KR20210011033A - Laplace Fourier domain complete waveform inversion apparatus and method using multiple attenuation and multiple offsets - Google Patents

Abstract

The present invention is a Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets, receiving an elastic wave signal of a measurement target area as measurement data, dividing the offset of the elastic wave signal from the measurement data into a predetermined number, and each sub Calculating attenuation coefficients for each offset, converting measurement data in the time domain into measurement data in the Laplace-Fourier domain using a plurality of attenuation coefficients for each sub-offset, and inputting parameters representing characteristics of the measurement target area Received, set an equation including parameters, and calculate modeling data by calculating the equation in the Laplace-Fourier region using attenuation coefficients for each sub-offset, and measuring data and modeling data in the Laplace-Fourier region for each sub-offset. Comparing and updating the parameters.

Description

Laplace Fourier domain complete waveform inversion apparatus and method using multiple attenuation and multiple offsets

The present invention relates to a technology for exploring underground structures, and in particular, to a technology for analyzing an underground structure through signal processing using full waveform inversion.

Full Waveform Inversion refers to a technique for estimating an underground velocity model using prestack seismic data.

Complete waveform inversion refers to a series of processes in which an initial model for an area of interest is created, measurements are obtained from the area, and then the initial model is repeatedly updated using the obtained measurements to obtain an underground structure model similar to the actual underground structure. Can be seen as. In this process, theoretical values are calculated from an arbitrary underground structure by a computer (modeling), and parameters representing the properties of the basement are iteratively calculated from the error between the theoretical value and the data obtained through field exploration until the error is minimized. The calculation is made while updating to

Complete waveform inversion is one of the objectives of the Earth's physical exploration, which is one of the methods of underground structure analysis. Numerous mathematical methods are being used. Recently, with the development of computers, simple inverse calculations are often solved with personal computers, and since there is usually no unique solution, an optimal solution is obtained by adding specific conditions.

There have been attempts to apply various attenuation coefficients according to errors for the stability of this complete waveform inverse solution.

First, there is a method of weighted L2 FWI that compensates for energy attenuation for errors by multiplying the L2 norm value by the square of time. This is effective for general seismic data, but there is a problem that a cycle skipping problem occurs. have.

Next, in order to correct the energy attenuation according to the distance, the shift Laplace domain is assumed to be attenuated from the first arrival travel time, and the decay function is shifted until the initial arrival time to correct the attenuation. (Shifted Laplace domain) In the case of FWI, it provides a stable solution compared to the non-shift method, but there are many errors during peaking of the first arrival pick, which degrades the accuracy of the inverse calculation.

Finally, the FWI using deconvolution object function, which uses deconvolution of real and model data as the objective function, can perform stable FWI without low frequency components, but the solution becomes extremely unstable at the notch frequency. It has a drawback.

The present invention provides a Laplace Fourier domain full waveform inversion apparatus and method using multiple attenuation and multiple offsets to improve stability and accuracy of a solution of a full waveform inversion.

The present invention is a Laplace Fourier region complete waveform inversion device using multiple attenuation and multiple offsets, an input unit for receiving an acoustic wave signal of a measurement target region as measurement data, and a predetermined number of offsets of the acoustic wave signal from the measurement data, and each sub An attenuation coefficient calculation unit that calculates attenuation coefficients for each offset, a Laplace calculation unit that converts measurement data in the time domain into measurement data in the Laplace-Fourier domain using a plurality of sub-offset attenuation coefficients, and a characteristic of the measurement target area. A modeling data generator and a Laplace-Fourier for calculating modeling data by receiving a parameter representing a parameter and setting an equation including the parameter, and calculating the equation in the Laplace-Fourier domain using attenuation coefficients for each sub-offset. And a parameter update unit that compares the measurement data of the region and modeling data to update a parameter.

The present invention is a Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets, receiving an elastic wave signal of a measurement target area as measurement data, dividing the offset of the elastic wave signal from the measurement data into a predetermined number, and each sub Calculating attenuation coefficients for each offset, converting measurement data in the time domain into measurement data in the Laplace-Fourier domain using a plurality of attenuation coefficients for each sub-offset, and inputting parameters representing characteristics of the measurement target area Received, set an equation including parameters, and calculate modeling data by calculating the equation in the Laplace-Fourier region using attenuation coefficients for each sub-offset, and measuring data and modeling data in the Laplace-Fourier region for each sub-offset. Comparing and updating the parameters.

According to the present invention, by dividing a suboffset according to an offset and applying a different attenuation coefficient for each section, the difference in energy within the section is balanced, thereby improving the stability and accuracy of the solution of Full Waveform Inversion. I can.

1 is a diagram schematically illustrating the principle of complete waveform inversion according to an embodiment of the present invention.
2 is a diagram showing a schematic configuration of an underground structure imaging apparatus to which a Laplace Fourier region complete waveform inversion apparatus using multiple attenuation and multiple offsets according to an embodiment of the present invention is applied.
3 is a diagram showing a detailed configuration of a signal processing unit according to an embodiment of the present invention.
4 is a diagram showing a detailed configuration for a Laplace Fourier domain complete waveform inversion using multiple attenuation and multiple offset in a signal processing unit.
5 is a diagram for describing multiple sub-offsets according to an embodiment of the present invention.
6 is a diagram for explaining applying multiple attenuation coefficients for multiple sub-offsets according to the present invention.
7 is a flowchart illustrating a Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In describing the present invention, if it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, a detailed description thereof will be omitted. In addition, terms to be described later are terms defined in consideration of functions in the present invention, which may vary according to user or operator intention or custom. Therefore, the definition should be made based on the contents throughout this specification.

Full Waveform Inversion according to an embodiment of the present invention refers to a process of inferring information about an underground structure (eg, a velocity model or a density model for a measurement target area) based on data actually measured in the field. Such waveform inversion may involve a modeling process in which an analyst sets an arbitrary underground structure model and then obtains a theoretical value for the set model.

For example, when imaging an underground structure using complete waveform inversion according to an embodiment of the present invention, a new underground structure model is created by comparing the theoretical values calculated through modeling with the measured values obtained through actual field exploration. It is possible to obtain an underground structure model similar to an actual underground structure by repeatedly comparing the theoretical values for the underground structure model with the measured values to minimize the error.

The complete waveform inversion according to an embodiment of the present invention includes a computer-readable recording medium in which a signal processing algorithm is recorded, a computing device for processing various signals to generate image data for imaging an underground structure of a measurement target area, It can be embodied by a method of imaging an underground structure through such a computing device or a recording medium.

First, a principle of complete waveform inversion according to an embodiment of the present invention will be schematically described with reference to FIG. 1.

In Fig. 1, V represents the characteristics of the underground structure, S represents the input applied to V, and D represents the output when S is applied to V.

The final purpose of the waveform inversion is to find the characteristic V of the underground structure using the measured D. On the other hand, if the velocity distribution (i.e., velocity model) of the seismic wave is identified among the characteristics of the underground structure, the above characteristic V is the velocity distribution, and the input S is the source data, and the output D is It is assumed to be seismic data.

The measured seismic data Dreal can be obtained through field exploration of the area to be measured, and the estimated seismic data Dest can be obtained from the theoretical values (Vest, Sest) modeling the area. At this time, if the initially estimated velocity data Vest and the source data Sest are updated to minimize the difference between the actual measured seismic data Dreal and the estimated seismic data Dest, and repeat this process, the estimated velocity distribution Vest is eventually converted to the actual velocity distribution Vreal. It can be identified with. At this time, V representing the underground structure may represent only the velocity distribution as above, or may represent the velocity/density, impedance, and Lame constant/density distribution.

FIG. 2 shows a schematic configuration of an underground structure imaging apparatus to which a Laplace Fourier domain complete waveform inversion apparatus using multiple attenuation and multiple offsets according to an embodiment of the present invention is applied.

Referring to FIG. 2, the apparatus for imaging an underground structure may include a transmission source 10, a receiver 20, a signal processing unit 100, and a display unit 40.

The transmission source 10 may generate a wave to the measurement target area 30, and the receiver 20 may receive an acoustic wave signal propagating from the measurement target area 30. The signal processing unit 100 receives an elastic wave signal from the receiver 20 and processes the received elastic wave signal so that the underground structure of the measurement target area 30 can be displayed on the display unit 40 to generate image data.

The signal processing of the signal processing unit 100 uses the above-described complete waveform inversion, and the signal processing unit 100 according to the present embodiment may perform a Laplace Fourier domain complete waveform inversion using multiple attenuation and multiple offsets.

For example, the signal processing unit 100 may perform domain transformation by multiplying an exponential attenuation function (e-st) having an input attenuation coefficient s and integrating the attenuation wavelength over time. The Laplace-Fourier transform for complete waveform inversion of the signal processing unit 100 is already well known and may obscure the subject matter of the present invention, so a detailed description thereof will be omitted.

By the way, the time when the seismic signal arrives from the measurement target area 30 to the receiver 20 has a close relationship with the depth of the underground layer. That is, when the attenuation coefficient is large, the elastic wave signal having a fast arrival time is relatively largely amplified, which is advantageous for inverse calculation of the shallow layer. On the other hand, when the attenuation coefficient is small, the seismic signal with a late arrival time is amplified relatively large, which is advantageous for inverse calculation of the deep layer.

On the other hand, the optimization technique used for complete waveform inversion is an algorithm that prioritizes updating grid points with a large gradient. Accordingly, a result of relative inversion may be poor for grid points in which the energy of measurement data and modeling data is small. In the case of using a single attenuation coefficient in the Laplace region, the difference between the maximum energy and the minimum energy is so great that the convergence of the solution is unstable and accurate inversion cannot be performed for the distant offset data having a small energy. There is a problem that should be done.

Accordingly, the signal processing unit 100 according to an exemplary embodiment of the present invention applies an attenuation coefficient value that is inversely proportional to the size of the offset so that the acoustic wave signal is efficiently amplified according to the depth of the measurement target area 30. Accordingly, the energy attenuation of the acoustic wave signal due to the distance can be relatively restored without artificial processing. That is, according to an embodiment of the present invention, the signal processing unit 100 performs complete waveform inversion in the Laplace region, but divides a suboffset according to an offset and applies a different attenuation coefficient for each section to perform complete waveform inversion. .

3 is a diagram showing a detailed configuration of a signal processing unit according to an embodiment of the present invention, and FIG. 4 is a diagram showing a detailed configuration for inverting a Laplace Fourier domain complete waveform using multiple attenuation and multiple offsets in the signal processing unit. 5 is a diagram for explaining multiple sub-offsets according to an embodiment of the present invention, and FIG. 6 is a diagram for describing application of multiple attenuation coefficients for multiple sub-offsets according to the present invention.

The first input unit 110 is connected to the receiver 20 to receive time domain data for a measurement target area. The first input unit 110 transmits the received time domain data to the conversion unit 120.

The conversion unit 120 converts the received time domain data into Laplace-Fourier domain data. For example, the transform unit 120 may convert data as shown in Equation 1 by using an attenuation coefficient given as a complex number.

는 라플라스-푸리에 영역으로 변환된 데이터를,

는 시간 영역의 데이터를,

는 감쇄 계수를 나타낸다.In <Equation 1>

Is the data converted to the Laplace-Fourier domain,

Is the data in the time domain,

Represents the attenuation coefficient.

However, according to an embodiment of the present invention, the transform unit 120 may perform a Laplace-Fourier transform using multiple attenuation coefficients for multiple offsets.

Specifically, referring to FIG. 4, the transform unit 120 may include an attenuation coefficient calculating unit 121 and a plurality of Laplace transform units 122-1, 122-2,..., 123-n. have.

As shown in FIG. 4, the attenuation coefficient calculating unit 121 divides the offset of the acoustic wave trace (common sound source collection data) into a predetermined number of sub-offsets, and the sub-offset at which the traces belonging to the sub-offset contribute to imaging, and The attenuation factor for each sub-offset is determined by calculating the attenuation rate according to the offset.

)을 이용한 라플라스 푸리에 변환일 수 있다. 여기서, 감쇄 계수들의 크기는

일 수 있다. The Laplace transform units 122-1, 122-2,..., 123-n use each of the n attenuation coefficients calculated by the attenuation coefficient calculation unit 121 to obtain a Laplace- Fourier transform is possible. That is, as shown in Fig. 6, the measurement data as shown in (a) is converted into attenuation coefficients for each sub-offset as shown in (b).

It may be a Laplace Fourier transform using ). Here, the magnitude of the attenuation coefficients is

Can be

The modeling data generation unit 130 performs a function of generating modeling data for an area to be measured. For example, when a parameter representing the characteristic of the measurement target area is input to the second input unit 140, the parameter storage unit 150 stores the input parameter, and the modeling data generation unit 130 is stored in the parameter storage unit 150. After receiving the stored parameters and setting an equation including the parameters, it is possible to generate modeling data by calculating the equation in the Laplace-Fourier domain.

According to an embodiment of the present invention, the modeling data generator 130 may generate modeling data for each attenuation coefficient.

Specifically, referring to FIG. 4, the modeling data generation unit 130 may include an equation setting unit 131 and a plurality of Laplace transform units 132-1, 132-2,..., 133-n. I can.

를 구할 수 있다. The equation setting unit 131 may express the wave equation in which the parameter representing the characteristic of the measurement target region is reflected as a matrix equation using the finite element method or the finite difference method.

Can be obtained.

Each of the Laplace transform units 122-1, 122-2,..., 123-n uses each of the n attenuation coefficients calculated by the attenuation coefficient calculation unit 121 to obtain the following <Equation 2>. We can do the Laplace-Fourier transform together.

는 라플라스-푸리에 영역으로 변환된 데이터를,

는 시간 영역의 데이터를,

는 감쇄 계수를 나타낸다.In <Equation 2>

Is the data converted to the Laplace-Fourier domain,

Is the data in the time domain,

Represents the attenuation coefficient.

Here, the output of the conversion unit 120 may refer to measurement data, and the output of the modeling data generation unit 130 may be regarded as estimated data.

와 모델링 데이터

간의 차이를 최소화시킬 수 있는 방향으로 기 저장된 파라미터를 업데이트하는 것이 가능하다.The parameter update unit 160 compares the output of the transform unit 120, that is, the measurement data of the Laplace-Fourier region and the output of the modeling data generation unit 130, that is, the modeling data of the Laplace-Fourier region, and the parameter storage unit 150 Update the parameters stored in ). At this time, the parameter update unit 160

And modeling data

It is possible to update the previously stored parameters in a direction that can minimize the difference between them.

와 모델링 데이터

간 차이를 계산하여 기 저장된 파라미터를 업데이트한다. According to an embodiment of the present invention, the parameter update unit 160 performs measurement data for each frequency.

And modeling data

The previously stored parameters are updated by calculating the difference between them.

와 변환부(120)에서 얻어진

를 비교하여 그 차이가 최소화되도록 파라미터 저장부(150)에 저장된 파라미터를 갱신하게 되는데, 이를 위해

와

간의 차이를 나타내는 목적 함수 E를 정의하고 목적 함수 E의 그래디언트를 이용하여 목적 함수 E를 감소시키는 방법으로 파라미터를 업데이트하는 것이 가능하다.That is, the parameter update unit 160 is obtained by the modeling data generation unit 130

And obtained in the conversion unit 120

The parameter stored in the parameter storage unit 150 is updated so that the difference is minimized.

Wow

It is possible to update the parameters by defining an objective function E representing the difference between and reducing the objective function E using the gradient of the objective function E.

는 가상 음원의 전치 행렬이고, S는 임피던스 행렬을 나타낸다. In <Equation 3>

Is the transposition matrix of the virtual sound source, and S is the impedance matrix.

Here, updating the parameter while minimizing the objective function E may be performed through a steepest descent method.

In this way, modeling data that minimizes the objective function E can be obtained by repeatedly adding the scaled update increments in the maximum slope direction starting from the initial parameters.

Since the parameters reflected in the modeling data minimizing the objective function E can be viewed as the same as the characteristics of the measurement target area through the update, the image data generator 170 uses the finally updated parameter to determine the image data for the measurement target area. Can be created.

7 is a flowchart illustrating a Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets according to an embodiment of the present invention.

The Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets according to an exemplary embodiment of the present invention may be implemented in the above-described subsurface imaging apparatus or a recording medium executable in the corresponding imaging apparatus.

In FIG. 7, step S210 is a step of receiving measurement data from an area to be measured. The measurement data may be data of seismic waves reflected from an area to be measured.

The measurement data is converted into data of the Laplace-Fourier domain through step S220.

According to an embodiment of the present invention, step S220 may perform Laplace-Fourier transform using multiple attenuation coefficients for multiple offsets.

In detail, step S221 divides the offset of the acoustic wave trace (common sound source collection data) into a predetermined number of sub-offsets, as shown in FIG. 4, and the depth and offset in which the traces belonging to the sub-offset contribute to imaging. The attenuation rate according to is calculated to determine the attenuation coefficient for each sub-offset.

)을 이용한 라플라스 푸리에 변환일 수 있다. 여기서, 감쇄 계수들의 크기는

일 수 있다. Next, in step S223, a Laplace-Fourier transform may be performed as shown in Equation 1 using each of the calculated n attenuation coefficients. That is, as shown in Fig. 6, the measurement data as shown in (a) is converted into attenuation coefficients for each sub-offset as shown in (b).

It may be a Laplace Fourier transform using ). Here, the magnitude of the attenuation coefficients is

Can be

Meanwhile, step S230 is a step of modeling an area to be measured. For example, step S230 may be a process of setting a matrix equation using a parameter representing the characteristics of the measurement target area, and calculating the equation to generate modeling data, and for this purpose, initial parameters for the measurement target area are separately input. May include a process.

In an embodiment of the present invention, in step S230, modeling data may be generated for each attenuation coefficient.

를 구할 수 있다. Specifically, in step S231, the wave equation in which the parameter representing the characteristics of the measurement target area is reflected can be expressed as a matrix equation using the finite element method or the finite difference method.

Can be obtained.

In step S233, each of the n attenuation coefficients calculated by the attenuation coefficient calculating unit 121 may be used to perform a Laplace-Fourier transform as shown in Equation 2 above.

와 모델링 데이터

간 차이를 계산하여 기 저장된 파라미터를 업데이트한다. Subsequently, an objective function reflecting the difference between the measurement data and the modeling data in the Laplace-Fourier region is generated through step S240. According to an embodiment of the present invention, measurement data for each frequency

And modeling data

The previously stored parameters are updated by calculating the difference between them.

Next, through steps S250 and S260, the initially set parameters are repeatedly updated in the direction of minimizing the objective function. The repetition of the update may be continued until the objective function falls below the threshold value by comparing the threshold value with the objective function regenerated using the updated parameter after setting a threshold value in advance.

For example, it is possible to compare the objective function and the threshold value in step S250 and terminate when the objective function is less than or equal to the threshold value, and otherwise update the parameter for generating modeling data in step S260. In this case, the parameter update may be performed in the direction of reducing the objective function.

Although the embodiments of the present invention have been described above, the present invention is not limited to the specific embodiments described above. That is, a person of ordinary skill in the technical field to which the present invention pertains can make a number of changes and modifications to the present invention without departing from the spirit and scope of the appended claims, and all such appropriate changes and modifications It should be considered that equivalents are also within the scope of the present invention.

Claims (6)

An input unit for receiving an acoustic wave signal of a measurement target area as measurement data;
An attenuation coefficient calculating unit that divides the offsets of the acoustic wave signal from the measured data into a predetermined number and calculates an attenuation coefficient for each sub-offset;
A Laplace calculation unit that converts measurement data in a time domain into measurement data in a Laplace-Fourier domain by using attenuation coefficients for each sub-offset;
A modeling data generator configured to receive a parameter representing a characteristic of a measurement target region, set an equation including the parameter, and calculate modeling data by calculating an equation in a Laplace-Fourier region using attenuation coefficients for each sub-offset; And
A parameter update unit for updating a parameter by comparing measurement data and modeling data of the Laplace-Fourier region for each sub-offset;
Laplace Fourier domain complete waveform inversion device using multiple attenuation and multiple offsets comprising a. The method of claim 1, wherein the attenuation coefficient calculation unit
Laplace Fourier domain complete waveform inversion using multiple attenuation and multiple offsets, characterized in that the attenuation coefficient for each sub-offset is determined by calculating the sub-offset and the sub-offset that each of the traces belonging to a plurality of sub-offsets contribute to imaging Device. The method of claim 1,
The parameter update unit generates an objective function representing the difference between the measurement data in the Laplace-Fourier region for each frequency and the modeling data, and updates the parameter in a direction of decreasing the objective function.The Laplace Fourier region using multiple attenuation and multiple offsets Full waveform inversion device. Receiving an acoustic wave signal of an area to be measured as measurement data;
Dividing the offset of the acoustic wave signal from the measured data into a predetermined number and calculating attenuation coefficients for each sub-offset;
Converting the measurement data in the time domain into measurement data in the Laplace-Fourier domain by using attenuation coefficients for each sub-offset;
Receiving a parameter representing a characteristic of a measurement target area, setting an equation including the parameter, and calculating modeling data by calculating an equation in a Laplace-Fourier area using attenuation coefficients for each sub-offset; And
Updating a parameter by comparing measurement data of a Laplace-Fourier region for each sub-offset and modeling data;
Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets, comprising a. The method of claim 4, wherein calculating the attenuation coefficient
Laplace Fourier domain complete waveform inversion using multiple attenuation and multiple offsets, characterized in that the attenuation coefficient for each sub-offset is determined by calculating the sub-offset and the sub-offset that each of the traces belonging to a plurality of sub-offsets contribute to imaging Way. The method of claim 4, wherein updating the parameter
Generating an objective function representing the difference between the measurement data in the Laplace-Fourier domain for each frequency and the modeling data,
Laplace Fourier domain complete waveform inversion method using multiple attenuation and multiple offsets, comprising the step of updating a parameter in a direction of decreasing the objective function.

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