KR101938724B1 - Seismic imaging of water column structure apparatus and method using frequency-domain reverse-time migration with analytic Green's function - Google Patents

Abstract

Disclosed are a medullary layer imaging device and method using an analytical green function and frequency-domain inverse time structure correction. When frequency-domain inverse time structure correction is applied to medullary layer imaging, a high-resolution medullary layer image including a high frequency component is efficiently obtained by replacing a numerical solution of a wave equation which requires a significant amount of calculation with a solution of the analytical green function. The present invention improves calculation efficiency of a computer for constructing the medullary layer image, and can construct the high-resolution medullary layer image including the high frequency component from seismic survey data obtained in the sea. An obtained high-resolution seismic medullary layer image can find distribution of properties (water temperature, salinity, etc.) of a continuous medullary layer in a survey area. The present invention performs marine physical research of confirming how different property ocean currents are mixed and to which level large-scale ocean current circulation is generated.

Description

[0001] The present invention relates to a water-based imaging apparatus and method using an analytic green function and a frequency-domain inverse time structure correction,

Field of the Invention The present invention relates to a water-based imaging apparatus and method using analytical Green's function and frequency-domain inverse time structure correction, and more particularly to a numerical solution of a wave equation requiring a large amount of computation in frequency- To a solution of an analytic Green function.

Two-way wave-equation based reverse-time migration using two-way wave equations requires much more computational resources than uni-directional structure correction. In addition to being able to process reflections, reflections, reflections, multiple reflections and multiple refraction waves, it is possible to visualize the underground structure without substantially limiting the underground structure's slope, And is now widely used due to the rapid development of computing technology. Conventionally, the frequency-domain inverse temporal correction method has been developed with a view to image acquisition of a complex underground medium, and thus a complex impedance matrix has to be solved for a heterogeneous medium. At this time, a multi-frontal direct solver has been used in consideration of the complexity of the complex impedance matrix and the multi-shot simulation of seismic exploration. By performing a single complex impedance matrix factorization with a direct solver, the computation of the modeling wave field required to obtain the inverse time structure correction and the backward propagation of the observed data are respectively forward / backward substituted Can be calculated efficiently. However, when constructing the complex impedance matrix using the finite element method, the acoustic wave modeling has a problem of calculation error, especially dispersion of errors and pollution according to the number of lattices per wavelength. For example, to solve the problem of the maximum frequency of 128 Hz, the grid size should be as small as 0.71 m. However, the three-dimensional waveform propagation modeling is required for 100 km (distance) x 2 ~ 3 km (depth) Calculations are difficult to implement in today's computing environments due to the speed and memory limitations of the cpu in the frequency-domain.

Korean Patent Laid-Open Publication No. 2013-0105493 (Seoul National University, Industry & University Collaboration) 2013. 9. 25. Patent Document 1 discloses an elastic wave imaging system using an inverse time structure correction algorithm. In Patent Document 1, Discloses a technique of rear propagating a ratio of a modeling wave field and convoluting backward propagated measurement data with a calculated virtual transmission source.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method and an apparatus for solving a problem in which a numerical solution of a wave equation requiring a large amount of calculation is replaced with a solution of an analytical Green function, Resolution inverse temporal structure correction to obtain a high-resolution water-layer image including the high-resolution water-

According to another aspect of the present invention, there is provided a water-based imaging apparatus using an analytic Green function and frequency-domain inverse time structure correction, the method comprising the steps of: A transmission source estimating unit estimating a transmission source; A transmission source deconvolution unit for deconvoluting observation data using the transmission source estimated by the transmission source estimation unit; And a structure corrector receiving the deconvoluted observation data information from the transmission source deconvolution unit and processing the frequency-domain inverse time structure correction using an analytic green function.

과 같이 수신기들로부터 측정된 관측 데이터와 송신원 위치

에서 수신기 위치

으로 전파하는 해석적 그린함수를 사용하여 송신원을 추정할 수 있다.The transmission source estimating unit

The measured data from the receivers and the source location

Receiver position in

The transmission source can be estimated using the analytical green function that propagates to the receiver.

과 같이 추정된 송신원을 이용해 수신기들로부터 측정된 관측 데이터를 디컨볼루션할 수 있다.The transmission source deconvolution unit

Lt; RTI ID = 0.0 > the < / RTI > receiver using the estimated source as shown in FIG.

Wherein the structure correcting unit comprises: a virtual sound source estimating unit for estimating a virtual sound source using an analytic Green function; A rear propagating unit for backward propagating the deconvoluted observation data using an analytic green function; And a post-processing unit for acquiring a water layer image using a result of backward propagation of the virtual sound source estimated through the virtual sound source estimation unit and the observation data deconvoluted through the rear propagation unit.

과 같이 송신원 위치

에서 산란 지점(scattering point)

으로 전파하는 해석적 그린 함수를 사용하여 가상음원을 추정할 수 있다.The virtual sound source estimating unit

The transmission source position

Scattering point < RTI ID = 0.0 >

The virtual sound source can be estimated using the analytical green function that propagates to the sound source.

와 같이 수신기 위치

에서 산란 지점

으로 전파하는 해석적 그린 함수를 사용하여 상기 송신원 디컨볼루션부에서 디컨볼루션된 관측 데이터를 후방 전파 처리할 수 있다.The rear-

Receiver position

Scattering point

The deconvoluted observation data in the transmission source deconvolution unit can be back propagated.

와 같이 상기 가상음원 추정부에서 추정된 가상음원과 상기 후방 전파부에서 디컨볼루션된 관측 데이터를 후방 전파 처리한 결과를 이용하여 수층 이미지를 획득할 수 있다.The post-

A water layer image can be acquired using the result of back propagation processing of the virtual sound source estimated by the virtual sound source estimating unit and the observation data deconvoluted at the rear propagating unit as shown in FIG.

According to another aspect of the present invention, there is provided a method of imaging a water layer using an analytic Green function and a frequency-domain inverse time structure correction, the method comprising the steps of: Estimating a transmission source; Deconvoluting observation data using an estimated transmission source; And processing the frequency-domain inverse time structure correction using the analytic green function by receiving the deconvoluted observation data information.

과 같이 수신기들로부터 측정된 관측 데이터와 송신원 위치

에서 수신기 위치

으로 전파하는 해석적 그린함수를 사용하여 송신원을 추정하는 것으로 이루어질 수 있다.The source estimating step

The measured data from the receivers and the source location

Receiver position in

And estimating the transmission source using an analytic Green function propagating to the receiver.

과 같이 추정된 송신원을 이용해 수신기들로부터 측정된 관측 데이터를 디컨볼루션하는 것으로 이루어질 수 있다.The deconvolution step

And deconvoluting the observed data measured from the receivers using the estimated transmission source as shown in FIG.

Wherein the structure correcting step comprises: estimating a virtual sound source using an analytic Green function; Backward propagating the deconvoluted observation data using an analytic Green function; And acquiring a water-layer image using a result of backward propagation of the observational data with the estimated virtual sound source and deconvolution.

과 같이 송신원 위치

에서 산란 지점(scattering point)

으로 전파하는 해석적 그린 함수를 사용하여 가상음원을 추정하는 것으로 이루어질 수 있다.The virtual sound source estimating step

The transmission source position

Scattering point < RTI ID = 0.0 >

And then estimating the virtual sound source using the analytic green function propagating to the virtual sound source.

와 같이 수신기 위치

에서 산란 지점

으로 전파하는 해석적 그린 함수를 사용하여 상기 송신원 디컨볼루션부에서 디컨볼루션된 관측 데이터를 후방 전파 처리할 수 있다.The back propagation step

Receiver position

Scattering point

The deconvoluted observation data in the transmission source deconvolution unit can be back propagated.

와 같이 추정된 가상음원과 디컨볼루션된 관측 데이터를 후방 전파 처리한 결과를 이용하여 수층 이미지를 획득하는 것으로 이루어질 수 있다.The water layer image acquiring step

And acquiring the water layer image using the result of back propagation processing of the estimated virtual sound source and the deconvoluted observation data as shown in FIG.

The water-based imaging apparatus and method using the analytical Green's function and the frequency-domain inverse time structure correction according to the present invention provide a numerical solution of the wave equation requiring a considerable amount of computation in the conventional frequency-domain inverse time structure correction algorithm Wave propagation modeling and the reverse propagation part of the observed data by solving the analytical green function to improve computation efficiency of the computer for the construction of the water layer image and to obtain the high resolution water layer image including the high frequency component at the sea, It can be constructed from data.

The obtained high-resolution seismic water-layer images can reveal the distribution of physical properties (water temperature, salinity, etc.) of successive water bodies in the exploration area. Furthermore, it is possible to find out how the different material currents are mixed, Of the ocean surface, and to determine whether it occurs up to the ocean.

1 is a block diagram for explaining a water layer imaging apparatus using an analytic Green function and a frequency-domain inverse time structure correction according to a preferred embodiment of the present invention.
FIG. 2 is a flowchart illustrating a water layer imaging method using an analytic Green function and frequency-domain inverse time structure correction according to a preferred embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the present embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.

First, referring to FIG. 1, a water layer imaging apparatus using an analytic Green function and frequency-domain inverse time structure correction according to a preferred embodiment of the present invention will be described.

1 is a block diagram for explaining a water layer imaging apparatus using an analytic Green function and a frequency-domain inverse time structure correction according to a preferred embodiment of the present invention.

Referring to FIG. 1, a water-level imaging apparatus (hereinafter referred to as a 'water-level imaging apparatus') 100 using an analytic Green function and a frequency-domain inverse time structure correction By replacing the numerical solution of the time wave equation with a solution of the analytical green function, a water layer image is obtained from the observation data. Accordingly, the water-based imaging apparatus 100 according to the present invention can reduce the amount of computation and obtain a water-layer image having an improved resolution than the prior art.

In addition, the water level imaging apparatus 100 according to the present invention can perform source deconvolution. Accordingly, the water-based imaging apparatus 100 according to the present invention can minimize the influence of bubble oscillation.

For this, the water layer imaging apparatus 100 according to the present invention may include a transmission source estimation unit 110, a transmission source deconvolution unit 130, and a structure correction unit 150.

The transmission source estimation unit 110 estimates a transmission source by inversely calculating a transmission waveform from observation data measured from a receiver (not shown) using an analytic Green function.

The transmission source deconvolution unit 130 deconvolutes the observation data using the transmission source estimated through the transmission source estimation unit 110.

The structure correcting unit 150 receives the information of the deconvoluted observation data through the transmission source deconvolution unit 130 and processes the inverse time structure correction in the frequency-domain using the analytic green function.

That is, the structure correcting unit 150 may include a virtual sound source estimating unit 151, a rear propagating unit 153, and a post-processing unit 155.

The virtual sound source estimating unit 151 can estimate a virtual sound source using an analytic Green function.

The backward propagating unit 153 can back-propagate the deconvoluted observation data through the transmission source deconvolution unit 130 using the analytic Green function.

The post-processing unit 155 post-processes the virtual sound source estimated through the virtual sound source estimating unit 151 and the observation data deconvoluted through the backward propagating unit 153 using the backward propagation result to obtain a water layer image .

The frequency-domain inverse time structure correction using the analytic Green function according to the present invention will now be described in more detail.

Virtual Source Imaging Conditions

은 수신기에서 기록된 파동장과 편미분 파동장의 상호상관(cross-correlation)에 의해 획득될 수 있다. 이는 주파수 영역에서 아래의 [수학식 1]과 같이 표현될 수 있다.Inverse time structure correction at k-th position

Can be obtained by cross-correlation between the recorded wave field and the partial wave field recorded at the receiver. This can be expressed in Equation (1) below in the frequency domain.

는 각주파수(the angular frequency)이고,

는 푸리에 변환된 관측 데이터(Fourier transformed data)이며,

는 주파수-영역 모델링 파동장(modeling wavefield in the frequency domain)이고,

는 k-번째 모델 변수(k-th model parameter)이며,

는 편미분 파동장(partial derivative wavefield;

의 변화에 따른

의 변화량)이고,

는 전치행렬 연산자(matrix transpose operator)이며, *는 복소켤레 연산자(the conjugate operator)이고,

은 복소수의 실수부를 나타낸다(Kim, Y., Min, D.-J., & Shin, C., 2011. Frequency-domain reverse-time migration with source estimation, GEOPHYSICS, 76(2), S41-S49). 여기서, 편미분 파동장을 직접 계산하는 것은 많은 계산을 요구하기 때문에 일반적으로 아래의 [수학식 2] ~ [수학식 9] 같이 가상음원(virtual source)를 이용하여 역시간 구조보정

을 계산한다.here,

Is the angular frequency,

Is Fourier transformed data,

Is a modeling wavefield in the frequency domain,

Is a k-th model parameter,

Is a partial derivative wavefield.

With changes in

, ≪ / RTI >

Is the matrix transpose operator, * is the conjugate operator,

Domain reverse-time migration with source estimation, GEOPHYSICS, 76 (2), S41-S49), which represents the real part of a complex number (Kim, Y., Min, D.-J., & Shin, . Since direct calculation of the partial derivative wave field requires a lot of calculations, it is generally necessary to use a virtual source as in Equation (2) to (9)

.

은 아래의 [수학식 2]인 헬름홀츠 방정식(Helmholtz equation)을 푸는 것으로 계산할 수 있다.Using a given acoustic background model, a frequency-domain modeling wavefront

Can be calculated by solving the Helmholtz equation (Equation 2) below.

및

는 각각 음향 매질의 음속과 밀도이고,

는 음원이며,

는 다중 채널 탄성파 탐사를 위한 점 송신원(point source)을 구현하기 위한 크로네커 델타 함수(Kronecker delta function)이다. 유한 요소법(finite element method) 또는 유한 차분법(finite difference method)에 의해 [수학식 2]는 아래의 [수학식 3]과 같이 행렬식으로 표현할 수 있다.here,

And

Are the sound velocity and density of the acoustic medium, respectively,

Is a sound source,

Is a Kronecker delta function for implementing a point source for multi-channel seismic exploration. The finite element method or the finite difference method can be expressed by the following mathematical expression as shown in the following equation (3).

는 복소 임피던스 행렬(complex impedance matrix)이고,

는 송신원 벡터이다(Virieux, J., Operto, S., Ben-Hadj-Ali, H., Brossier, R., Etienne, V., Sourbier, F., Giraud, L., & Haidar, A., 2009. Seismic wave modeling for seismic imaging, The Leading Edge, 28(5), 538-544). 유한 요소법(Jensen, F. B., 2011. Computational Ocean Acoustics, 2nd edn)을 이용하여 복소 임피던스 행렬

은 아래의 [수학식 4]와 같이 각 요소(element)의 강성 행렬(stiffness matrix)

, 감쇠 행렬(damping matrix)

및 질량 행렬(mass matrix)

으로 구성할 수 있다.here,

Is a complex impedance matrix,

Is the source vector (Virieux, J., Operto, S., Ben-Hadj-Ali, H., Brossier, R., Etienne, V., Sourbier, F., Giraud, L., & Haidar, A., 2009. Seismic wave modeling for seismic imaging, The Leading Edge, 28 (5), 538-544). Using a finite element method (Jensen, FB, 2011. Computational Ocean Acoustics, 2nd edn), a complex impedance matrix

Is a stiffness matrix of each element as shown in Equation (4)

A damping matrix,

And a mass matrix

.

이다. 편미분 파동장

은 아래의 [수학식 5]와 같이 모델 변수

에 대하여 [수학식 3]을 미분하는 것으로 획득할 수 있다.Where ne is the total number of elements,

to be. Partial Wave Waves

Is expressed by the following equation (5)

Can be obtained by differentiating [Equation (3)] with respect to Equation (3).

Rearranging the above equation (5) results in the following equation (6).

Here, a virtual source is defined as Equation (7) below.

은 산란 파동장의 지향성(radiation pattern of scattered wavefield)을 결정하는 복소 임피던스 행렬의 미분값

과 모델링 파동장

의 곱으로 정의된다. 유한 요소법에서 각각의 모델 변수는 해당 고유 요소(unique element)에서만 정의되기 때문에([수학식 [4] 및 Shin, C., Yoon, K., Marfurt, K. J., Park, K., Yang, D., Lim, H. Y., Chung, S., & Shin, S. 2001. Efficient calculation of a partial-derivative wavefield using reciprocity for seismic imaging and inversion, GEOPHYSICS, 66(6), 1856-1863) [수학식 7]에서

의 계산은

으로 감소할 수 있다. 예컨대, k번째 요소의 음속에 대한 복소 임피던스 행렬의 편미분은 아래의 [수학식 8]과 같이 k번째 질량 행렬

에 대한 미분만으로 감소할 수 있다.Here,

Is the derivative of the complex impedance matrix that determines the radiation pattern of the scattered wavefield

And modeling wave field

. Since each model parameter in the finite element method is defined only by the unique element ([4] and Shin, C., Yoon, K., Marfurt, KJ, Park, K., Yang, D. (6), 1856-1863). In Eq. (7), Eq. (7) can be expressed by the following equation

The calculation of

. ≪ / RTI > For example, the partial differentiation of the complex impedance matrix with respect to the sound velocity of the k-th element is expressed by the following equation (8)

Lt; / RTI >

의 대칭 특성 (symmetricity)을 이용하여 아래의 [수학식 9]를 도출할 수 있다.Equation (6) is substituted into Equation (1), and in the isotropic modeling of isochronous acoustic wave propagation, a complex impedance matrix

The following equation (9) can be derived by using the symmetric property of the antenna.

의 컨볼루션(convolution)으로 계산할 수 있다. 멀티 프론탈 다이렉트 솔버를 이용해 모델링 파동장과 관측된 데이터의 후방 전파를 효율적으로 계산(Virieux, J., Operto, S., Ben-Hadj-Ali, H., Brossier, R., Etienne, V., Sourbier, F., Giraud, L., & Haidar, A., 2009. Seismic wave modeling for seismic imaging, The Leading Edge, 28(5), 538-544)할 수 있다고 하더라도 [수학식 9]는 고해상도 수층 이미지 구축에 적용하기 어려움이 있다. 예를 들어, 최대 주파수 128 Hz에 해당하는 고해상도 이미지를 획득하기 위해서는 유한 요소법의 파장당 격자 수(Deraemaeker, A., Babuska, I., & Bouillard, P., 1999. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions, International Journal for Numerical Methods in Engineering, 46(4), 471-499) 때문에 0.71 m 정도의 격자 크기를 사용해야 한다. 이러한 격자 크기로 100 km(distance) x 2~3 km(depth) 영역에 대해 구성된 복소 임피던스 행렬을 인수분해(factorization) 하는데에는 현실적으로 불가능한 메모리 할당량을 필요로 한다(Gupta, A., Karypis, G., & Kumar, V., 1997. A Highly Scalable Parallel Algorithm for Sparse Matrix Factorization, IEEE Transactions on Parallel and Distributed Systems, 8(5), 502-520). 또한, [수학식 9]는 송신원의 에너지,

이 포함되어 있기 때문에([수학식 2]; [수학식 15]; Jang, U. (2012). Comparison of scaling technique in steepest-descent method for the frequency-domain 2d acoustic waveform inversion. Seoul National University) 송신기에서 상대적으로 거리가 가까운 해수 이미지 구축에 적합하지 않다.Therefore, the inverse time structure correction of Equation (1) uses a virtual source and backward propagated observation data using Equation (9) without direct calculation of a partial derivative wave field

As shown in FIG. Efficient computation of back propagation of modeling wave fields and observed data using a multi-frontal direct solver (Virieux, J., Operto, S., Ben-Hadj-Ali, H., Brossier, R., Etienne, V. (5), 538-544), although Equation (9) can be applied to high-resolution images, even if it is possible to do so (Sourbier, F., Giraud, L., & Haidar, A., 2009. Seismic wave modeling for seismic imaging, The Leading Edge, It is difficult to apply it to the construction of a water layer image. For example, to obtain a high-resolution image with a maximum frequency of 128 Hz, the number of gratings per wavelength in the finite element method (Deraemaeker, A., Babuska, I., & Bouillard, P., 1999. Dispersion and pollution of the FEM solution For the Helmholtz equation in one, two and three dimensions, International Journal of Numerical Methods in Engineering, 46 (4), 471-499), a grid size of about 0.71 m should be used. It is practically impossible to factorize the complex impedance matrix constructed for a region of 100 km (distance) x 2 to 3 km (depth) with such a lattice size (Gupta, A., Karypis, G. et al. , & Kumar, V., 1997. A Highly Scalable Parallel Algorithm for Sparse Matrix Factorization, IEEE Transactions on Parallel and Distributed Systems, 8 (5), 502-520). Further, Equation (9) represents the energy of the transmission source,

Jang, U. (2012). Comparison of scaling technique for steepest-descent method for the frequency-domain 2d acoustic waveform inversion. Seoul National University) Is not suitable for building sea-level images relatively close to each other.

Analytic Green's Function Application

Assuming a constant sound velocity and density in the water layer, the analytical Green's function (3D analytic Green's function for half space) in the three-dimensional semi-infinite medium exists as shown in Equation (10) below.

에서 수신기 위치

로 전파하는 3차원 무한매질의 해석적 그린 함수(3D analytic Green's function for free space)이고, 두번째 항은 가상음원

에서 수신기 위치

로 전파하는 3차원 무한매질의 해석적 그린 함수(3D analytic Green's function for free space)이다. 이는

에서 반사계수가 -1인 경우 송신기 위치

에서 수신기 위치

으로 전파하는 직접파(direct arrival)와 해수면 반사파(free-surface reflection)로 각각 해석되고, [수학식 10]은 아래의 [수학식 11]의 조건에서 [수학식 2] 혹은 [수학식 3]의 풀이가 된다(Duffy, D. G. (2001). Green's Functions with Applications (Vol. 38). Chapman and Hall/CRC).Here, the first term to the right of the equation is the actual source position

Receiver position in

(3D analytic Green's function for free space), and the second term is a virtual sound source

Receiver position in

(3D analytic Green's function for free space). this is

If the reflection coefficient is -1, the transmitter position

Receiver position in

(2) or (3) under the conditions of the following Equation (11): " (11) " (Duffy, DG (2001), Green's Functions with Applications (Vol.38), Chapman and Hall / CRC).

는 수층의 음속이다. [수학식 7]의 가상음원(virtual source)

은 아래의 [수학식 12]와 같이 송신원 위치

에서 산란 지점(scattering poiont)

으로 전파하는 해석적 그린 함수를 이용하여 계산할 수 있다. 즉, 가상음원 추정부(151)는 [수학식 12]를 통해 가상음원을 추정할 수 있다.here,

Is the sound velocity of the water layer. The virtual source of Equation (7)

Is expressed by the following equation (12)

The scattering point in the < RTI ID = 0.0 >

Can be calculated using the analytical green function that propagates to the surface. That is, the virtual sound source estimator 151 can estimate the virtual sound source through Equation (12).

에서 산란 지점(scattering point)

으로 전파하는 해석적 그린 함수를 사용하여 계산할 수 있다(Sommerfeld, A. (1912). Die Greensche Funktion der Schwingungslgleichung. Jajresbericht Der Deutschen Mathematiker-Vereinigung, 21. 309-352; Schot, S. H. (1992). Eighty years of Sommerfeld's radiation condition. Historia Mathematica, 19(4), 385-401).The back-propagated wavefield of the measured data is calculated by the following equation (13)

Scattering point < RTI ID = 0.0 >

Can be calculated using the analytical green function that propagates to the surface (Sommerfeld, A. (1912).) Die Greensche Funktion der Schwingungslgleichung.Jajresbericht Der Deutschen Mathematiker-Vereinigung, 21. 309-352; Schot, SH of Sommerfeld's radiation condition, Historia Mathematica, 19 (4), 385-401).

Substituting Equations (12) and (13) into Equation (9) yields Equation (14) below.

이 포함되어 있기 때문에([수학식 11]; [수학식 15]; Jang, U. (2012). Comparison of scaling technique in steepest-descent method for the frequency-domain 2d acoustic waveform inversion. Seoul National University) 송신기에서 상대적으로 거리가 가까운 해수 이미지 구축에 여전히 적합하지 않다.Equation (14) solves the numerical solution of the wave equation that requires a considerable amount of computation in the conventional frequency-domain inverse time structure correction algorithm (wave propagation modeling by Equation (9) and back propagation portion of the observed data) Unlike the conventional frequency-domain inverse time structure correction, it is not necessary to construct and solve a complex impedance matrix. However, Equation (14) can be expressed as a transmission source included in the observation data measured from the receivers,

Jang, U. (2012). Comparison of scaling technique for steepest-descent method for the frequency-domain 2d acoustic waveform inversion. Seoul National University) Is still unsuitable for building sea-level images that are relatively close in distance.

Source deconvolution

Airguns used in marine seismic surveys cause bubble oscillations, especially when the size of the bubble is larger than the magnitude of the reflected wave in the water layer (which is mostly the case) It is difficult to obtain an accurate water-layer image by simply using it. Especially, the image of the deep water layer of 20 to 100 m depth, which is important for understanding the circulation of the hot water of seawater, is covered by the bubble. The source deconvolution can minimize the impact of these bubbles and can greatly help improve the quality of the resulting image. Can deconvolute the source in the frequency-domain from the measured data from the receivers via < EMI ID = 15.0 >

는 송신 파형(source signature)이다. 즉 송신원 디컨볼루션부(130)는 [수학식 15]을 통해 송신원이 디컨볼루션된 관측 데이터를 처리할 수 있다. 송신 파형

는 측정된 송신원(Ziolkowski, A., 1991. Why don’t we measure seismic signatures?, GEOPHYSICS, 56(2), 190-201)을 이용하거나 또는 [수학식 16]과 같이 주파수-영역에서 최소제곱을 이용한 최적화(least-square optimization)를 통해 추정한 송신원(estimated source)

를 사용할 수 있다(Kim, Y., Min, D.-J., & Shin, C., 2011. Frequency-domain reverse-time migration with source estimation, GEOPHYSICS, 76(2), S41-S49).here,

Is a source signature. That is, the transmission source deconvolution unit 130 can process the deconvoluted observation data using the formula (15). Transmission waveform

Can be obtained using the measured source (Ziolkowski, A., 1991. Why do not we measure seismic signatures ?, GEOPHYSICS, 56 (2), 190-201) (Estimated source) through least-square optimization

Kim, Y., Min, D.-J., & Shin, C., 2011. Frequency-domain reverse-time migration with source estimation, GEOPHYSICS, 76 (2), S41-S49).

에서 수신기 위치

으로 전파하는 해석적 그린함수와 수신기로부터 측정된 관측 데이터를 사용하여 추정할 수 있다. 이때, 수신기로부터 측정된 관측 데이터에 대한 시간 영역에서의 적절한 시간 윈도잉(time windowing)의 수행은 [수학식 16]을 이용한 송신원 추정의 안정성을 높일 수 있다(Koo, N.-H., Shin, C., Min, D.-J., Park, K.-P., & Lee, H.-Y., 2011. Source estimation and direct wave reconstruction in Laplace-domain waveform inversion for deep-sea seismic data, Geophysical Journal International, 187(2), 861-870). 즉, 송신원 추정부(110)는 [수학식 16]을 통해 송신원을 추정할 수 있다. [수학식 15]를 [수학식 13]에 대입하면 아래의 [수학식 17]과 같다.In the frequency-domain, the source is the transmitter location

Receiver position in

Can be estimated using the analytical Green function propagating to the receiver and observation data measured from the receiver. At this time, performing an appropriate time windowing in the time domain with respect to the observed data measured by the receiver can increase the stability of the source estimation using Equation (16) (Koo, N.-H., Shin Domain waveform inversion for deep-sea seismic data, direct wave reconstruction, Geophysical Journal International, 187 (2), 861-870). That is, the transmission source estimating unit 110 can estimate the transmission source through Equation (16). Substituting Equation (15) into Equation (13) yields Equation (17).

That is, the backward propagating unit 153 can backward propagate the source deconvoluted field data through the source through Equation (17).

Substituting Equations (12) and (17) into Equation (9) yields Equation (18) below.

Therefore, the inverse time structure correction of [Equation 1] for constructing the water layer image is calculated by convolution of the virtual source and the back propagated observation data in a formally similar manner to the conventional frequency-domain structure correction . However, in the calculation of the virtual sound source, it is possible to calculate the water image irrespective of the transmission waveform, using the analytical green function and the source propagating the descaled spectral data backward (Jang, U. (2012). in steepest-descent method for the frequency-domain 2d acoustic waveform inversion. Seoul National University). That is, the post-processing unit 155 can process the water layer image using the result of backward propagation of the source deconvoluted field data with the virtual sound source and the source through Equation (18).

를 후방 전파하기 때문에 기존의 다른 시도에서는 불가능했던 20 ~ 100 m 깊이의 천부 수층의 이미지까지도 선명하게 계산 가능하다.Since the modified inverse time structure correction in the present invention replaces the numerical solution of the wave equation with the use of the analytical green function, it is not necessary to construct and solve the complex impedance matrix unlike the conventional frequency-domain inverse time structure correction . Furthermore, it can be determined that the modified lattice size of the inverse temporal structure correction takes into account only the spatial resolution, not the number of lattices per wavelength according to the maximum frequency (Virieux, J., & Operto, S (2009). An overview of full-waveform inversion in explorarion geophysics. GEOPHYSICS, 74 (6), WCCI-WCC26). For example, in the case of the present invention, when a maximum frequency of 128 Hz is used, a grating size of 2.0 m is sufficient, which is about three times larger than the grating size 0.71 m required at the same frequency using the conventional finite element method. 18] requires very little memory. Therefore, the inverse temporal structure correction technique according to the present invention can generate a high-resolution water-level image without a clear memory requirement. Further, in the present invention, when the inverse temporal structure correction calculation uses the estimated source as the deconvoluted data

, It is possible to calculate the image of the deep water layer 20 to 100 m deep, which was impossible in other attempts.

Referring to FIG. 2, a water layer imaging method using an analytic Green function and frequency-domain inverse time structure correction according to a preferred embodiment of the present invention will be described.

FIG. 2 is a flowchart illustrating a water layer imaging method using an analytic Green function and frequency-domain inverse time structure correction according to a preferred embodiment of the present invention.

Referring to FIG. 2, the water-level imaging apparatus 100 estimates a transmission source by inversely calculating a transmission waveform from observation data measured from receivers using an analytic Green function (S110). More specifically, the water-level imaging apparatus 100 can estimate the transmission source through Equation (16) above.

The water-level imaging device 100 may then deconvolute the observed data measured using the estimated source (S130). More specifically, the water-level imaging apparatus 100 can deconvolute the transmission source estimated through Equation (15) above.

Then, the water-level imaging apparatus 100 receives the deconvolved observation data information from the transmission source and processes the inverse temporal structure correction in the frequency-domain using the analytic green function.

That is, the water-level imaging apparatus 100 estimates a virtual sound source using an analytic Green function (S150). More specifically, the water-level imaging apparatus 100 can estimate a virtual sound source through Equation (12) above.

In addition, the water-level imaging apparatus 100 back-propagates the deconvoluted observation data using the analytic Green function (S170). More specifically, the water-level imaging apparatus 100 can back-propagate observation data deconvoluted through the above equation (17).

Then, the water-level imaging apparatus 100 post-processes the result of backward propagation of the estimated virtual sound source and the deconvoluted observation data to obtain a water-layer image (S190)

Thus, by replacing the wave propagation modeling by the numerical solution of the wave equation requiring a considerable amount of computation in the conventional frequency-domain inverse time structure correcting algorithm and the solution of the back propagation part of the observation data by the solution of the analytical green function, The computational efficiency of the computer for construction can be improved and a high-resolution water-layer image containing high-frequency components can be constructed from seafloor seismic data. The obtained high-resolution seismic water-layer images can reveal the distribution of physical properties (water temperature, salinity, etc.) of successive water bodies in the exploration area. Furthermore, it is possible to find out how the different material currents are mixed, Of the ocean surface, and to determine whether it occurs up to the ocean.

The present invention can also be embodied as computer-readable codes on a computer-readable recording medium. A computer-readable recording medium includes all kinds of recording apparatuses in which data that can be read by a computer is stored. Examples of the computer-readable recording medium include a ROM, a RAM, a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device. In addition, the computer-readable recording medium may be distributed to computer devices connected to a wired / wireless communication network, and a computer-readable code may be stored and executed in a distributed manner.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, It will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the scope of the appended claims.

100: water layer imaging apparatus, 110: transmission source estimating unit,
130: transmission source deconvolution unit, 150: structure correction unit,
151: virtual sound source estimation unit, 153: rear propagation unit,
155: Post-

Claims (14)

A transmission source estimating unit that estimates a transmission source by inversely calculating a transmission waveform by using an analytic green function from measured data measured from receivers;
A transmission source deconvolution unit for deconvoluting observation data using the transmission source estimated by the transmission source estimation unit; And
A structure corrector receiving the deconvoluted observation data information from the transmission source deconvolution unit and processing the frequency-domain inverse time structure correction using an analytic green function;
/ RTI >
The structure correcting unit may include: a virtual sound source estimating unit that estimates a virtual sound source using an analytic Green function; A rear propagating unit for backward propagating the deconvoluted observation data using an analytic green function; And a post processor for acquiring a water layer image using a result of backward propagation of the virtual sound source estimated through the virtual sound source estimation unit and the observation data deconvoluted through the rear propagation unit, Water - based imaging system using temporal correction. The method of claim 1,
The transmission-

The measured data from the receivers and the source location

Receiver position in

Which estimates a transmission source using an analytical green function propagating to the receiver,
Water - based imaging system using analytical green function and frequency - domain inverse time structure correction. The method of claim 1,
Wherein the transmission source deconvolution unit comprises:

And < RTI ID = 0.0 > deconvoluting < / RTI > the observed data measured from the receivers using an estimated source,
Water - based imaging system using analytical green function and frequency - domain inverse time structure correction. delete The method of claim 1,
Wherein the virtual sound source estimating unit comprises:

The transmission source position

Scattering point < RTI ID = 0.0 >

, Which is an analytic Green function,
Water - based imaging system using analytical green function and frequency - domain inverse time structure correction. The method of claim 1,
The rear-

Receiver position

Scattering point

And the backward propagation processing of the deconvoluted observation data in the transmission source deconvolution unit using an analytic Green function propagating to the transmission source deconvolution unit,
Water - based imaging system using analytical green function and frequency - domain inverse time structure correction. The method of claim 1,
The post-

And a backward propagation process of the deconvoluted observation data at the back propagation unit and the virtual sound source estimated by the virtual sound source estimating unit,
Water - based imaging system using analytical green function and frequency - domain inverse time structure correction. Estimating a transmission source by inversely calculating a transmission waveform from an observation data measured from receivers using an analytic green function;
Deconvoluting observation data using an estimated transmission source; And
Receiving deconvoluted observation data information and processing frequency-domain inverse time structure correction using an analytic green function;
/ RTI >
The structure correcting step may include: estimating a virtual sound source using an analytic green function; Backward propagating the deconvoluted observation data using an analytic Green function; And acquiring a water-layer image using a result of backward propagation of the observational data with the estimated virtual sound source and deconvolution, and a water layer imaging method using the analytical Green function and the frequency-domain inverse time structure correction. 9. The method of claim 8,
Wherein the transmitting source estimating step comprises:

The measured data from the receivers and the source location

Receiver position in

And estimating a transmission source using an analytic Green function propagating to the base station,
Water - based imaging method using analytical Green 's function and frequency - domain inverse time structure correction. 9. The method of claim 8,
Wherein the deconvolution step comprises:

And deconvoluting the observed data measured from the receivers using an estimated source such as < RTI ID = 0.0 >
Water - based imaging method using analytical Green 's function and frequency - domain inverse time structure correction. delete 9. The method of claim 8,
The virtual sound source estimating step may include:

The transmission source position

Scattering point < RTI ID = 0.0 >

Which is obtained by estimating a virtual sound source by using an analytic green function propagating to a speaker,
Water - based imaging method using analytical Green 's function and frequency - domain inverse time structure correction. 9. The method of claim 8,
The back propagation step includes:

Receiver position

Scattering point

And a backward propagation process of the deconvoluted observation data in the transmission source deconvolution unit using an analytic Green function propagating to the transmission source deconvolution unit.
Water - based imaging method using analytical Green 's function and frequency - domain inverse time structure correction. 9. The method of claim 8,
The water layer image acquiring step includes:

And obtaining a water layer image using a result of back propagation processing of the estimated virtual sound source and the deconvoluted observation data,
Water - based imaging method using analytical Green 's function and frequency - domain inverse time structure correction.

Images