KR101108260B1 - apparatus and method for waveform inversion using multiple transform in Laplace-Fourier domain - Google Patents
apparatus and method for waveform inversion using multiple transform in Laplace-Fourier domain Download PDFInfo
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- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
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Abstract
The present invention relates to underground exploration techniques and in particular to imaging techniques of underground structures that model underground structures using waveform inversion in the Laplace region. The disclosed underground structure imaging apparatus includes a measurement data processor for converting measurement data input from receivers into data corresponding to the result of Laplace transform by multiplying the gain of the p-square form of time, and initial modeling set for the underground structure. Update the parameter, but includes an underground structure modeling section that is repeatedly updated in a direction that minimizes the objective function including the differential term relating to the Laplace attenuation constant s related to the error of the measurement data and the modeling data calculated from any initial model. .
Description
The present invention relates to underground exploration techniques and in particular to imaging techniques of underground structures that model underground structures using waveform inversion in the Laplace region.
Korean Patent Application No. 2008-25876, filed by the present applicant, discloses a technique for imaging underground structures by modeling wave equations in the Laplace region. This technique calculates modeling parameters for the underground structure by performing Laplace domain waveform inversion on the seismic signals obtained from receivers arranged in the measurement target area.
Modeling parameters are calculated by iterative method. The underground structure is first estimated by the initial modeling parameters, which are outlined, and a signal that can be obtained at the receivers, i.e. modeling data, is obtained when an input from the source is applied to the estimated model. Next, the modeling parameters are updated to reduce the error between the calculated modeling data and the actual acoustic wave signal measured by the receiver. Thereafter, the above-described process is repeated using the updated modeling parameter. If the error between the modeling data and the actual acoustic wave signal measured by the receiver falls below a predetermined value, then the modeling parameters are taken as the imaging data for the final underground structure. The modeling parameters can be speed or density values in the underground medium, and the underground imaging device expresses these parameters as color images.
The wave field in the Laplace domain can be regarded as the zero frequency component of the wave field attenuated in the time domain. Thus, waveform inversion in the Laplace region improves the interpretation of the low frequency parts. However, in the time domain, attenuation attenuates late signals reaching the receiver from the basement depth, making it difficult to estimate the structure of the basement depth.
SUMMARY OF THE INVENTION The present invention has been made to solve such a problem, and an object thereof is to improve the structural estimation of the deep underground in the waveform inversion of the Laplace region.
According to one aspect of the present invention, an underground imaging apparatus includes: a measurement data processor configured to convert measurement data input from receivers into data corresponding to a result of Laplace transform by multiplying a gain in the form of a p power of time; And to update the initial modeling parameters set for the underground structure, with respect to the error of the measurement data and the modeling data calculated from any initial model, and to minimize the objective function including the derivative term for the Laplace attenuation constant s. It includes an underground structure modeling unit to be updated repeatedly.
According to an aspect, the measurement data processor includes an amplifier that multiplies the measurement data input from the receiver by a p power form of time, and a Laplace transformer that Laplace transforms data output from the amplifier.
According to another aspect, the measurement data processing unit may convert the measurement data input from the receiver into the data of the Laplace region, and differentiate the data output from the Laplace transform unit p times with respect to the attenuation constant s of the Laplace region. And a differential processing unit for outputting.
This is because multiplying the seismic data by the p-function of time in the time domain has the same effect as differentiating the seismic data by the attenuation constant s in the Laplace domain.
According to a characteristic aspect of the present invention, the underground structure modeling unit is a modeling data calculation unit for calculating modeling data detected at each receiver when a wave caused from a transmission source propagates to an underground structure specified by a modeling parameter, and the modeling data. An objective function calculation unit for calculating an objective function related to the error between the modeling data calculated in the calculation unit and the measurement data processed in the measurement data processing unit and including a derivative term relating to the Laplace attenuation constant s; The modeling parameter updater updates the modeling parameter in the direction of decreasing the objective function calculated by the controller and supplies it to the modeling data calculator, and when the size of the objective function calculated by the objective function calculator is less than or equal to a predetermined value, Export the calculated modeling parameters to the underground model And a subterranean output.
The present invention multiplies the seismic data in the Laplace region by the attenuation constant s by multiplying or equalizing the seismic data in the form of p times of the time in the waveform inversion in the Laplace region, or by the equalization process, and the derivative term for the attenuation constant s. By updating the modeling parameters through the objective function including, it is possible to accurately image the underground structure by sufficiently reflecting the wave field reflected from the deep underground.
1 is a block diagram showing a schematic configuration of an underground imaging apparatus according to an embodiment of the present invention.
2 is a block diagram showing a schematic configuration of an underground imaging apparatus according to another embodiment of the present invention.
The foregoing and additional aspects of the present invention will become more apparent through the following embodiments. Hereinafter, the present invention will be described in detail so that those skilled in the art can easily understand and reproduce the present invention through embodiments.
1 is a block diagram showing a schematic configuration of an underground imaging apparatus according to an embodiment of the present invention. As shown, the underground imaging apparatus according to an aspect of the present invention is a measurement data processing unit for converting measurement data input from receivers into data substantially equivalent to the result of Laplace transform by multiplying a gain in the form of p power of time ( 350) and to update the initial modeling parameters set for the underground structure, while minimizing the objective function including the derivative term for the Laplace attenuation constant s, which is related to the error of the measurement data and the modeling data calculated from any initial model. It includes the underground
To explore underground structures at sea, the exploration vessel measures the reflected waves detected at each receiver as the receivers drag a streamer mounted on the grid and continuously fire the air gun as the transmitter. A streamer is, for example, a hydrophone cable filled with floating oil therein. Inside the cable is a piezoelectric receiver that detects a change in pressure. They are used to connect as necessary length, usually composed of about 24 to 96 channels.
Giving the measurement function a time function gain amplifies the signal that reaches the later time, that is, the signal from deep inside the ground, so that more information can be obtained from the ground deep. That is, t p is multiplied by the measured data sequentially input. It is a variable gain amplifier that amplifies more late signals. This allows us to do a better job of inverting deeper speeds.
According to an aspect, the
As shown, the underground
An apparatus and method for imaging an underground structure by waveform inversion in a Laplace region according to the prior art are disclosed in the above-mentioned Korean Patent Publication. The measured signal is converted into data of the Laplace area by the
According to an additional aspect of the present invention, an underground structure imaging apparatus includes an underground structure output unit for color imaging an underground structure from the calculated modeling parameters. The size of the speed value or density value for each location can be mapped to color and output as a color image.
The present invention has a configuration different from that of the prior art, particularly in the objective function and in the
In one embodiment, the objective function of the
Formula (1)
(N f is the number of attenuation constants, N s is the number of shots from the transmitter, N r is the number of receivers, N p is the highest differential order for s in the wave field, s is the Laplace attenuation constant, u is the Laplace region) Wave field modeling data at, d is the seismic data in the Laplace region)
In FIG. 1, the
In the Newton inversion method, the update direction of modeling parameters is defined as the following equation.
Where v is the propagation velocity of the wave field in the medium, a modeling parameter. v k denotes a velocity value in the k th iteration, and the above expression expresses how the velocity is updated by the recursive method. Δ v , which corresponds to the velocity update in the equation, is a wave field, or Hessian matrix, which is divided into two modeling parameters.
The update direction of velocity, a modeling parameter in Gauss-Newton inversion, is defined as follows using approximated Hessian.
Where J is the wavefield Jacobian matrix, which is a partial derivative of the modeling parameter fk.
In the above equation, the derivative of the modeling parameter of the objective function, that is, the gradient direction, is calculated as follows.
(l = 1,…, N m )
Where N m is the number of modeling parameters, E is the objective function, ν is the modeling parameter, s is the Laplace attenuation constant, N f is the number of attenuation constants, N s is the number of shots from the transmitter, N r is the receiver The number, N p, is the highest differential order for s of the wave field, u is the wave field modeling data in the Laplace region, and d is the seismic data in the Laplace region.
Hessian is used when using the Newton method and Hessian is approximated when using the Gaussian-Newtonian inversion. There are several ways to invert and calculate δ v through approximated Hessian. In one embodiment, there is a method using the entire approximated Hessian matrix. This method solves δ v by solving matrix equation below.
Where r is the logarithmic difference between the actual wave field and the calculated wave field, that is, residual. In the gradient expression above, Jacobian
In another embodiment, δ v is obtained by solving using singular value decomposition.
J δ v = -r
In another embodiment, the gradient is divided using only the diagonal component of the approximated Hessian to obtain δ v .
According to another aspect of the present invention, the
According to an additional aspect of the present invention, the
Since waveform inversion in the Laplace domain is less sensitive to the initial velocity model than inversion in the frequency domain, the velocity model in a homogeneous medium can be used as the initial velocity model. For velocity models in homogeneous media, there is an analytic solution for the Laplace domain, which can be used to calculate Jacobian and Hessian or approximated Hessian for a fairly accurate velocity increment at once. This can improve the speed of obtaining modeling parameters. After the velocity is updated once by applying a method such as a line search to the velocity increment obtained, a more accurate velocity model can be obtained by using a conventional waveform inversion method.
That is, in order to calculate the objective function in the
Considering the Lloyd mirror effect due to the free surface, assuming that the actual transmission source 10 and the virtual transmission source 20 are assumed, the solution can be obtained as follows.
This green function is multiplied by the source amplitude for each attenuation constant s to obtain the wave field. From the wave field, the differential field for s and the partial derivative for velocity are as follows. Here, source amplitude is assumed to be 1 for convenience of calculation.
here
On the other hand, the seismic wave equation in the Laplace region can be expressed as follows.
Where s is the Laplace attenuation constant, c is the propagation velocity (constant) of the medium, u is the modeling parameter of the wavefield of the Laplace region, that is, the propagation velocity, and f is the source function in the Laplace region. to be. Using the finite difference method or finite element method, the seismic wave equation can be expressed as a system of linear algebraic equations.
Su = f
Where S is the derivative operator
Differentiate both sides of the linear algebraic equation with the modeling parameters,
Therefore, the partial differential wave field required for gradient calculation can be obtained as follows.
From here,
to be.
In addition, the partial differential wave field differentiated by the damping constant s is as follows.
2 is a block diagram showing a schematic configuration of an underground imaging apparatus according to another embodiment of the present invention. In the illustrated embodiment, the measurement
This embodiment is substantially the same as the embodiment shown in FIG. 1, where multiplying the seismic data by the time function gain in the form of p times of time in the time domain is such as the derivative of the seismic data by the attenuation constant s in the Laplace region. Because it has an effect.
Formula (2)
Therefore, when inverting the waveform in the Laplace region, including the derivative term for the attenuation constant s in the objective function can be inverted even to the depth of depth.
On the other hand, according to another aspect of the present invention, the objective function may be modified as follows by weighting each term.
In this case, the gradient of the objective function related to the increment is obtained as follows.
The present invention has been described above with reference to the embodiments described with reference to the drawings, but is not limited thereto. Therefore, the present invention should be construed by the claims, which are intended to cover many variations that can be obviously derived from this described embodiment.
300: underground structure modeling unit
310: modeling parameter updating unit 330: modeling data calculation unit
350: measurement data processing unit 351: amplification unit
353: Laplace converter 355: Laplace converter
357: derivative processing unit 370: objective function calculation unit
390: memory
500: underground structure output unit
Claims (20)
Update the initial modeling parameters set for the underground structure, with repeated updates in order to minimize the objective function, which relates to the error of the measurement data and the modeling data calculated from any initial model, and includes a derivative term for the Laplace attenuation constant s. Underground structure modeling unit;
Underground imaging device comprising a.
An amplifier for multiplying the measured data input from the receiver by a p power form of time;
A Laplace transform unit for Laplace transforming data output from the amplifier;
Underground imaging device comprising a.
A Laplace transform unit converting the measurement data input from the receiver into the Laplace area data;
A derivative processor for differentiating the data output from the Laplace converter by p times with respect to the attenuation constant s of the Laplace region;
Underground imaging device comprising a.
A modeling data calculator which calculates modeling data detected at each receiver when a wave caused from a transmission source propagates in an underground structure specified by a modeling parameter;
An objective function calculator for calculating an objective function related to an error between the modeling data calculated by the modeling data calculator and the measurement data processed by the measurement data processor, and including a derivative term relating to the Laplace attenuation constant s;
A modeling parameter updating unit updating the modeling parameter in a direction in which the objective function calculated by the objective function calculating unit decreases and supplying the modeling parameter to the modeling data calculating unit;
An underground structure output unit for outputting the modeling parameter calculated by the modeling parameter updating unit as an underground structure model when the size of the objective function calculated by the objective function calculating unit is less than or equal to a predetermined value;
Underground imaging device comprising a.
(N f is the number of attenuation constants, N s is the number of shots from the transmitter, N r is the number of receivers, N p is the highest differential order for s in the wave field, s is the Laplace attenuation constant, u is the Laplace region) Wave structure modeling data in, d is a seismic data in the Laplace region).
An underground structure imaging apparatus for recalculating an incremental value of the modeling parameter by the Newton method, and updating the existing modeling parameter by an iteration method.
The underground structure imaging apparatus which obtains the incremental value of the modeling parameter by inversely calculating by Gauss-Newton method and updates the existing modeling parameter by the iteration method.
And the modeling parameter updating unit calculates a gradient of the modeling parameter of the objective function using the following equation in applying the Gauss-Newton method.
(l = 1,…, N m ), where N m is the number of modeling parameters, E is the objective function, ν is the modeling parameter, s is the Laplace attenuation constant, N f is the number of attenuation constants, and N s is the source The number of shots, N r is the number of receivers, N p is the highest differential order for s of the wave field, u is wave field modeling data in the Laplace region, and d is the seismic data in the Laplace region.
An underground imaging apparatus for color imaging underground structures from the calculated modeling parameters.
Update the initial modeling parameters set for the underground structure, with repeated updates in order to minimize the objective function, which relates to the error of the measurement data and the modeling data calculated from any initial model, and includes a derivative term for the Laplace attenuation constant s. Underground structure modeling step;
Underground imaging method comprising a.
Multiplying the measurement data input from the receiver by multiplying the gain of the p power form of time;
Laplace transforming the amplified data;
Underground imaging method comprising a.
Converting the measurement data input from the receiver into data of the Laplace region;
Differentiating the Laplace transformed data p times with respect to the attenuation constant s of the Laplace region;
Underground imaging method comprising a.
A modeling data calculation step of calculating modeling data detected at each receiver when a wave caused from a transmission source propagates in an underground structure specified by a modeling parameter;
An objective function calculation step of calculating an objective function related to an error between the modeling data calculated in the modeling data calculation step and the measurement data processed in the measurement data processing step and including a derivative term relating to the Laplace attenuation constant s;
A modeling parameter updating step of updating a modeling parameter in a direction of decreasing the objective function calculated in the objective function calculating step and supplying the modeling parameter to the modeling data calculation step to repeat the next processing;
An underground structure outputting step of outputting the modeling parameter calculated in the modeling parameter updating step as an underground structure model when the size of the objective function calculated in the objective function calculating step is equal to or less than a predetermined value;
Underground imaging method comprising a.
(N f is the number of attenuation constants, N s is the number of shots from the transmitter, N r is the number of receivers, N p is the highest differential order for s in the wave field, s is the Laplace attenuation constant, u is the Laplace region) Wave field modeling data in, d is the seismic data in the Laplace region.
The underground structure imaging method of calculating the incremental value of the modeling parameter inversely by the Newton method and updating the existing modeling parameter by the iteration method.
An underground structure imaging method in which an incremental value of the modeling parameter is obtained by inverse calculation by a Gauss-Newton method, and the existing modeling parameter is updated by an iteration method.
And the modeling parameter updating unit calculates a gradient of the modeling parameter of the objective function using the following equation in applying the Gauss-Newton method.
Where E is the gradient of the objective function, ν is the modeling parameter, s is the Laplace attenuation constant, N f is the number of attenuation constants, N s is the number of shots from the transmitter, N r is the number of receivers, and N p is the wave Highest differential order for s of field, u is wave field modeling data in the Laplace region, d is seismic data in the Laplace region)
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| KR101355107B1 (en) | 2012-06-29 | 2014-01-23 | 서울대학교산학협력단 | Method and apparatus of estimating underground structure using denoising |
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| KR101693310B1 (en) * | 2015-11-20 | 2017-01-06 | 한국지질자원연구원 | Full-waveform inversion using plane wave method in anisotropic media |
| WO2021010508A1 (en) * | 2019-07-15 | 2021-01-21 | 서울대학교 산학협력단 | Laplace-fourier-domain full waveform inversion device and method using multi-attenuation and multi-offset |
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| KR20000036978A (en) * | 2000-04-03 | 2000-07-05 | 석창성 | System for detecting a pipe under the ground using elastic wave |
| KR20080053005A (en) * | 2006-12-08 | 2008-06-12 | 한국지질자원연구원 | 4-d inversion of geophysical data and 4-d imaging method of geologic structure using it |
| KR20080114488A (en) * | 2007-06-26 | 2008-12-31 | 신창수 | An apparatus for imaging a subsurface structure using waveform inversion in the laplace domain and methods thereof |
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| US6865489B2 (en) * | 2002-10-02 | 2005-03-08 | Exxonmobil Upstream Research Company | Method for compensating mild lateral velocity variations in pre-stack time migration in the frequency-wave number domain |
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| KR20000036978A (en) * | 2000-04-03 | 2000-07-05 | 석창성 | System for detecting a pipe under the ground using elastic wave |
| KR20080053005A (en) * | 2006-12-08 | 2008-06-12 | 한국지질자원연구원 | 4-d inversion of geophysical data and 4-d imaging method of geologic structure using it |
| KR20080114488A (en) * | 2007-06-26 | 2008-12-31 | 신창수 | An apparatus for imaging a subsurface structure using waveform inversion in the laplace domain and methods thereof |
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| KR101355107B1 (en) | 2012-06-29 | 2014-01-23 | 서울대학교산학협력단 | Method and apparatus of estimating underground structure using denoising |
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