately obtain the attenuation travel time, which brings great resistance to the development of near-surface Q-value tomography modeling. To solve the problem of obtaining the attenuation travel time in Q-value tomography, the present invention uses pre-stack original shot record data. First, the first arrival waveform information is picked up, and the optimal wavelet is extracted from it. Taking the wavelet extracted at the minimum offset as the reference, the ray Q and the corresponding first arrival attenuation travel time are extracted by the spectral ratio method using the optimal wavelet corresponding to each trace of seismic data. The present invention can quickly pick up accurate and reliable first arrival attenuation travel time information from the original shot record using the first arrival waveform information, providing strong technical support for near-surface Q-value modeling.

[0138] Finally, it should be noted that the above technical solution is only one implementation manner of the present invention. For those skilled in the art, based on the disclosed application methods and principles of the present invention, it is very easy to make various types of improvements or deformations, not limited to the methods described in the above specific implementation manner of the present invention. Therefore, the method described above is only preferred and does not have a restrictive meaning.

Claims

1. A method for extracting attenuated travel time based on the optimal wavelet, characterized in that: The method for extracting attenuated travel time based on the optimal wavelet extracts the first arrival waveform signal at the first arrival time, converts the first arrival waveform signal to the complex cepstrum domain, extracts the optimal wavelet in the complex cepstrum domain, and then obtains the attenuated travel time by using the optimal wavelet. The method includes: (1) Extract the first arrival waveform signal at the first arrival position of the pre-stack shot record; (2) Convert the first arrival waveform signal to the complex cepstrum domain; (3) Extract the optimal wavelet, including: Use the following optimal wavelet filtering formula to perform low-pass filtering on the cepstrum time series of the first arrival waveform signal to obtain the optimal wavelet: Among them, x0 is the minimum offset, and x i is the offset of the i-th seismic trace, and f c is the main frequency of the first arrival waveform signal at the minimum offset, and h(f) is the optimal wavelet; (4) Convert the optimal wavelet to the time domain to obtain the optimal wavelet time domain signal; (5) Process each seismic trace in each shot record sequentially through steps (1) to (4) to obtain the optimal wavelet for each seismic trace; then establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position; (6) Obtain the attenuation slope, and further obtain the attenuated travel time.

2. The decay traveltime extraction method based on the optimal wavelet according to claim 1, wherein: The operation of step (1) includes: Pick up the first arrival information on the pre-stack shot record; Extract the first arrival waveform signal at the first arrival position of the pre-stack shot record through a Hamming window.

3. The attenuation traveltime extraction method based on the optimal wavelet according to claim 2, wherein: The operation of step (2) includes: Use the following formula to convert the first arrival waveform signal to the complex cepstrum domain to obtain the complex cepstrum time series of the first arrival waveform signal: in, That is, the time series of the complex spectrum of the first arrival waveform signal, s(t) is the first arrival waveform signal, F is the Fourier transform, F -1 is the inverse Fourier transform.

4. The decay traveltime extraction method based on the optimal wavelet according to claim 1, wherein: The operation of establishing the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position in step (5) includes: According to the principle of the spectral ratio method, establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position as follows: where f represents frequency, w i (f) represents the spectrum obtained by Fourier transform of the optimal wavelet corresponding to the i-th seismic data trace, w min-offset (f) represents the spectrum obtained by Fourier transform of the optimal wavelet at the minimum offset, C is a constant, t * is the attenuation travel time.

5. The method for extracting the attenuated travel time based on the optimal wavelet according to claim 4, wherein: The operation of step (6) includes: Determine the attenuation slope of the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position through least squares linear fitting: k * = -πt * where k * is the attenuation slope, π is the pi, and t * is the attenuation travel time; Calculate and obtain the attenuated travel time by using the following formula:

6. The attenuation travel time extraction method based on the optimal wavelet according to claim 5, characterized in that: The empirical frequency band range used for the least-squares linear fitting is: 1 Hz to 3·f c .

7. The method for extracting the attenuated travel time based on the optimal wavelet according to claim 6, characterized in that: The method further includes: (7) Calculate and obtain the ray Q value by using the following formula: Among them, Q ray is the ray Q value, t is the first arrival time, and t * is the attenuated travel time corresponding to the path.

8. A decay travel time extraction system based on the optimal wavelet, characterized in that: The system includes: a memory, a processor, and a computer program stored on the memory. When the computer program is run by the processor, the following steps are executed: (1) Extract the first arrival waveform signal at the first arrival position of the pre-stack shot record; (2) Convert the first arrival waveform signal to the complex cepstrum domain; (3) Extract the optimal wavelet, including: Use the following optimal wavelet filtering formula to perform low-pass filtering on the cepstrum time series of the first arrival waveform signal to obtain the optimal wavelet: Among them, x0 is the minimum offset, and x i is the offset of the i-th seismic trace, and f c is the main frequency of the first arrival waveform signal at the minimum offset, and h(f) is the optimal wavelet; (4) Convert the optimal wavelet to the time domain to obtain the optimal wavelet time domain signal; (5) Process each seismic trace in each shot record sequentially through steps (1) to (4) to obtain the optimal wavelet for each seismic trace; then establish the relationship between the optimal wavelet at the minimum offset and the optimal wavelet at any position; (6) Obtain the attenuation slope, and further obtain the attenuated travel time.

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