KR20160107702A - An efficient wavenumber-space-time-domain finite-difference modeling method of acoustic wave equation for synthesizing CMP gathers - Google Patents

Abstract

The present invention relates to an efficient sound wave equation finite difference method modeling scheme for combining wave number-space-time-domain common midpoint collection data. More specifically, the efficient sound wave equation finite difference method modeling scheme for combining wave number-space-time-domain common midpoint collection data is derived from a two-dimensional time area wave equation for a horizontal stratigraphic medium and comprises the following steps: calculating a wave number-space-time-domain wave equation by performing Fourier transform with respect to an x direction which is one of spatial variables while the derived wave equation is calculated by using the finite difference method; generating common midpoint collection data by adding a parallel shifting term without sorting data processing; and limiting a range of the wave number even though many wave number elements to be calculated by sampling theorem.

Description

An efficient acoustic wave equation finite difference method modeling method for wavenumber-space-time domain common midpoint collection data is proposed. The finite difference modeling method is an efficient wavenumber-space-time-domain finite-difference modeling method for synthesizing CMP gathers.

The present invention relates to a numerical modeling technique for synthesizing a common midpoint collection data for an underground structure, and more particularly, to an efficient acoustic wave equation finite difference modeling method for synthesizing a wavenumber-space-time domain common midpoint collection data .

Generally, numerical modeling method of wave equation is an important tool that has been widely used for several decades in seismic data synthesis and underground structure identification for underground velocity model.

The numerical modeling method of the wave equation is widely used not only to synthesize seismic data for arbitrary velocity models but also to invert the properties of underground structures in the past several decades.

However, modeling work can entail massive computation time burden when conducting experiments on higher dimensions at finer intervals over a wider range of areas.

Numerous efforts have been made to reduce computation time for such numerical modeling and inversion.

The modeling technique is an important technique for understanding underground information and resource existence. However, as the surveyed area becomes wider and the higher resolution data is acquired, the time and resources required for numerical calculation and underground structure research become widespread .

Therefore, an efficient modeling technique is needed to overcome the problems of computation time and cost that occur during modeling.

Korean Registered Patent No. 10-1262990 (registered on May 03, 2013) (references) Versteeg, R. (1994). The Marmousi experience: Velocity model determination on a synthetic complex data set. The Leading Edge, 13, 927-936.

The present invention has been made in order to overcome the above-mentioned problems, and a wave-space-time domain wave equation according to the present invention is derived from a two-dimensional time domain wave equation for a horizontal layered medium, Space-time domain wave equation by performing Fourier transform on the in-x direction, and the wave equation thus derived can be used to synthesize a wavenumber-space-time domain common midpoint collection data which can be calculated using a finite difference method And to provide an efficient acoustic wave equation finite difference modeling method.

In addition, the object of the present invention is to provide a method and apparatus for generating a common midpoint (CMP) collection data by adding a shifting term without going through sorting data processing, And to provide an efficient acoustic wave equation finite difference method modeling method for point collection data synthesis.

In order to achieve the object of the present invention, an efficient acoustic wave equation finite difference modeling method for synthesizing a waveness-space-time domain common midpoint collection data according to the present invention is characterized in that a wavenumber- Time domain wave equation by performing a Fourier transform on the x direction which is one of the spatial variables, the wave equation being derived from a two-dimensional time domain wave equation of And is calculated using a difference method.

The present invention relates to a method of generating a common intermediate point (CMP) vowel data by adding a shifting term without going through sorting data processing, Further comprising the step of limiting the range.

As described above, the technical problem solving pursued by the present invention is advantageous in that a common midpoint (CMP) collection data can be generated by adding a shifting term without going through sorting data processing.

The present invention is advantageous in that it is possible to generate the common midpoint collection data that is the same as the result of the common midpoint collection data generated from the two-dimensional modeling technique in a shorter time.

The modeling algorithm of the present invention is advantageous in that it can be used for common in-vowel data inversion and AVO (Amplitude-versus-offset) inverse calculation.

Figure 1 is an illustration of a wave spectrum extracted from any common midpoint (CMP) vowel data in the waveness-time domain according to the present invention.
2 (a) and 2 (b) are wave spectra of a common midpoint (CMP) collection data including only direct waves, reflected waves, and reflected waves according to the present invention.
Figure 3 is a simple three-layer velocity model arbitrarily made to verify the applicability and utility of the present invention.
4 (a) and 4 (b) are comparative diagrams comparing common common midpoint collection data obtained in the conventional 2D space-time domain and the wavenumber-space-time domain modeling.
5 (a) and 5 (b) are comparative diagrams comparing amplitudes in the vicinity of 100 m offset and 1,100 m offset behind the common midpoint collection data shown in Fig.
6 is a view showing the velocity distribution type of the Marmousi 2 model.
FIGS. 7 (a) and 7 (b) are comparative diagrams comparing common intermediate point collection data obtained in the conventional 2D space-time domain and the wavenumber-space-time domain modeling design.
FIG. 8 is a comparative chart comparing amplitudes of the common midpoint collection data shown in FIG. 7 at an offset of about 100 m and a backward distance of 1,700 m.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. Further, the preferred embodiments of the present invention will be described below, but it is needless to say that the technical idea of the present invention is not limited thereto and can be practiced by those skilled in the art.

FIG. 1 is an exemplary view of a wave spectrum extracted from an arbitrary common midpoint (CMP) collection data in a waveness-time domain according to the present invention, and FIGS. 2 (a) and 2 (CMP) collection data including only reflected waves, and FIG. 3 is a simple three-layer velocity model arbitrarily made to confirm applicability and utility of the present invention.

As shown in FIGS. 1 to 3, an efficient acoustic wave equation finite difference modeling method for synthesizing a wavenumber-space-time domain common midpoint collection data according to a preferred embodiment of the present invention is a modeling method for a 1.5-dimensional medium relates, the effective frequency derived from a two-dimensional acoustic wave equation in order to shorten the computation time for inversion with the common midpoint collection material - is for the time domain (k _x -zt) acoustic wave equation modeling space.

The wavenumber-space-time domain wave equation can be solved using a finite difference method in the same manner as the one-dimensional acoustic wave equation. In addition, although the modeling method of the present invention can be used only for horizontal parallel models, it produces the same results as the results obtained from the two-dimensional modeling technique, while exhibiting high efficiency (fast calculation) of the one-dimensional modeling technique.

The common midpoint collection data may be generated using an inverse Fourier transform and a shifting theorem. As such, the common midpoint collection data can be directly produced as a result, so there is no need for additional data processing such as iterative modeling and sorting of the transmitter at other locations. Therefore, the modeling technique of the present invention can be efficiently used for the inversion of AVO which requires common intermediate point collection data in the future.

Hereinafter, the process of deriving the wave-space-time domain wave equation using the finite difference method for performing the modeling according to the present invention will be described, and the stability and dispersion analysis contents will be omitted. To improve the efficiency of the modeling, the wave field of the wave component is analyzed and the inverse Fourier transform is explained. In addition, the results obtained from general two-dimensional time-domain modeling are compared with the results obtained by the modeling technique of the present invention.

The Fourier transformed wave equation according to the present invention first derives a Fourier transformed wave equation from a two-dimensional acoustic wave equation. The two-dimensional wave equation for the space-time ( xzt ) region is shown in Equation (1).

Here, u is acoustic wave field, v is p wave velocity, t is time, x and z are variables for space, (x ₀ , z ₀ ) is the position of transmission point, and f is a transmission function.

In addition, Fourier transform of Equation (1) with respect to the spatial variable x and rearranging can be written as follows.

Here, k _x means the number of waves with respect to the x-axis.

와

는 각각 푸리에 변환 된 파동장과 송신 함수를 나타내고, j는 허수 단위를 나타낸다. 수학식2를 풀기 위해서 유한차분법을 사용한다.

Wow

Represents a Fourier transformed wave field and a transmission function, respectively, and j represents an imaginary unit. To solve Equation (2), a finite difference method is used.

는 송신항이다.Where the superscript n and subscript i denote the location of time and space, respectively, and Δt and Δz denote time lattice spacing and space lattice spacing, respectively.

Is a transmission term.

The inverse Fourier transform and integration for the common intermediate point (CMP) collection data according to the present invention can be modeled in the wavenumber-space-time domain by solving Equation (3) Can be obtained.

Inverse Fourier transform is performed to convert it into space-time domain and generate it as CMP collection data.

By applying the parallel movement theorem of the Fourier transform, CMP collection data can be generated.

If the wavenumber spectrum is observed in the wavenumber-time domain, it becomes very vibrated as shown in Fig.

Therefore, a method of integrating such a wave spectrum by using the Gaussian quadrature method is not appropriate. Instead, the traverses lying at the vertically incident transmission point positions calculated within the wavenumber-space-time domain are multiplied by the translation term and all are superimposed. This applies the inverse Fourier transform and generates the common midpoint (CMP) collection data.

Equation (4) is a mathematical expression summarized for the process described above.

Here, x ₀ represents the x-coordinate of the transmission point position. This means not only the position of the transmission point but also the distance of the spreading distance.

This is because the spreading distance is equal to the x-coordinate of the position of the transmission point.

The range of the wave number to be calculated in Equation (4) is expressed by Equation (5).

는 최대 각주파수,

는 매질 내 최소 속도,

는 반사면에 대한 최대 입사각을 의미한다. 입사각과 지질학적인 정보 사이에 존재하는 삼각함수 공식에 따라 수학식5는 다음과 같이 수학식6으로 정리할 수 있다.here,

The maximum angular frequency,

Is the minimum velocity in the medium,

Means the maximum incident angle to the reflective surface. According to the trigonometric formula existing between the incident angle and the geological information, Equation (5) can be summarized as Equation (6) as follows.

는 최대중간 벌림거리이고,

는 가장 얕은 깊이의 반사면이다. 만약 직접파와 고스트 효과(ghost effect)를 표현하고 싶다면 더 높은 파수의 범위까지 사용해야 하지만 실제로 지하구조 규명 시에는 반사파에만 관심을 갖기 때문에 수학식6에서 유도된 최대 파수를 초과하는 더 높은 파수 성분은 고려하지 않아도 된다.here,

Is the maximum intermediate spreading distance,

Is the shallowest reflective surface. If you want to express the direct wave and ghost effect, you have to use it to a higher wave number range, but because you are only interested in the reflected wave in the underground structure identification, the higher wave number component exceeding the maximum wave number You do not have to do.

= Numerical example =

First, the common midpoint (CMP) collection data obtained from general two-dimensional finite difference modeling is compared with the modeling technique of the present invention, and it is confirmed whether the modeling technique of the present invention generates accurate common midpoint (CMP) collection data .

For accurate comparison, all the variables and conditions are the same except for the time interval when performing general two-dimensional finite difference modeling and modeling according to the present invention.

In order to minimize the calculation time and to use the wave component efficiently, we choose a method of modeling only the reflection wave, except the direct wave.

As shown in FIG. 2, it is difficult to quickly perform the modeling because a considerably large wave range is required to accurately combine the direct waves and a long calculation time is required. On the other hand, since the reflected wave is accurately represented by only a small amount of wave components, instead of performing the modeling quickly, a method of eliminating the direct wave that is not properly expressed is selected.

In the case where both the direct wave and the reflected wave are expressed as a result of Fourier transforming the seismic wave data in the space-time domain by the Fourier transform and observing the wave spectrum, as shown in FIG. 2 (a) A large energy is observed in the range, but when only the reflected wave is expressed, the energy is observed only in the extremely low frequency range as shown in FIG. 2 (b).

As shown in FIG. 2 (b), if only the number of waves contributing to modeling is selected and modeling is performed, the calculation time can be considerably reduced. If you use only a very small amount of wave, you have to eliminate it because it is quite inaccurate.

In addition, inaccurate direct wave cancellation is performed by modeling the homogeneous model using only the first layer velocity and subtracting it from the originally obtained seismic data.

As shown in FIG. 3, the first experimental numerical model is a three-level horizontal model at speeds of 1500 m / s, 3000 m / s and 4500 m / s, respectively. The horizontal distance of the model is 10 km and the depth is 3 km. The spatial lattice spacing in the z direction is 5 m.

Both the general two-dimensional modeling and the modeling according to the present invention use a Ricker transmission waveform, with the main frequency being 5 Hz and the recording time being 3 seconds. The generated CMP collection data has a maximum spreading distance of 2100 m, a minimum spreading distance of 100 m, and a spacing of 10 m.

As described above, the present invention minimizes the burden on the calculation time by eliminating the direct wave and using only a small number of wave components.

4 (a) and 4 (b) are comparative diagrams comparing common common midpoint collection data obtained in the conventional 2D space-time domain and wavenumber-space-time domain modeling, Is a comparison chart comparing amplitudes in the vicinity of 100 m offset and 1,100 m behind the common midpoint collection data shown in Fig.

The wavenumber-space-time domain modeling uses only a very small range of wave number corresponding to the whole range (0 to 250 cycles / km) determined by the sampling theorem in the range of 3% (0 to 7.5 cycles / km).

The results thus obtained are the same as those obtained using general modeling as shown in Figs. 4 (a) and 4 (b).

In order to compare the amplitudes of the common midpoint (CMP) collection data, traces located at far and wide distances from the common midpoint (CMP) collection data of the two modeling results are extracted and compared . Here, the near-break distance is 100 m and the far-away distance is 1100 m.

The amplitude values are the same and it is observed that there is no problem using wavenumber-space-time domain modeling instead of general time domain modeling.

Although the wavenumber-space-time domain modeling has the same accuracy as the existing modeling, the existing method requires 32.76 seconds to generate the CMP collection data, whereas the developed modeling ends only in 1.23 seconds.

6 (a) and 6 (b) are graphs showing the comparison of the common midpoint collection data obtained by modeling the conventional 2D space-time domain and the wavenumber-space-time domain, And FIG. 8 is a comparative chart comparing the amplitudes of the common midpoint collection data shown in FIG. 7 in the vicinity of 100 m offset and 1,700 m backward.

The second model is the Marmousi2 model, which has a complex geological structure and a large velocity change (Versteeg, 1994). Since the modeling technique according to the present invention is applicable to the horizontal structure as shown in FIG. 6, one velocity profile of the Marmousi2 model is extracted and used as a horizontal structure. That is, we assume a velocity model in which there is no velocity change in the horizontal direction but only in the z space direction.

Both modeling methods use a Licker transmit waveform with a 1.25 m spatial lattice spacing and a dominant frequency of 13.4 Hz, with a write time of 3 seconds.

The common intermediate point (CMP) collection data has a maximum spreading distance of 2100 m and a spreading distance of 10 m. Since only the reflected wave is generated for efficient calculation, many wave components for direct wave generation are unnecessary.

As shown in Figs. 7 (a) and 7 (b), the wavenumber-space-time modeling also accurately generates the CMP collection data for a velocity model having a complicated velocity change.

As shown in FIGS. 8 (a) and 8 (b), the results of comparing the traces located at the near and far distances of the CMP collection data generated from general two-dimensional modeling and wavenumber-space-time modeling are shown.

Here, the near-break distance is 100 m and the far-away distance is 1700 m. We can confirm that the calculation time of the 2 - dimensional modeling calculation is 2139 seconds and the calculation time of the wavenumber - space - time domain modeling is 22.91 seconds, and the wavenumber - space - time domain modeling calculation is more efficient.

As described above, according to the present invention, the wave-space-time domain wave equation modeling technique for synthesizing the CMP collection data is based on the inverse Fourier transform using the finite difference method and the parallel motion theorem, And the calculation time can be reduced by excluding the direct wave calculation, and the CMP collection data can be efficiently synthesized. In addition, although the wavenumber-space-time domain modeling technique according to the present invention performs modeling in less time than the two-dimensional modeling technique, it can synthesize accurate CMP collection data as much as the two-dimensional modeling result. The modeling technique according to the present invention can be used for inversion of AVO using propagation inversion or CMP data in the future, and can be extended to three-dimensional modeling and inversion.

It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. It will be possible.

Therefore, the embodiments disclosed in the present invention and the accompanying drawings are intended to illustrate and not to limit the technical spirit of the present invention, and the scope of the technical idea of the present invention is not limited by these embodiments and the accompanying drawings .

The scope of protection of the present invention should be construed according to the following claims, and all technical ideas within the scope of equivalents thereof should be construed as being included in the scope of the present invention.

Claims (8)

The wavenumber-space-time domain wave equation is derived from a two-dimensional time domain wave equation for the horizontal stratosphere medium. The wave-space-time domain wave equation is derived from the two- ≪ / RTI >
Wherein the derived wave equation is calculated using a finite difference method. 2. The method of claim 1, wherein the derived wave equation is calculated using a finite difference method.
The method according to claim 1,
Generating a common intermediate point (CMP) collection data by adding a shifting term without going through sorting data processing;
The method of claim 1, further comprising the step of limiting the range of wavenumbers even though there are many wavenumber components to be calculated according to the sampling theorem. The method of modeling an efficient acoustic wave equation finite difference method for waveness-space-time domain common midpoint collection data synthesis.
3. The method according to claim 1 or 2,
The Fourier transformed wave equation may be expressed as:
A two-dimensional wave equation is derived from a two-dimensional acoustic wave equation and a two-dimensional wave equation for a space-time ( xzt ) domain is defined as in Equation (1) Efficient Acoustic Wave Equation Finite Difference Modeling Method for Data Synthesis.
[Equation 1]

Here, u is acoustic wave field, v is p wave velocity, t is time, x and z are variables for space, (x ₀ , z ₀ ) is the position of transmission point, and f is a transmission function.
The method of claim 3,
Time domain common median point collection data is Fourier-transformed and rearranged according to Equation (1) with respect to the spatial variable x. Way.
&Quot; (2) "

Here, k _x means the number of waves with respect to the x-axis.

Wow

Represents a Fourier transformed wave field and a transmission function, respectively, and j represents an imaginary unit.
5. The method of claim 4,
The finite difference method is used for solving Equation (2), and is defined as Equation (3). Equation (3) is an efficient acoustic wave equation finite difference modeling method for synthesizing a wavenumber- .
&Quot; (3) "

Where the superscript n and subscript i denote the location of time and space, respectively, and Δt and Δz denote time lattice spacing and space lattice spacing, respectively.

Is a transmission term.
6. The method of claim 5,
Wherein an inverse Fourier transform and an inverse Fourier transform for synthesizing the common intermediate point (CMP) collection data are defined as in Equation (4), and an efficient acoustic wave equation finite difference method Modeling method.
&Quot; (4) "

Here, x ₀ represents the x-coordinate of the transmission point position. This means not only the position of the transmission point but also the distance of the spreading distance.
The method according to claim 6,
Wherein the wavenumber range to be calculated in Equation (4) is defined as Equation (5). ≪ EMI ID = 6.0 >
&Quot; (5) "

here,

The maximum angular frequency,

Is the minimum velocity in the medium,

Means the maximum incident angle to the reflective surface.
8. The method of claim 7,
(5) is defined by Equation (6) according to a trigonometric function formula existing between the incident angle and the geological information. An efficient acoustic wave equation finite difference Method modeling method.
&Quot; (6) "

here,

Is the maximum intermediate spreading distance,

Is the depth of the shallowest reflective surface.

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