Seismic data driven physical modeling seismic data amplitude directivity correction method

Abstract

This invention provides a seismic data-driven physical simulation seismic data amplitude directivity correction method. Starting with seismic data acquired in a physical simulation laboratory, this method performs conventional amplitude compensation and correction to approximate the amplitude variation characteristics with offset, where only transducer directivity is an issue. An exponential function is used to describe this characteristic, giving it broad applicability. The exponential function coefficients for different transducer radii are determined using a least-squares fitting algorithm, and the determined amplitude attenuation curve is used to compensate for the amplitude of seismic data acquired at arbitrary offsets. This method offers significantly higher compensation accuracy than existing theoretical formula compensation methods and superior operability compared to laboratory measurements.

Description

Technical Field

[0001] This invention relates to the field of seismic data processing, and more specifically to a method for amplitude directivity correction of seismic data driven by physical simulation. Background Technology

[0002] In physical earthquake simulation technology, the transducer amplitude directivity is caused by the vibration characteristics of the transducer surface of a certain size. This characteristic has a significant impact on data acquisition. However, due to manufacturing limitations of the transducer itself, this problem cannot be fundamentally solved. Therefore, corresponding directivity compensation of the acquired data has become a very common solution. Currently, there are two approaches to solving this problem: one is to experimentally test the transducer's amplitude attenuation curve; the other is to calculate the corresponding amplitude attenuation curve of the transducer using theoretical formulas. Experimental testing requires specific experimental conditions. When experimental conditions are not mature, calculating the transducer's directivity characteristic curve using theoretical formulas is the best solution to the transducer amplitude directivity problem. However, there are two problems when using theoretical formulas to calculate the transducer directivity characteristic curve in the past: First, when using theoretical formulas for transducer amplitude compensation, only the source transducer was considered, and the directivity of the receiving transducer was not taken into account; Second, the theoretical attenuation curve calculated using the formula derived from the Bessel function has outliers when used to compensate for the amplitude of seismic data. These problems lead to insufficient accuracy or failure of compensation when using theoretical formulas to compensate for the directivity of far-off-track amplitude of seismic data.

[0003] In summary, there is a lack of mature and usable data-driven compensation methods to address the orientation problem of existing physical simulation seismic data. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to take seismic data collected in a physical simulation laboratory as a starting point, perform conventional amplitude compensation and correction on the data, approximate the amplitude variation characteristics with offset distance with only transducer directivity issues, and use an exponential function to describe these characteristics, making them widely applicable. Furthermore, the exponential function coefficients under different transducer radii are determined using a least squares fitting algorithm, and the amplitude attenuation curve determined by the exponential function is used to compensate for the amplitude of seismic data collected at arbitrary offset distances.

[0005] To solve the above problems, the solution of the present invention is:

[0006] A method for amplitude directivity correction of seismic data based on seismic data-driven physical simulation includes:

[0007] The reference gather selection step involves determining the reference gather and obtaining statistical information on the attenuation relationship between the amplitude energy of the seismic data in the reference gather and the offset.

[0008] The attenuation curve determination step involves spherical diffusion and compensation of the statistical information on the attenuation relationship between amplitude energy and offset distance, and correction of the compensation data to obtain an amplitude attenuation curve with offset distance that only exists due to the transducer directivity.

[0009] The pointing curve determination step involves decomposing the amplitude decay curve with offset distance to obtain the single transducer amplitude pointing characteristic curve.

[0010] The attenuation function determination step involves constructing an exponential function of the amplitude attenuation coefficient with offset, and using a nonlinear least squares algorithm to calculate the undetermined coefficients of the exponential function under the constraint of the transducer amplitude directivity characteristics calculated based on measured physical simulation seismic data, to obtain the data-driven amplitude attenuation function.

[0011] The pointing correction step involves calculating the amplitude compensation coefficient for each trace by substituting the incident angle of the reflected wave. The cubic B-spline interpolation method is used to obtain the compensation coefficient for each sampling point, thereby obtaining the amplitude compensation coefficient trace corresponding to that trace. The amplitude pointing correction of the physical simulation seismic data is achieved through convolution.

[0012] Preferably, in the above-mentioned physical simulation seismic data amplitude directivity correction method based on seismic data, in the reference gather selection step, shot gather data that conforms to the energy propagation law is selected as the reference gather, and the attenuation relationship of the seismic data amplitude energy with offset is statistically analyzed by giving a time window and shot number.

[0013] Preferably, in the above-mentioned method for amplitude directivity correction of seismic data based on seismic data-driven physical simulation, the attenuation curve determination step involves spherical diffusion based on the statistical information of the attenuation relationship between amplitude energy and offset distance, using the following formula:

[0014]

[0015] In the formula, D is the total attenuation factor of spherical diffusion and absorption attenuation on the reflection amplitude, and t is...

[0016] The propagation time of seismic waves, where:

[0017]

[0018]

[0019] Where v i For the velocity of each layer, t i This is the ratio of layer thickness to layer velocity.

[0020] Preferably, in the above-mentioned method for amplitude directivity correction of physical simulation seismic data driven by seismic data, the statistical information on the attenuation relationship between amplitude energy and offset is compensated in the attenuation curve determination step, including Q compensation. The Q compensation is calculated based on the following formula using two time points of any two traces in the common shot point set of the physical simulation seismic data:

[0021]

[0022] In the formula, Q is the quality factor, f is the frequency, B(f,t) is the amplitude spectrum of the seismic wave at travel time t, and A(t) represents other influences unrelated to frequency; Q compensation is performed using the Q value to calculate the statistical information on the attenuation relationship between the amplitude energy and the offset distance.

[0023] Preferably, in the above-mentioned method for amplitude directivity correction of seismic data based on seismic data-driven physical simulation, the attenuation curve determination step includes AVO correction for the compensation data. The AVO correction calculates the reflection coefficient layer by layer based on the following model:

[0024]

[0025] In the formula, α, β, α′, β′ are the reflection and refraction angles of the longitudinal and transverse waves, respectively, and v p1 v p2 ,ρ1,v s1 ,v s2 ρ2 represents the longitudinal and transverse wave velocities and the medium density, respectively, in the upper and lower media; R PP R PS T PP T PS These are the P-wave reflection coefficient, the converted S-wave reflection coefficient, and the P and S-wave transmission coefficients, respectively.

[0026] Preferably, in the above-mentioned method for amplitude directivity correction of seismic data based on physical simulation driven by seismic data, the attenuation function determination step is based on an exponential function of the amplitude attenuation coefficient with offset, constructed according to the following formula:

[0027]

[0028] In the function, F is the amplitude attenuation coefficient with offset distance, a is the seismic wave opening angle representing the offset distance, γ and τ are the influence factors affected by the transducer radius, the dominant frequency of the source, and the model velocity, and are the undetermined coefficients in the function.

[0029] Therefore, compared with the prior art, the physical simulation seismic data amplitude directivity correction method provided by this invention has the following advantages: 1. This method is based on data-driven approaches, using the seismic data acquired through physical simulation as a constraint condition in the calculation process of the exponential function coefficients; 2. This method decomposes the transducer amplitude directivity characteristics calculated based on measured data into a single transducer, improving the accuracy of transducer directivity characteristic research; 3. An exponential function is introduced to describe the amplitude directivity characteristics of a single transducer calculated based on measured data, and the undetermined coefficients in the exponential function are calculated using the nonlinear least squares method to obtain the amplitude attenuation curve of the transducer of the current size, and this curve is used to compensate for the amplitude of seismic data acquired at any offset; the compensation accuracy is far higher than that of existing theoretical formula compensation methods, and the operability is better than that of laboratory measurements. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the process for correcting the amplitude directivity of earthquake data driven by physical simulation, according to an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram of the amplitude statistics curve of reflected waves from the physical simulation earthquake data in this embodiment of the invention, as well as the amplitude statistics curve after spherical diffusion and attenuation compensation, Q compensation, and AVO correction.

[0033] Figure 3 This is a schematic diagram comparing the amplitude directivity curve of a transducer with a radius of 5.5 mm calculated according to theoretical formulas and its envelope with the transducer amplitude directivity curve calculated from measured data in an embodiment of the present invention. It can be seen that there is a large error in using theoretical formulas to compensate for the transducer amplitude directivity.

[0034] Figure 4 The diagram shows the amplitude attenuation curve calculated from measured data for a 5.5mm radius transducer in this embodiment of the invention, the amplitude attenuation curve driven by seismic data, and a comparison diagram with the amplitude attenuation curve calculated based on the theoretical formula of Bessel function. The comparison shows that the amplitude compensation method of physical simulation transducer driven by seismic data is much more accurate than the existing amplitude compensation method of physical simulation transducer based on theoretical formula.

[0035] Figure 5The diagram shows the original amplitude coefficient of a single seismic shot acquired by a transducer with a radius of 5.5 mm in this embodiment of the invention, the amplitude coefficient of a single shot acquired by numerical simulation of the same model, the amplitude coefficient of physically simulated seismic data corrected by theoretical formula, and the amplitude coefficient of physically simulated seismic data corrected by the data-driven method proposed in this invention. The comparison shows that this invention greatly improves the correction effect of the amplitude directivity problem of physically simulated seismic data caused by the transducer compared with the existing theoretical formula correction method. The amplitude of the corrected seismic data is close to the amplitude of numerical simulated seismic data without transducer directivity problem, which proves the effectiveness of the method.

[0036] Figure 6 This is a schematic diagram of a single gun before and after physical simulation amplitude directivity correction in an embodiment of the present invention. Detailed Implementation

[0037] 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 some embodiments of the present invention, and not all embodiments. 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.

[0038] This invention provides a method for correcting the amplitude directivity of physically simulated seismic data driven by seismic data. The method includes: establishing a driving dataset by selecting seismic data corresponding to the stable region of the target layer; statistically analyzing the attenuation relationship of seismic data amplitude energy with offset in the dataset; sequentially performing spherical diffusion and attenuation compensation, Q compensation, and AVO correction on the dataset to obtain a curve showing the amplitude attenuation with offset caused only by transducer directivity, and obtaining a single transducer amplitude directivity characteristic curve; constructing an exponential function based on the above curve shape and using a nonlinear least squares algorithm to calculate the undetermined coefficients in the exponential function to replace the theoretical formula for simulating the amplitude attenuation characteristics caused by the transducer, thereby obtaining the target layer amplitude attenuation function; calculating the amplitude compensation coefficient corresponding to each target layer for each trace, using cubic B-spline interpolation to obtain the amplitude compensation coefficient trace for each offset trace, and implementing physical simulation of seismic data amplitude directivity correction through a convolution algorithm.

[0039] Figure 1 This is a schematic flowchart of a physical simulation earthquake data amplitude directivity correction method driven by earthquake data provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method mainly includes the following steps:

[0040] Step 101: Select a reference gather and statistically analyze the attenuation relationship of seismic data amplitude energy with offset in the gather.

[0041] Step 102: Perform spherical diffusion and attenuation compensation, Q compensation, and AVO correction on the reference gather in sequence to obtain an amplitude attenuation curve with offset distance caused only by transducer directivity.

[0042] Step 103: Decompose to obtain the amplitude pointing characteristic curve of a single transducer;

[0043] Step 104: Construct an exponential function and use a nonlinear least squares algorithm to calculate the undetermined coefficients in the exponential function to obtain the data-driven amplitude decay function;

[0044] Step 105: Substitute the incident angle on each seismic trace into the amplitude attenuation function corresponding to that layer to obtain the attenuation coefficient of that seismic trace. Calculate the derivative of this coefficient to obtain the amplitude compensation coefficient of that trace. Convolution is used to correct the amplitude directionality of the physical simulation seismic data.

[0045] In step 101, the main step is to select a reference gather and statistically analyze the attenuation relationship of the amplitude energy of the seismic data in the gather with the offset distance. This is because the method is based on measured data and selects shot gather data whose energy propagation conforms to the attenuation law of amplitude energy with offset distance and which does not have abnormal structural reactions such as faults or goaf areas as reference gathers. The attenuation relationship of the amplitude energy of the seismic data in the gather with offset distance is statistically analyzed by giving a time window and shot number.

[0046] In step 102, spherical diffusion and attenuation compensation, Q compensation, and AVO correction are performed sequentially. The formula for the spherical diffusion and absorption attenuation amplitude compensation curve is as follows:

[0047]

[0048] Where D is the total attenuation factor of spherical diffusion and absorption attenuation on the reflected amplitude, t is the propagation time of the seismic wave, and a and β are calculated in detail below:

[0049]

[0050]

[0051] Where v i For the velocity of each layer, t i This is the ratio of layer thickness to layer velocity.

[0052] The amplitude energy calculated in step 101 is compensated for by spherical diffusion and absorption attenuation according to the above formula, and then Q-compensation is performed on the compensated information. The key point in the Q-compensation process is the calculation of the quality factor, considering that the amplitude spectrum expression of the physically simulated seismic data is:

[0053]

[0054] In the above equation, f is the frequency, B(f,t) is the amplitude spectrum of the seismic wave at travel time t, Q is the quality factor, B(f,t0) is the amplitude spectrum of the seismic wave at the initial time t0, and A(t) represents scattering attenuation, including geometric diffusion, reflection, and projection. Taking two time points and dividing the above equation yields the following equation:

[0055]

[0056] By taking any two traces from the common shot point ensemble of the physical simulation seismic data and calculating the Q value at two different times on each of these two traces, this method is known as the spectral ratio method (i.e., formulas (3) and (4)). After removing outliers from the Q values ​​calculated from multiple traces, the average value is taken to obtain the Q value for a single stratum. For multi-layered cases, the equivalent Q principle is used, assuming there are n strata, and the attenuation factors for each stratum are Q1, Q2…Q… n The two-way travel time of seismic waves at each level is t1, t2…t. n The equivalent Q value of the formation Q 1.eff Q 2.eff …Q n.eff All of these can be obtained by inverting the spectral ratio method described above based on seismic data. Treating the equivalent Q value as the root mean square Q value of the nth stratum, the Q value Q of the nth stratum can be derived. n for

[0057]

[0058] Where t 0,n Let be the self-sufficiency time of the nth layer.

[0059] After calculating the Q value, the Q compensation coefficient of the target layer can be obtained. This compensation coefficient is then used to perform Q compensation on the data after amplitude compensation for spherical diffusion and absorption attenuation. AVO correction is then performed on this data, based on the Zoeppritz equation:

[0060]

[0061] Where α, β, α′, β′ are the reflection and refraction angles of the longitudinal and transverse waves, and v p1 v p2 These represent the longitudinal wave velocities of the seismic wave in the upper and lower media, respectively; v s1 ,v s2 R represents the shear wave velocity of the seismic wave in the upper and lower media, respectively; ρ1 and ρ2 represent the media density of the seismic wave in the upper and lower media, respectively. PP R PS T PP T PSThese are the P-wave reflection coefficient, the converted S-wave reflection coefficient, and the P and S-wave transmission coefficients, respectively. The reflection and transmission coefficients corresponding to the model are calculated based on the model parameters. The reflection coefficient is then calculated layer by layer, and these coefficients are used to perform AVO correction on the seismic data after the above two compensation steps.

[0062] In step 103, considering that the source and receiver transducers use the same radius and type of transducer during the physical simulation of seismic data acquisition, based on the principle of source-receiver interchangeability and the simplified model of piston transducers, the transducer amplitude pointing characteristics obtained after various corrections are as follows:

[0063] F = F S *F R (7)

[0064] In the above formula, F S As a characteristic of the focal directionality, F R The directional characteristics of the detector point are the same, and transducers of the same type and size have the same directional characteristics, i.e., F. S =F R Therefore, the directivity characteristics of the source transducer can be obtained as follows.

[0065] F S =sqrt(F) (8)

[0066] In step 104, the following exponential function is constructed based on the transducer curve shape calculated from the actual data:

[0067]

[0068] In the formula, F is the amplitude attenuation coefficient with offset distance, a is the seismic wave opening angle representing the offset distance, and its value is calculated by ray tracing based on the model acquisition system. γ and τ are the influence factors affected by the transducer radius, the dominant source frequency, and the model velocity, and are the undetermined coefficients in this function. Under the constraint of the transducer amplitude directivity characteristics calculated from measured physical simulation seismic data, the undetermined coefficients are calculated using a nonlinear least squares algorithm. When the transducer radius is 5.5 mm, the dominant source frequency is 300 kHz, and the model equivalent velocity is 1480 m / s, the influence factors γ = 1.476 and τ = 1.9814 are obtained based on data-driven calculation. Therefore, the amplitude attenuation function can be obtained as follows:

[0069]

[0070] Once the above function is obtained, when the transducer radius, source frequency, and model velocity are the same as the parameters mentioned above during model data acquisition, the above function can be used to correct the transducer amplitude directivity problem for seismic data with arbitrary opening angles. If the transducer radius, source frequency, and model velocity differ from those calculated in the above function, a suitable influence factor can be calculated based on the measured physical simulation seismic data to obtain the correct correction parameters.

[0071] In step 105, based on the above attenuation function, the amplitude attenuation coefficient corresponding to each seismic trace can be calculated by substituting the incident angle corresponding to the target layer of the reflected wave. The amplitude compensation coefficient p corresponding to the reflected wave (time t) of each seismic trace can be obtained by deriving the amplitude attenuation coefficient. Considering that amplitude compensation does not change the background noise, amplitude energy compensation is performed within a certain time window corresponding to the reflected wave. The time window is selected based on the data conditions, for example... Figure 6 The model selects a time interval of 20ms above the target layer and 120ms below the target layer for amplitude compensation. Therefore, the following time and amplitude compensation coefficient sampling points can be obtained: (0,1.0), (t-20,p), (t,p), (t+120,p), and (800,1.0). Substituting these discrete points into the cubic B-spline interpolation formula, the compensation coefficient of each sampling point can be obtained, which is the compensation coefficient trace. By using the compensation coefficient trace provided by this algorithm and the acquired seismic data for convolution calculation, the amplitude directivity correction of the physical simulation seismic data can be achieved.

[0072] Figure 2 This is a schematic diagram of the amplitude statistics curve of the first layer reflected wave of the physical simulation seismic data in this embodiment of the invention, as well as the amplitude statistics curve after spherical diffusion and attenuation compensation, Q compensation, and AVO correction. Figure 3 This diagram illustrates the comparison between the amplitude directivity curve calculated from theoretical formulas and its envelope for a 5.5mm radius transducer and the transducer amplitude directivity curve calculated from measured data. Figure 3 The comparison shows that the current theoretical formula for calculating transducer amplitude directivity has correction errors in the process of correcting seismic data; Figure 4 The diagram shows the amplitude attenuation curve calculated from measured data for a 5.5mm radius transducer in this embodiment of the invention, the amplitude attenuation curve driven by seismic data, and a comparison diagram with the amplitude attenuation curve calculated based on the theoretical formula of Bessel function. The comparison shows that the amplitude compensation method of physical simulation transducer driven by seismic data is much more accurate than the existing amplitude compensation method of physical simulation transducer based on theoretical formula. Figure 5The diagram shows the original amplitude coefficient of a single seismic shot acquired by a transducer with a radius of 5.5 mm in this embodiment of the invention, the amplitude coefficient of a single shot acquired by numerical simulation of the same model, the amplitude coefficient of physically simulated seismic data corrected by theoretical formula, and the amplitude coefficient of physically simulated seismic data corrected by the data-driven method proposed in this invention. The comparison shows that this invention greatly improves the correction effect of the amplitude directivity problem of physically simulated seismic data caused by the transducer compared with the existing theoretical formula correction method. The amplitude of the corrected seismic data is close to the amplitude of numerical simulated seismic data without transducer directivity problem, which proves the effectiveness of the method. Figure 6 The diagram shows a single shot before and after physical simulation amplitude directivity correction in an embodiment of the present invention. By comparison, it can be seen that the method in the present invention has good adaptability in correcting the amplitude directivity problem of physical simulation seismic data.

[0073] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0074] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven methods, characterized in that, include: The reference gather selection step involves determining the reference gather and obtaining statistical information on the attenuation relationship between the amplitude energy of the seismic data in the reference gather and the offset. The attenuation curve determination step involves spherical diffusion and compensation of the statistical information on the attenuation relationship between amplitude energy and offset distance, and correction of the compensation data to obtain an amplitude attenuation curve with offset distance that only exists due to the transducer directivity. The pointing curve determination step involves decomposing the amplitude decay curve with offset distance to obtain the single transducer amplitude pointing characteristic curve. The attenuation function determination step involves constructing an exponential function of the amplitude attenuation coefficient with offset, and using a nonlinear least squares algorithm to calculate the undetermined coefficients of the exponential function under the constraint of the transducer amplitude directivity characteristics calculated based on measured physical simulation seismic data, to obtain the data-driven amplitude attenuation function. The pointing correction step involves substituting the incident angle corresponding to the target layer of each seismic trace's reflected wave into the amplitude attenuation function to calculate the amplitude attenuation coefficient corresponding to that trace. By differentiating the amplitude attenuation coefficient, the amplitude compensation coefficient corresponding to the reflected wave of the target layer of each seismic trace can be obtained. The compensation coefficient of each sampling point is obtained by interpolation using the cubic B-spline interpolation method, thus obtaining the amplitude compensation coefficient trace corresponding to that trace. The amplitude pointing correction of the physical simulation seismic data is achieved through convolution.

2. The method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven approach according to claim 1, characterized in that, In the reference gather selection step, shot gather data that conforms to the energy propagation law is selected as the reference gather, and the attenuation relationship of the amplitude energy of the seismic data in the gather with the offset is statistically analyzed by giving a time window and shot number.

3. The method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven approach according to claim 1, characterized in that, In the attenuation curve determination step, spherical diffusion is performed based on the statistical information of the attenuation relationship between the amplitude energy and the offset distance, according to the following formula: ； In the formula, D is the total attenuation factor of spherical diffusion and absorption attenuation on the reflected amplitude, and t is the propagation time of the seismic wave, where: in For the speed of each layer, This is the ratio of layer thickness to layer velocity.

4. The method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven approach according to claim 1, characterized in that, In the attenuation curve determination step, the statistical information on the attenuation relationship between the amplitude energy and the offset is compensated, including Q compensation. The Q compensation is calculated based on the following formula, taking two times from any two traces in the common shot point set of the physical simulation seismic data: ; In the formula, For quality factors, For frequency, The amplitude spectrum of the seismic wave at travel time t. Other effects independent of frequency are indicated; Q compensation is performed using the statistical information on the attenuation relationship of the amplitude energy with offset distance using the Q value.

5. The method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven approach according to claim 1, characterized in that, In the attenuation curve determination step, the compensation data correction includes AVO correction, which calculates the reflection coefficient layer by layer based on the following model: ; In the formula, For longitudinal wave reflection angle, The angle of reflection of the transverse wave. Longitudinal wave refraction angle, The angle of refraction of the transverse wave. , These represent the longitudinal wave velocities of the seismic waves in the upper and lower media, respectively. , are the shear wave velocities of the seismic wave in the upper and lower media, respectively; , where R is the density of the seismic wave in the upper and lower media; pp R ps T pp T ps These are the P-wave reflection coefficient, the converted S-wave reflection coefficient, the P-wave transmission coefficient, and the S-wave transmission coefficient, respectively.

6. The method for amplitude directivity correction of physical simulation seismic data based on seismic data-driven approach according to claim 1, characterized in that, In the attenuation function determination step, an exponential function of the amplitude attenuation coefficient with offset distance is constructed based on the following formula: ; In the function, F is the amplitude attenuation coefficient with respect to offset distance. It is the seismic wave opening angle representing the offset distance. is the influencing factor affected by the transducer radius, the dominant frequency of the seismic source, and the model velocity, and is the undetermined coefficient in this function.

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