Fast broadband vibroseis viscoelastic forward modeling method

Abstract

The present application provides a kind of quick broadband controllable seismic source viscoelasticity forward method, the quick broadband controllable seismic source viscoelasticity forward method includes: step 1: in controllable seismic source exciting point position loading pulse vertical force source function;Step 2: calculate the viscoelasticity equation Green function of controllable seismic source exciting point position;Step 3: according to the convolution broadband controllable seismic source function and viscoelasticity equation Green function generates the controllable seismic source record of the position excitation;Step 4: according to observation system, linear combination single shot synthetic seismogram, form combined shot controllable seismic source synthetic seismogram.The quick broadband controllable seismic source viscoelasticity forward method effectively reduces the calculation cost of long time record broadband viscoelasticity forward simulation, realizes high efficiency broadband controllable seismic source viscoelasticity forward simulation.The present application realizes controllable seismic source high-precision high-efficiency seismic simulation under complex geological conditions, provides important tool for controllable seismic source observation system design and analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of geophysical exploration seismic data acquisition and processing, and in particular to a fast broadband controllable vibroseis viscoelastic forward simulation method. Background Art

[0002] Vibroseis viscoacoustic forward modeling technology is an important technology in the field of geophysical exploration and is widely used in oil and gas resource exploration, geological disaster warning, and marine resource development.

[0003] In actual seismic exploration, the subsurface medium exhibits viscosity, attenuation, and dispersion effects, which reduce the dominant frequency and amplitude of seismic waves. This reduces the resolution of seismic imaging, inaccurately locates subsurface structures, and compromises the reliability of seismic interpretation. The viscoelastic wave equation provides a theoretical tool for seismological research. Within the viscoelastic wave equation, the viscoelastic properties of the formation must be considered to calculate the Green's function. This means that both the elastic and viscosity parameters of the formation affect the calculated Green's function. Conventional methods include the finite difference method, the finite element method, the optical source method, and methods based on compressed sensing. The finite difference method is widely used in the numerical calculation of the Green's function due to its simplicity, stability, and efficiency. In the field of seismology, Green's function calculation methods for the viscoelastic wave equation and viscoelastic forward modeling of earthquake sources have become important research areas.

[0004] The synthesis of seismic records is a crucial component of seismological research, helping us understand the propagation of seismic waves and the properties of strata. In practice, seismic records can be synthesized by convolving the source time function with the Green's function, leveraging the linear time-invariance of the viscoelastic wave equation. In this process, the source time function describes the temporal variation of the source intensity, while the Green's function describes the propagation of seismic waves in the strata.

[0005] Traditional narrow-band forward modeling technology only considers energy transfer along the wave propagation path, while ignoring energy transfer along the sides of the wave propagation path. Therefore, it can only simulate seismic records within a narrow frequency band, but cannot simulate wide-band seismic records. Multiple forward modeling simulations are required to obtain seismic records within different frequency bands, resulting in a large amount of data and increasing the difficulty of data processing and storage. Wide-band forward modeling technology can simulate a wider frequency band and more comprehensively reflect the characteristics of the underground medium. Only a single forward modeling simulation is required to obtain seismic records within a wide frequency band. This can greatly reduce the amount of data, making data processing and storage more convenient, thereby improving the detection accuracy of seismic exploration and ensuring the reliability of exploration results.

[0006] In recent years, broadband vibroseis viscoelastic forward modeling has been widely researched and applied. This technique can simulate seismic waves across a wide frequency range, thereby better simulating the propagation of seismic waves. Furthermore, this technique can simulate different vibration conditions by controlling the parameters of the seismic source.

[0007] In the Chinese patent application with application number CN201210408060.8, a numerical simulation method for forward modeling of a synchronous scanning wave field of a vibroseis source is disclosed, which belongs to the field of petroleum exploration. The method comprises: (1) inputting simulation parameters; (2) calculating and obtaining the simulation parameters of the synchronous scanning wave field of a vibroseis source based on the simulation parameters input in step (1), and outputting these parameters to a parameter file; the simulation parameters of the synchronous scanning wave field of a vibroseis source include: the location of each source, the start and end scanning time and the synchronous source to which they belong, the continuous recording time length, and the scanning signal of each synchronous element; (3) obtaining the simulation record by high-order finite difference wave field extension calculation; (4) outputting the simulation result. The method of the invention can simulate the synchronous scanning wave field of a vibroseis source in various modes such as sliding scanning, independent synchronous scanning, pseudo-random scanning, distance-spaced synchronous scanning technology, and V1, and the forward modeling continuous recording of any number of vibroseis sources by controlling the input parameters according to the actual simulation needs.

[0008] In the Chinese patent application with application number CN201510272589.5, a parallel forward modeling method based on a vibroseis sliding scanning method is disclosed. The parallel forward modeling method based on the vibroseis sliding scanning method includes: step 1, inputting simulation parameters, including conventional observation system parameters and vibroseis sliding scanning parameters; step 2, calculating vibroseis sliding scanning simulation parameters based on the input simulation parameters; step 3, performing vibroseis sliding scanning forward simulation based on the vibroseis sliding scanning simulation parameters; and step 4, outputting the parallel forward modeling results. Compared with conventional serial forward modeling, the numerical simulation results of the parallel forward modeling method based on the vibroseis sliding scanning method are more accurate, and the greatest advantage is that the computational efficiency of the present invention is greatly improved compared with serial forward modeling.

[0009] The Chinese patent application with application number CN202111271143.2 involves a controllable source forward modeling method, device, storage medium, and electronic equipment, including: establishing a velocity model based on the geological characteristics of the target desert area; setting the observation system, source wavelet type, frequency scanning mode, frequency scanning range, and signal scanning length according to the velocity model; starting the forward modeling to obtain a scanning signal and source record; cross-correlating the scanning signal and the source record to obtain a single-shot record. This invention can accurately simulate the acquisition of controllable source data on the desert surface, meet the current research needs for noise suppression of data acquired by controllable source on the desert surface, and provide technical support for the analysis of the noise formation mechanism of seismic exploration in desert areas and for targeted noise suppression research.

[0010] The above existing technologies are all significantly different from the present invention and fail to solve the technical problem we want to solve. Therefore, we have invented a new fast broadband controllable source viscoelastic forward modeling method. Summary of the Invention

[0011] The purpose of the present invention is to provide a method for rapidly performing broadband vibroseis viscoelastic forward modeling, thereby providing an important tool for the design and analysis of vibroseis observation systems under complex geological conditions.

[0012] The object of the present invention can be achieved by the following technical measures: a fast broadband vibroseis viscoelastic forward modeling method, the fast broadband vibroseis viscoelastic forward modeling method comprising:

[0013] Step 1: Load the pulse vertical force source function at the vibrator excitation point;

[0014] Step 2: Calculate the Green's function of the viscoelastic equation at the vibrator excitation point;

[0015] Step 3: Generate a vibroseis record excited at the location based on the convolution of the broadband vibroseis function and the Green's function of the viscoelastic equation;

[0016] Step 4: According to the observation system, linearly combine the single-shot synthetic seismic records to form the combined-shot vibroseis synthetic seismic record.

[0017] The purpose of the present invention can also be achieved by the following technical measures:

[0018] In step 1, the pulse vertical force source function is loaded according to the position of the vibrator excitation.

[0019] In step 1, the impulse vertical force source function can be expressed as:

[0020]

[0021] Where x0 = (x0, y0, z0) is the spatial position of the point force source, g(t, t0, ω) is the source time function, which is a function of the arrival time t0 and the frequency ω; (F x ,F y ,F z ) T are the three components of the force vector, F0 is the amplitude of the force; for the controllable vibrator, only the vertical force is considered, that is, F x =F y = 0, but it is also applicable to the simulation of earthquake sources with force vectors in different directions.

[0022] In step 1, the earthquake source time function g(t, t0, ω) adopts the impulse function δ(t-t0). The impulse function is a special function that is zero at all times except t=t0. In addition, the integral of the function is 1. Assuming that the function f(t) is a continuous function, the impulse function satisfies the following conditions:

[0023] ∫f(t)δ(t-t0)dt=f(t0), (2).

[0024] In step 1, at time grid t n =nΔt discretizes the pulse function, where Δt is also the time step for solving the viscoelastic wave equation; the discretized pulse function sequence is expressed as d n ,n=0,1,2,…; According to the properties of the impulse function, for the polynomial function f(t)=t q ,q=0,1,…,Q,time series d n The following conditions must be met:

[0025]

[0026] According to the Q+1 equations above, the time series d can be solved n ; Solved d n Except near t=t0, it is zero everywhere else.

[0027] In step 2, at the vibrator excitation point, the pulse time function is loaded, the viscoelastic wave equation is solved, and the Green's function of the viscoelastic wave equation is obtained.

[0028] In step 2, consider a linear viscoelastic model composed of n standard linear solids, and the corresponding governing equation is:

[0029]

[0030] Where ρ is the density, u is the displacement vector, λ0 and μ0 are the medium parameters at the reference frequency, λ v and μ vare the viscoelastic medium parameters (ν=1,2,…,n), and the spatial operator L is:

[0031]

[0032] Auxiliary variables Solve the following equation:

[0033]

[0034] where the relaxation frequency ω ν >0,v=1,2,…,n。

[0035] In step 2, the Green's function of the viscoelastic wave equation is calculated, which requires solving 3+3n partial differential equations, where n is the number of standard linear solids. Taking into account both accuracy and efficiency, n is generally set to 3.

[0036] In step 3, a single-shot synthetic seismic record can be generated by convolving the time function of the controllable source and the Green's function of the viscoelastic wave equation. Since the viscoelastic wave equation is a linear time-invariant system with respect to the source time function, the impulse response, i.e., the Green's function, can fully characterize the characteristics of the forward simulation system of the viscoelastic wave equation.

[0037] In step 3, the vibrator excites a continuous sweep signal, usually a linear sinusoidal sweep signal:

[0038] s(t)=a(t)sin[2πφ(t)+ψ]. (7)

[0039] Where ψ is a constant phase and the amplitude term a(t) is:

[0040]

[0041] Where T is the duration;

[0042] The phase term φ(t) is:

[0043]

[0044] Where f1 and f2 are the starting scanning frequency and the ending scanning frequency respectively.

[0045] The purpose of the present invention can also be achieved through the following technical measures: a fast broadband controllable source viscoelastic forward modeling system, which uses a fast broadband controllable source viscoelastic forward modeling method to perform high-precision and high-efficiency controllable source earthquake simulation under complex geological conditions during oil drilling accidents.

[0046] The fast, broadband vibroseis forward modeling method of the present invention numerically calculates the Green's function of the viscoelastic wave equation and, utilizing the linear time-invariant characteristics of the viscoelastic wave equation, synthesizes seismic records by convolving the source time function. Compared with existing methods, the present invention has the following advantages: (1) the computational cost is independent of the length of the source time function, resulting in high computational efficiency; and (2) after the Green's function is prepared, it can be applied to different vibroseis observation systems, including those with different vibroseis spatial distributions, different excitation times, and different source time functions, thus providing great flexibility.

[0047] The fast broadband vibroseis viscoelastic forward modeling method of this invention effectively reduces the computational cost of long-duration broadband viscoelastic forward simulations, enabling high-efficiency broadband vibroseis viscoelastic forward modeling. This method enables high-precision and high-efficiency earthquake simulations of vibroseis under complex geological conditions, providing an important tool for the design and analysis of vibroseis observation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flowchart of a specific embodiment of the fast broadband vibroseis viscoelastic forward modeling method of the present invention;

[0049] Figure 2 is a viscoelastic velocity model in a specific embodiment of the present invention;

[0050] Figure 3 is the viscoelastic Green's function calculated in one embodiment of the present invention;

[0051] Figure 4 The broadband vibroseis time function and its time-frequency spectrum in a specific embodiment of the present invention;

[0052] Figure 5 A seismic record synthesized by convolving a viscoelastic Green's function and a vibroseis time function in a specific embodiment of the present invention;

[0053] Figure 6 The result of cross-correlating the vibroseis synthetic record and the vibroseis time function in a specific embodiment of the present invention;

[0054] Figure 7 Spectra of viscoelastic Green's functions, synthetic seismic records, and cross-correlation records in one embodiment of the present invention;

[0055] Figure 8 This is a synthetic seismic record produced by delayed excitation of a controllable source in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0056] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0057] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations and / or combinations thereof.

[0058] In conventional controllable source forward modeling, the source time function is directly loaded to solve the viscoelastic wave equation, and the calculation time depends on the length of the source time function. Since the controllable source is a continuous time signal that may last for a long time, the computational cost of the existing method increases linearly with the increase in duration. By calculating the Green's function and utilizing the linear time-invariant characteristics of the forward simulation system, the present invention can effectively avoid this computational cost problem. Increasing the length of the controllable source time function will not increase the computational cost of solving the Green's function, but will only slightly increase the computational cost of one-dimensional convolution. Compared with solving the viscoelastic wave equation, the computational cost of one-dimensional convolution is negligible, realizing fast broadband controllable source viscoelastic forward modeling.

[0059] The fast, broadband vibroseis forward modeling method of the present invention involves numerically calculating the Green's function of the viscoelastic wave equation and synthesizing seismic records by convolving the source-time function using the linear time-invariant characteristics of the viscoelastic wave equation. This method rapidly calculates synthetic seismic records from vibroseis in viscoelastic media and can be used for the design and analysis of vibroseis observation systems.

[0060] The following are several specific embodiments of the present invention:

[0061] Example 1

[0062] In a specific embodiment 1 of the present invention, Figure 1 As shown, Figure 1 The flowchart of the fast broadband vibroseis viscoelastic forward modeling method of the present invention includes the following steps:

[0063] Step 1: Load the pulse vertical force source function at the vibrator excitation point;

[0064] According to the position of the vibrator excitation, the pulse function is discretized and used as a vertical force source to realize the loading of the source time function.

[0065] Step 2: Calculate the Green's function of the viscoelastic equation at the vibrator excitation point;

[0066] At the vibrator excitation point, the pulse time function is loaded, the viscoelastic wave equation is solved, and the Green's function of the viscoelastic wave equation is obtained.

[0067] Step 3: Convolve the broadband vibroseis function and the Green's function of the viscoelastic equation to generate the vibroseis record excited at that location;

[0068] By convolving the time function of the vibrator with the Green's function of the viscoelastic wave equation, a single-shot synthetic seismic record can be generated. Since the viscoelastic wave equation is a linear time-invariant system with respect to the source time function, the impulse response (Green's function) can fully characterize the characteristics of the viscoelastic wave equation forward simulation system.

[0069] Step 4: Combine the vibroseis records at each location to form a combined shot vibroseis record.

[0070] According to the observation system, the single-shot synthetic seismic records are linearly combined to form the combined-shot vibroseis synthetic seismic record.

[0071] Example 2

[0072] In a second specific embodiment of the present invention, the present invention provides a fast broadband vibroseis viscoelastic forward modeling method, comprising the following steps:

[0073] 1. Load the pulse vertical force source function at the vibrator excitation point

[0074] According to the position of the vibrator excitation, the pulse vertical force source function is loaded. The pulse vertical force source function can be expressed as:

[0075]

[0076] Where x0 = (x0, y0, z0) is the spatial position of the point force source, g(t, t0, ω) is the time function of the source, which is a function of the arrival time t0 and frequency ω. (F x ,F y ,F z ) T are the three components of the force vector, and F0 is the amplitude of the force. For a controllable vibrator, generally only the vertical force is considered, that is, F x =F y =0, but this method is also applicable to earthquake source simulations with force vectors in different directions.

[0077] The earthquake source time function g(t, t0, ω) uses the impulse function δ(t-t0). The impulse function is a special function that is zero at all times except t=t0; in addition, the integral of the function is 1. Assuming that the function f(t) is a continuous function, the impulse function satisfies the following conditions:

[0078] ∫f(t)δ(t-t0)dt=f(t0), (2)

[0079] In the time grid t n =nΔt discretizes the impulse function, where Δt is also the time step for solving the viscoelastic wave equation. The discretized impulse function sequence is expressed as d n ,n=0,1,2,…. According to the properties of the impulse function, for the polynomial function f(t)=t q ,q=0,1,…,Q,time series d n The following conditions must be met:

[0080]

[0081] According to the Q+1 equations above, the time series d can be solved n . Solve for d n Except for the vicinity of t = t0, all other places are zero. It should be noted that this method does not require t0 to fall on the time grid point, and has good adaptability to the time grid.

[0082] 2. Calculate the Green's function of the viscoelastic equation at the vibrator excitation point

[0083] Consider a linear viscoelastic model composed of n standard linear solids. The corresponding governing equation is:

[0084]

[0085] The spatial operators are:

[0086]

[0087] Auxiliary variables Solve the following equation:

[0088]

[0089] where the relaxation frequency ω v >0,v=1,2,…,n。

[0090] In this step, to obtain the Green's function of the viscoelastic wave equation, 3+3n partial differential equations must be solved, where n is the number of standard linear solids. To balance accuracy and efficiency, n is generally set to 3. Therefore, compared to elastic wave forward modeling (which requires solving three partial differential equations), viscoelastic wave forward modeling is much more computationally intensive.

[0091] 3. Convolve the broadband vibroseis function and the Green's function of the viscoelastic equation to generate the vibroseis record excited at that location

[0092] By convolving the time function of the vibrator with the Green's function of the viscoelastic wave equation, a single-shot synthetic seismic record can be generated. Since the viscoelastic wave equation is a linear time-invariant system with respect to the source time function, the impulse response (Green's function) can fully characterize the characteristics of the viscoelastic wave equation forward simulation system.

[0093] In this step, the vibrator excites a continuous sweep signal, usually a linear sinusoidal sweep signal:

[0094] s(t)=a(t)sin[2πφ(t)+ψ]. (7)

[0095] The amplitude term is:

[0096]

[0097] Where T is the duration.

[0098] The phase term is:

[0099]

[0100] Where f1 and f2 are the starting scanning frequency and the ending scanning frequency respectively.

[0101] 4. Combine the vibroseis records at each location to form a combined gun vibroseis record

[0102] By combining single-shot synthetic seismic records, a combined-shot controlled-source synthetic seismic record can be formed. In conventional controlled-source forward simulation, the source time function is directly loaded to solve the viscoelastic wave equation, and the calculation time depends on the length of the source time function. Since the controlled source is a continuous time signal that may last for a long time, the computational cost of the existing method increases linearly with the increase in duration. By calculating the Green's function and utilizing the linear time-invariant characteristics of the forward simulation system, the present invention can effectively avoid this computational cost problem. The increase in the length of the controlled-source time function will not increase the computational cost of solving the Green's function, but will only slightly increase the computational cost of the one-dimensional convolution. Compared with solving the viscoelastic wave equation, the computational cost of the one-dimensional convolution is negligible, realizing fast broadband controlled-source viscoelastic forward simulation.

[0103] Example 3

[0104] In a specific embodiment 3 of the present invention, the fast broadband vibroseis viscoelastic forward modeling method of the present invention is described in detail:

[0105] Figure 2 The viscoelastic P-wave velocity model used in this section was designed based on real geological conditions and incorporates complex geological features such as thin interbeds, pinch-outs, and strongly reflecting interfaces. The S-wave velocity, density, P-wave quality factor, and S-wave quality factor are derived using empirical formulas. Figure 3 The viscoelastic Green's function is obtained by applying a pulsed vertical force source to the middle of the model surface (x = 4000 m). As can be seen from the figure, the viscoelastic seismic wavefield is very complex, containing strong surface waves and surface wave scattering energy. Furthermore, due to the influence of the viscoelastic medium itself, the reflected wave energy decays rapidly, which inevitably poses challenges for imaging deep reflectors.

[0106] Figure 4 This is a common vibrator sweep signal and its amplitude spectrum, with a start frequency of 1 Hz and an end frequency of 60 Hz. Figure 5 The synthetic seismic record obtained by convolving the vibrator time function and the Green function. Since the vibrator time function is a duration signal, the seismic record after convolution also has an obvious tailing effect. Generally, before processing the vibrator seismic record, it is necessary to cross-correlate the vibrator record and the source time function. The result after cross-correlation is as follows Figure 6 As shown in the figure, it can be seen that the tailing effect of the event axis is suppressed. Figure 7 These are the amplitude spectra of the Green's function, the vibroseis synthetic seismic record, and the cross-correlation result, respectively. As can be seen from the figure, the convolution and cross-correlation operations essentially do not destroy the characteristics of the amplitude spectrum, thus verifying the correctness and reliability of the present invention. The present invention was further applied to different vibroseis observation methods. Figure 8 Two different vibroseis observation methods are shown. If the conventional vibroseis viscoelastic forward modeling method is used, three 3.5-second viscoelastic forward calculations are required. However, the method introduced in this invention only requires two 3.5-second viscoelastic forward calculations, significantly reducing the computational cost.

[0107] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

[0108] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A fast broadband vibroseis viscoelastic forward modeling method, characterized by: The fast broadband vibroseis viscoelastic forward modeling method includes: Step 1: Load the pulse vertical force source function at the vibrator excitation point; Step 2: At the vibrator excitation point, load the pulse time function, solve the viscoelastic wave equation, and obtain the Green's function of the viscoelastic wave equation; Step 3: Generate a single-shot synthetic seismic record by convolving the time function of the vibrator with the Green's function of the viscoelastic wave equation; Step 4: Linearly combine the single-shot synthetic seismic records according to the observation system to form a combined-shot vibroseis synthetic seismic record; In step 2, consider a linear viscoelastic model composed of n standard linear solids, and the corresponding governing equation is: Where ρ is the density, u is the displacement vector, λ0 and μ0 are the medium parameters at the reference frequency, λ v and μ v is the viscoelastic medium parameter, F is the pulse vertical force source function, and L is the spatial operator, where: Among them, the auxiliary variables Solve the following equation: where the relaxation frequency ω v >0,v=1,2,…,n; To calculate the Green's function of the viscoelastic wave equation, it is necessary to solve 3+3n partial differential equations, where n is the number of standard linear solids.

2. The fast broadband vibroseis viscoelastic forward modeling method according to claim 1, characterized in that: In step 1, the impulse vertical force source function F can be expressed as: Where x0 is the spatial position of the point force source, g(t,t0,ω) is the source time function, which is a function of the arrival time t0 and frequency ω; (F x ,F y ,F z ) T are the three components of the force vector, F0 is the amplitude of the force; for controllable seismic sources, only the vertical force is considered.

3. The fast broadband vibroseis viscoelastic forward modeling method according to claim 2, characterized in that: In step 1, the earthquake source time function g(t, t0, ω) adopts the impulse function δ(t-t0); the impulse function is a special function that is zero at all times except t=t0; in addition, the integral of the impulse function is 1; Assuming that the function f(t) is a continuous function, the impulse function satisfies the following conditions: ∫f(t)δ(t-t0)dt=f(t0) (2).

4. The fast broadband vibroseis viscoelastic forward modeling method according to claim 3, characterized in that: In step 1, at time grid t i = iΔt discretized pulse function, where Δt is the time step for solving the viscoelastic wave equation; the discretized pulse function sequence is expressed as d i ,i=0,1,2,…; According to the properties of the impulse function, for the polynomial function f(t)=t q ,q=0,1,…,Q, where the pulse function sequence d i The following conditions must be met: According to the Q+1 equations above, the pulse function sequence d can be solved i .

5. The fast broadband vibroseis viscoelastic forward modeling method according to claim 1, characterized in that: In step 3, the vibrator excites a continuous sweep signal, usually a linear sinusoidal sweep signal s(t): s(t) = a(t)sin[2πφ(t)+ψ] (7) Where ψ is a constant phase and the amplitude term a(t) is: Where T is the duration, The phase term φ(t) is: Where f1 and f2 are the starting scanning frequency and the ending scanning frequency respectively.

6. Fast broadband vibroseis viscoelastic forward modeling system, characterized by: The fast broadband vibroseis viscoelastic forward modeling system adopts the fast broadband vibroseis viscoelastic forward modeling method described in any one of claims 1 to 5 to perform high-precision and high-efficiency vibroseis earthquake simulation under complex geological conditions for oil seismic exploration.

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