KR101111685B1 - Apparatus and Method for imaging a subsurface using accumulated energy of wavefield - Google Patents

Abstract

An apparatus for imaging a subterranean structure of a region to be measured, the apparatus comprising: an observation wave field acquisition unit obtaining an observed wavefield based on elastic wave data of a region to be measured, and a parameter storing characteristic parameters of the region to be measured A model wave field generator for generating a modeled wavefield corresponding to the observed wave field by using characteristic parameters stored in the storage unit and the parameter storage unit, and accumulate with time for each observed wave field and the model wave field. An energy calculator for calculating the accumulated energy defined as the energy to be calculated, and a parameter for updating the characteristic parameter stored in the parameter storage unit so that a difference between the accumulated energy of the calculated observation wave field and the accumulated energy of the calculated model wave field is reduced. An apparatus including an update unit is provided.

Description

Apparatus and Method for imaging a subsurface using accumulated energy of wavefield

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to underground structure exploration techniques, and more particularly to techniques for imaging underground structures through signal processing using waveform inversion.

Waveform inversion refers to a technique for estimating the underground velocity model using prestack seismic data.

Waveform inversion refers to a series of processes that create an initial model for a region of interest, obtain measurements from that region, and then repeatedly update the initial model using the measurements obtained to obtain an underground model similar to the actual underground structure. can see. This process computes the theoretical values from any underground structure by computer (modeling) and iteratively repeats the parameters representing the underground properties until the error is minimized from the error between the theoretical value and the data obtained through the field survey. The calculation takes place while updating.

Waveform inversion is a method of underground structure analysis, which is one of the goals of geophysical exploration, and many methods are mathematically operated. A representative example is the iterative least square method. Recently, a simple inversion is solved by a personal computer due to the development of a computer, and since there is usually no unique solution, an optimal solution is obtained by adding certain conditions. It is optional to focus on convergence or to obtain a more precise solution from a given measurement. The inversion model not only simplifies, but often requires extreme assumptions, so that inversion, the geological preliminary information on the physical properties of the planet is maximized.

The most important of the geophysical properties to image accurate underground structures is the velocity of seismic waves in underground media. Recently, in order to obtain this, an artificial wave is generated in a certain region to be measured and seismic waves are measured to obtain seismic velocity of underground medium by performing waveform inversion in time domain or frequency domain on measured seismic data. Many are being performed.

An underground imaging apparatus and method are provided that can efficiently utilize the low frequency components of field data to obtain velocity models similar to real underground structures.

In the underground structure imaging apparatus according to an aspect of the present invention, an observation wave field acquisition unit obtaining an observed wavefield based on an acoustic wave data of an area to be measured, and a parameter storage to store characteristic parameters of the area to be measured. The model wave field generator generates a modeled wavefield corresponding to the observed wave field using the characteristic parameters stored in the parameter storage unit, and accumulates with time for each observed wave field and the model wave field. An energy calculation unit for calculating the accumulated energy defined as energy, and a parameter update for updating the characteristic parameters stored in the parameter storage unit so that the difference between the accumulated energy of the calculated observation wave field and the accumulated energy of the calculated model wave field is reduced. It may include wealth.

In the underground structure imaging method according to an aspect of the present invention, obtaining an observed wavefield based on elastic wave data of a measurement target region, setting a characteristic parameter of the measurement target region, and using the set characteristic parameter Generating a modeled wavefield corresponding to the observed wave field, calculating an accumulated energy defined as energy accumulated over time for each observed wave field and the model wave field, And updating the characteristic parameter set to reduce the difference between the calculated energy of the observed wave field and the calculated energy of the model wave field.

According to the disclosed contents, the observed wave field and the modeled wave field are converted into energy forms to perform waveform inversion, so that low frequency components lacking in the field data can be efficiently used, and thus obtaining a velocity model similar to the actual structure is obtained. It is possible.

According to the disclosed contents, the observed wave field and the modeled wave field are converted into energy forms to perform waveform inversion, so that low frequency components lacking in the field data can be efficiently used, and thus obtaining a velocity model similar to the actual structure is obtained. It is possible.

Hereinafter, specific examples for carrying out the present invention will be described in detail with reference to the accompanying drawings.

1 illustrates a schematic configuration of an underground imaging apparatus according to an embodiment of the present invention.

Referring to FIG. 1, the underground structure imaging apparatus may include a transmission source 102, a receiver 103, and a signal processing device 104 installed in a measurement target area 101. The transmission source 102 generates sound waves or vibration waves. The generated sound or vibration waves are transmitted to the measurement target area 101. The receiver 103 measures the sound wave or vibration wave generated from the transmission source 102 at each point of the measurement target area 101. The characteristics of the acoustic wave or the vibration wave measured by each receiver 103 may vary depending on the underground structure of the region to be measured 101. The signal processing apparatus 104 generates the image data for the measurement target area 101 by processing the sound wave or vibration wave measured by the receiver 103.

In order to generate image data, the signal processing apparatus 104 may generate a velocity model for the measurement target area 101. The velocity model may represent a velocity distribution of elastic waves with respect to the measurement target region 101. For example, the velocity of the seismic wave within the region to be measured varies depending on the characteristics (eg, the type or density of the medium) of each point within the region to be measured 101, and thus represents the velocity distribution of the velocity of the seismic wave. By obtaining the model, it is possible to easily image the underground structure of the measurement target area 101 from the obtained velocity model.

In addition, the signal processing apparatus 104 may generate a velocity model through waveform inversion. Waveform inversion is obtained by creating an initial model for a region of interest, obtaining measurements from the same region of interest, and then repeatedly updating an initial model made using the obtained measurements to obtain a model with characteristics that are similar to those of the region of interest. It means a series of processes. For example, the signal processing apparatus 104 sets a velocity model of the measurement target region 101, obtains seismic data from the measurement target region 101, and then sets the obtained velocity data. By repeatedly updating the velocity model, it is possible to obtain a velocity model that is similar to the velocity distribution of the actual acoustic wave in the region to be measured 101.

Figure 2 illustrates the principle of waveform inversion in accordance with an embodiment of the present invention.

Referring to FIG. 2, the area to be measured 201 has some characteristic V. FIG. This characteristic V may be various characteristics such as velocity, density, or temperature of the acoustic wave for each part of the region to be measured 201. If any input S is applied to the area to be measured 201, output d can be observed according to its characteristic V. At this time, the output d depends on the input S and the characteristic V. For example, even if the same input S is given, if the characteristic V of the measurement target area 201 is different, the output d may also be different. Since the underground structure can be easily understood by knowing the velocity distribution of the elastic waves among the various characteristics of the region to be measured 201, it is assumed in the present embodiment that the characteristic V is the velocity of the elastic waves for each part of the region to be measured 201. .

In FIG. 2, if the characteristic V is the velocity characteristic of the region to be measured 201, the region to be measured 201 may be modeled using a parameter m related to the velocity. Since the parameter m relating to the speed is updated repeatedly afterwards, all of them may be initially set to have a uniform speed distribution. When the velocity parameter m is set, the output u when the virtual input S is applied to the modeled measurement target region 202 can be obtained. That is, the output u corresponds to the output d. If the speed parameter m is set equal to the actual characteristic V, the output u will have the same value as the output d. Conversely, by adjusting the speed parameter m such that the output u is equal to the output d, it is possible to obtain a parameter m equal to the actual characteristic V.

Through such waveform inversion, the underground imaging apparatus according to the present embodiment obtains the measurement data d and the modeling data u, and adjusts the velocity parameter m so that the difference between the measurement data d and the modeling data u is minimized. After estimating the characteristic V for the region, the velocity model and the image data may be generated using the obtained velocity parameter m (or the estimated characteristic V).

3 illustrates a detailed configuration of an underground imaging apparatus according to an embodiment of the present invention. This may be an example of some configuration of the signal processing device 104 of FIG.

Referring to FIG. 3, the underground structure imaging apparatus 300 includes an observation wave field acquisition unit 301, a parameter storage unit 302, a model wave field generation unit 303, an energy calculation unit 304, and a parameter updating unit ( 305, and a velocity model generator 306.

The observation wave field acquisition unit 301 obtains an observed wavefield from the measurement target area. The observed wave field can be the seismic data measured at the region to be measured. According to the present embodiment, the observation wave field will be referred to as d.

The parameter storage unit 302 stores characteristic parameters related to the measurement target area. For example, the parameter storage unit 302 may store a velocity parameter indicating the velocity of the acoustic wave for each point in the measurement target area. The initial value of the characteristic parameter stored in the parameter storage unit 302 may be set by the user and then updated by the parameter update unit 305. According to the present embodiment, the speed parameter stored and updated in the parameter storage unit 302 will be referred to as m.

The model wave field generator 303 generates a modeled wavefield corresponding to the observation wave field by using the characteristic parameter stored in the parameter storage unit 302. According to this embodiment, the model wave field will be referred to as u. The method of generating the model wave field is described in more detail as follows.

Fourier transforming the wave equation in the time domain for a region to be measured leads to the wave equation in the frequency domain:

는 각 주파수를,

는 이산화된 파동장을, M은 질량행렬을, C는 점성감쇠행렬을, K는 강성행렬을,

는 주파수 영역에서의 송신파형을 나타낸다. 그리고 수학식 1을 간단히 표현하면 다음과 같다.In Equation 1,

Each frequency,

Is the discretized wave field, M is the mass matrix, C is the viscous decay matrix, K is the stiffness matrix,

Denotes a transmission waveform in the frequency domain. Equation 1 is simply expressed as follows.

In Equation 2, S denotes a complex impedance matrix, and this value reflects characteristic parameters, for example, velocity parameters, related to the measurement target area. In other words, the model wave field generator 303 obtains the complex impedance matrix S using the velocity parameter m stored in the parameter storage unit 302 and calculates the model wave length u according to the obtained complex impedance matrix S and the transmission waveform f. It is possible to define.

When the observation wave field d and the model wave field u are obtained, the energy calculation unit 304 accumulates the accumulated energy defined as energy accumulated over time for each observation wave field d and the model wave field u in the time domain. Calculate For example, the energy calculation unit 304 may calculate the stored energy based on the integral of the absolute value of each observed wave length d and the model wave length u times p times. . As an example, the accumulated energy of the model wave field u can be calculated as follows.

는 모델 파동장 u에 절대값을 취하고, 여기에 p번 거듭제곱한 값을 τ_min부터 τ_max까지 적분한 값으로 주어짐을 알 수 있다. 적분 구간은 관측 파동장과 모델 파동장에 적용한 시간 윈도우(time-window)로 나타낼 수 있다. 예를 들어, 시간 윈도우의 크기는 τ_min부터 τ_max까지가 될 수 있으며, 그 시간 윈도우의 크기는 다양하게 설정될 수 있다. In Equation 3, the accumulated energy of the model wave field u

Is taken as the absolute value of the model wave field u, and is given as the integral of τ _min to τ _max . The integration period may be represented by a time-window applied to the observation wave field and the model wave field. For example, the size of the time window may be from τ _min to τ _max , and the size of the time window may be variously set.

As such, when the energy calculator 304 converts the observation wave field d and the model wave field u into energy forms, a low frequency component may be used in the waveform inversion, thereby providing more accurate velocity model and image data. It is possible to get For example, referring to FIGS. 6A and 6B, FIG. 6A shows the observation wave field and FIG. 6B shows the energy of the observation wave field. Looking at the data from 0 to 2 seconds, there is almost no low frequency component of less than 5Hz in the original data of Figure 6a, while in contrast to the low-frequency component of 5Hz or less in Figure 6b of the data converted to energy form Able to know.

와 모델 파동장 u의 축적 에너지

가 계산되면, 파라미터 갱신부(305)는 계산된 관측 파동장의 축적 에너지

와 계산된 모델 파동장의 축적 에너지

간의 차이가 줄어들도록 파라미터 저장부(302)에 저장된 특성 파라미터를 갱신한다. 예를 들어, 파라미터 갱신부(305)는 관측 파동장의 축적 에너지

와 모델 파동장의 축적 에너지

간의 차이를 나타내는 목적 함수(objective function)를 정의하고, 정의된 목적 함수의 구배(gradient)를 이용하여 파라미터 저장부(303)에 저장된 특성 파라미터를 갱신하는 것이 가능하다. 그리고, 일 실시예에 따라, 목적 함수는 관측 파동장의 축적 에너지

및 모델 파동장의 축적 에너지

를 이용하여 정의되는 것이 가능하다. 이를 구체적인 수식을 통해 살펴보기 위해 먼저 본 실시예에 따른 축적 에너지를 푸리에 변환 형태로 다시 나타내면 다음과 같다.3 again, the accumulated energy of the observed wave field d

Accumulated energy of model wave field u with

Is calculated, the parameter updating unit 305 calculates the stored energy of the observed wave field

And calculated energy of model wave field

The characteristic parameter stored in the parameter storage unit 302 is updated to reduce the difference therebetween. For example, the parameter update unit 305 stores the accumulated energy of the observation wave field.

And energy accumulation of the model wave field

It is possible to define an objective function representing the difference between and update the characteristic parameter stored in the parameter storage unit 303 by using a gradient of the defined objective function. And, according to one embodiment, the objective function is the accumulated energy of the observed wave field

And energy of model wave field

It is possible to be defined using. In order to examine this through a specific equation, first, the accumulated energy according to the present embodiment is represented as a Fourier transform form as follows.

In Equation 4, m represents a characteristic parameter and t _max represents a maximum recording time. If time integration is performed on the first and zero frequency components of the measurement wave field (that is, τ ₀ = 0 and ω = 0), Equation 4 may be expressed as follows.

와 모델 파동장의 축적 에너지

간의 차이를 최소화하도록 다음과 같이 정의될 수 있다.Referring to Equations 3, 4, and 5, it can be seen that the accumulated energy of the model wave field u is taken as an absolute value of the model wave field u, and is equal to the zero frequency component of the value raised to p times. On the other hand, the objective function is the accumulated energy of the observed wave field

And energy accumulation of the model wave field

To minimize the difference between

In Equation 6, j represents a sample of each zero frequency component, and each sample may be obtained by adjusting the magnitude of the time-window or the τ value. In Equation 6, the characteristic parameter m in the direction in which the objective function is reduced can be updated as follows.

는 랑그랑지 승수 및 정규화 정도를,

는 목적 함수의 구배(gradient)를 나타낸다. 그리고 수학식 7에서, 목적 함수의 구배는 최대 경사 방향을 통해 다음과 같이 계산될 수 있다.In equation (7), m ^{l +1} represents the updated characteristic parameter. H _a is approximated Hessian, J is Jacobian,

The Langer's multiplier and normalization degree,

Denotes the gradient of the objective function. And in Equation 7, the gradient of the objective function can be calculated as follows through the maximum slope direction.

In addition, in Equation 8, the partial differential value for the characteristic parameter of the accumulated energy of the model wave field can be approximated according to the finite differential method using Jacobian as follows.

In FIG. 3, when the parameter updater 305 updates the feature parameter as shown in Equations 4 to 9, the updated feature parameter is stored in the parameter storage unit 302 and the model wave field generator 303 updates the updated feature parameter. This process can be repeated until the model is newly modeled using the parameter and the objective function is smaller than the specified threshold.

Meanwhile, according to another embodiment of the present invention, the objective function may be defined using a value obtained by taking a log of the accumulated energy of the observed wave field and the accumulated energy of the model wave field. For example, the objective function may be defined as follows.

In addition, when an objective function is defined using a log as shown in Equation 10, a maximum descent direction for updating a characteristic parameter may be given as follows.

In FIG. 3, if the update of the characteristic parameter is repeated until the objective function is smaller than the predetermined threshold value, the speed model generator 306 generates a speed model for the measurement target area by using the finally updated characteristic parameter. . The velocity model generated by the velocity model generator 306 may be an initial velocity model for generating image data. As described above, since the modeling and the objective function according to the present embodiment are based on accumulated energy and low frequency components, more accurate underground structure images can be obtained by generating image data regarding the underground structure using this initial velocity model.

4 illustrates an underground imaging method according to an embodiment of the present invention.

1, 3 and 4, the underground structure imaging method according to the present embodiment will be described.

First, an observation wave field of a region to be measured is obtained (401). For example, it is possible for the observation wave field acquisition unit 301 to receive the acoustic wave data from the receiver 103 installed in the plurality of measurement target regions 101 and to obtain the observation wave field d.

Then, the characteristic parameter about the measurement target area is set (402). For example, the initial value of the speed parameter may be stored in the parameter storage unit 302.

In operation 403, a model wave field corresponding to the observation wave field is generated using the set characteristic parameter. For example, the model wave field generation unit 303 can generate the model wave field u as shown in equations (1) and (2).

와 모델 파동장의 축적 에너지

를 계산하는 것이 가능하다.The stored energy is calculated for each of the observed wave length d and the model wave field u. For example, the energy calculation unit 304 stores the stored energy of the observation wave field as in Equation 3 below.

And energy accumulation of the model wave field

It is possible to calculate.

Then, the characteristic parameter is updated to minimize the difference in each wave field converted into the form of accumulated energy (405). For example, the parameter update unit 305 can update the characteristic parameter as shown in equations (4) to (11).

When the characteristic parameter is finally updated, a speed model for the measurement target area is generated using the updated characteristic parameter (406). For example, it is possible for the speed model generator 306 to generate a speed model using the last parameter stored in the parameter storage 302.

5 illustrates a characteristic parameter updating method according to an embodiment of the present invention.

과 모델 파동장의 축적 에너지

간의 차이가 줄어드는 방향으로 특성 파라미터를 갱신하기 위하여, 먼저 각각의 축적 에너지를 이용하여 목적 함수를 정의한다(501). 예컨대, 파라미터 갱신부(305)가, 수학식 6 또는 10과 같이, 목적 함수를 정의할 수 있다.Referring to FIG. 5, the accumulated energy of the observed wave field

And energy accumulation of the model wave field

In order to update the characteristic parameter in a direction in which the difference between them is reduced, first, an objective function is defined using each accumulated energy (501). For example, the parameter updater 305 may define an objective function as in Equation 6 or 10.

Once the objective function is defined, it is determined 502 whether the difference in the objective function or each of the stored energies is less than or equal to a predetermined threshold. If the objective function does not fall within a predetermined threshold range, a gradient of the objective function is calculated (503) in order to update the characteristic parameter in the decreasing direction of the objective function. For example, the parameter updater 305 may calculate a gradient of the objective function, as shown in Equations 8, 9, and 11.

Once the gradient of the objective function is calculated, the characteristic parameter is updated using the calculated gradient (504). For example, the parameter updating unit can update the characteristic parameter as in Equation (7).

When the characteristic parameter is updated, the model wave field u is regenerated using the updated characteristic parameter (505), and the above process is repeated until the objective function falls within the threshold range. Then, if the objective function is smaller than the threshold, a velocity model is generated using the last updated characteristic parameter (506).

As described above, according to the disclosed apparatus and method, since waveform inversion is performed after converting the wave field into the form of energy accumulated over time, it is possible to efficiently use low frequency components to obtain more accurate underground structure images. It is possible.

Meanwhile, the embodiments of the present invention can be embodied as computer readable codes on a computer readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored.

Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, floppy disks, optical data storage devices, and the like, which may also be implemented in the form of carrier waves (for example, transmission over the Internet). Include. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. In addition, functional programs, codes, and code segments for implementing the present invention can be easily deduced by programmers skilled in the art to which the present invention belongs.

Furthermore, the above-described embodiments are intended to illustrate the present invention by way of example and the scope of the present invention will not be limited to the specific embodiments.

Claims (18)

In the device for imaging the underground structure of the measurement target area,
An observation wave field acquisition unit for obtaining an observed wavefield based on the seismic data of the measurement target area;
A parameter storage unit for storing characteristic parameters relating to a measurement target area;
A model wave field generator for generating a modeled wavefield corresponding to the observation wave field using the characteristic parameter stored in the parameter storage unit;
An energy calculation unit that calculates an accumulated energy defined as energy accumulated over time for each observation wave model and a model wave field; And
A parameter updating unit for updating the characteristic parameter stored in the parameter storage unit such that a difference between the calculated energy of the observed wave field and the calculated energy of the model wave field is reduced; Device comprising a.
The method of claim 1, wherein the energy calculation unit
And an apparatus for calculating the accumulated energy based on a time-integrated value of each of the observed wave field and the absolute power of the model wave field.
The method of claim 1, wherein the parameter update unit
Define an objective function representing the difference between the accumulated energy of the observed wave field and the accumulated energy of the model wave field over various time-windows, and update the characteristic parameter using a gradient of the defined objective function. Device.
The method of claim 3, wherein the parameter update unit
And define the objective function using the accumulated energy of the observed wave field and the accumulated energy of the model wave field.
The method of claim 3, wherein the parameter update unit
And a logarithm of the accumulated energy of the observed wave field and the accumulated energy of the model wave field.
The method of claim 3, wherein the parameter update unit
And calculate the gradient using Jacobian for the characteristic parameter of the accumulated energy of the model wave field.
The method of claim 6, wherein the parameter update unit
And approximating Jacobian for a characteristic parameter of accumulated energy of the model wave field by a finite difference method.
The method of claim 1 wherein the characteristic parameter is
And a velocity of the acoustic wave with respect to the area to be measured.
The method of claim 1,
A speed model generator for generating a speed model of the measurement target area by using the updated characteristic parameter; Device further comprising.
In the method for imaging the underground structure of the area to be measured,
Obtaining an observed wavefield based on the seismic data about the region to be measured;
Setting a characteristic parameter for the measurement target area and generating a modeled wavefield corresponding to the observation wave field using the set characteristic parameter;
Calculating an accumulated energy defined as energy accumulated over time for each observation wave field and model wave field; And
Updating the characteristic parameter set to reduce a difference between the calculated energy of the observed wave field and the calculated energy of the model wave field; How to include.
The method of claim 10, wherein calculating the accumulated energy
And calculating the accumulated energy based on a time-integrated value of the absolute power of each of the observed wave field and the model wave field.
The method of claim 10, wherein updating the characteristic parameter is
Define an objective function representing the difference between the accumulated energy of the observed wave field and the accumulated energy of the model wave field over various time-windows, and update the characteristic parameter using a gradient of the defined objective function. How to include.
The method of claim 12, wherein updating the characteristic parameter is
And defining the objective function using the accumulated energy of the observed wave field and the accumulated energy of the model wave field.
The method of claim 12, wherein updating the characteristic parameter is
And defining the objective function using a logarithm of the accumulated energy of the observed wave field and the accumulated energy of the model wave field.
The method of claim 12, wherein updating the characteristic parameter is
Calculating the gradient using Jacobian for the characteristic parameter of the accumulated energy of the model wave field.
The method of claim 15, wherein updating the characteristic parameter is
And approximating the Jacobian for the characteristic parameter of the accumulated energy of the model wave field by a finite difference method.
11. The method of claim 10 wherein the characteristic parameter is
And a velocity of the acoustic wave relative to the area to be measured.
The method of claim 10,
Generating a speed model of the area to be measured using the updated characteristic parameter; How to include more.

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