KR101108260B1 - Waveform Inverter Using Multiple Transforms in Laplace Domain - Google Patents

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

Apparatus and method for waveform inversion using multiple transform in Laplace-Fourier domain}

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 structure modeling unit 300 to update repeatedly in the direction.

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 measurement data processor 350 may further include an amplifier 351 for multiplying the measured data input from the receiver by a p power form of time, and Laplace for laplace transforming the data output from the amplifier 351. The conversion unit 353 is included. That is, the measurement data is Laplace transformed after t ^p is multiplied.

As shown, the underground structure modeling unit 300 according to an embodiment is a modeling data calculation unit for calculating the modeling data detected by each receiver when a wave caused from a transmission source propagates to the underground structure specified by the modeling parameters ( 330 and an objective function related to an error between the modeling data calculated by the modeling data calculation unit 330 and the measurement data processed by the measurement data processing unit 350 and including a derivative term relating to the Laplace attenuation constant s. A modeling parameter updating unit for updating the modeling parameter in the direction in which the objective function calculating unit 370 to calculate and the objective function calculated by the objective function calculating unit 370 decreases and supplying the modeling parameter to the modeling data calculating unit 330 ( 310 and the model calculated by the modeling parameter update unit 310 when the size of the objective function calculated by the objective function calculator 370 is equal to or less than a predetermined value. And a geologic structure output unit 500 for outputting a ring parameters in the underground structure model.

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 measurement data processor 350 and stored in the memory 390. The modeling parameter updater 310 has parameter values of the initial model of the underground structure. The initial value can be set arbitrarily. The modeling data calculator 330 calculates modeling data that can be detected at each reception point when a wave caused from an equivalent transmission source propagates in the underground structure specified by the modeling parameters. Modeling data can be obtained by solving wave equations specified by modeling parameters using numerical analysis techniques such as finite element method or finite difference method. The objective function calculator 370 calculates an error between the measurement data stored in the memory 390 and the modeling data calculated from an arbitrary initial model. The objective function is a function for calculating this error. For example, L2 norm, the difference between the log values of two values, the power of p, and the integral value can be variously selected. If the error is larger than the predetermined value, the modeling parameter updater 310 updates the modeling parameter in a direction in which the error decreases. This is done by calculating the gradient of the objective function for each model parameter and calculating the model parameter that minimizes the objective function. The modeling data calculation unit 330 calculates modeling data that can be detected at each reception point when a wave caused from a transmission source propagates in the underground structure specified by the updated modeling parameter. The objective function calculator 370 calculates an error between the measurement data stored in the memory 390 and the modeling data calculated from the updated model. If the error is larger than the predetermined value, the updating of the modeling parameter is repeated. If the error is smaller than the predetermined value, the modeling parameter at that time is determined as the final modeling parameter for the underground structure and output to the outside. Modeling parameters correspond to the coefficients of the wave equation, and can be, for example, velocity, density, etc. in an underground medium.

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 modeling parameter updater 310 which updates the modeling parameters using the objective function.

In one embodiment, the objective function of the objective function calculator 370 may be given as in the following equation.

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 modeling parameter updater 310 updates the objective function by using a derivative value, that is, a gradient, with respect to the modeling parameter. That is, it is updated in the direction of minimizing the objective function. There are two methods for updating the objective function: the Newton inversion method and the Gauss-Newton inversion method.

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.

에 해당하고, 차분(residual)은

에 해당한다. 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

, And the residual is

Corresponds to

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 modeling parameter updater 310 calculates an increment of the modeling parameter by adding white noise to the Hessian or approximated Hessian matrix. The Hessian or approximated Hessian matrix can have very small terms, which can result in a singular value at δ v . To prevent this, the Levenberg-Marquardt method is used to add white noise to the Hessian or approximated Hessian.

According to an additional aspect of the present invention, the modeling parameter updater 310 adds a plurality of white noises having different magnitudes to the Hessian or approximated Hessian matrix, obtains increments of the modeling parameters, normalizes each increment, and sums them all together. Output in final increments. In one embodiment, δ v is obtained by setting 100 white noises from 10 ⁻³ times to 10 ⁻¹ times the maximum value of the Hessian or approximated Hessian matrix, normalizing each of them, and adding them all together to stabilize them. Get the (robust) value.

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 objective function calculator 370, the partial differential wave length for the wave field u _ijk in the Laplace region, the partial derivative for the attenuation constant s of the wave field, and the velocity is calculated. According to one aspect of the invention these values use the Laplace region green function in a three-dimensional homogeneous medium.

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.

이다.here

to be.

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

를 근사화하는 임피던스 행렬이고, u 는 라플라스 영역 파동장 벡터이며, f 는 송신원 벡터이다. Where S is the derivative operator

Is an impedance matrix approximating, u is a Laplace region wave field vector, and f is a source vector.

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 data processing unit 350 converts the measurement data input from the receiver into the data of the Laplace area, and the Laplace area 355 to convert the data output from the Laplace conversion unit 355. And a derivative processing unit 357 which differentiates and outputs p times with respect to the attenuation constant of s.

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)

A measurement data processing unit for converting the measurement data input from the receivers into data substantially equivalent to the result data of the Laplace transform by multiplying a gain in the form of a p power of time;
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.
The method of claim 1, wherein the measurement data processing unit
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.
The method of claim 1, wherein the measurement data processing unit
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.
According to claim 2 or 3, wherein the underground structure modeling unit
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.
The object function of claim 4, wherein the object function of the object function calculation unit is

(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).
The method of claim 4, wherein the modeling parameter update unit
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 method of claim 4, wherein the modeling parameter update unit
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.
The method of claim 7, wherein
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. 8. The underground imaging apparatus of claim 7, wherein the modeling parameter updater calculates an increment of the modeling parameter by adding white noise to a Hessian or approximated Hessian matrix.
10. The underground structure imaging apparatus according to claim 9, wherein an increment of modeling parameters is obtained by adding a plurality of white noises having different magnitudes to a Hessian or approximated Hessian matrix, normalizing each incremental value, and adding all of them to a final incremental value. .
The method of claim 4, wherein the underground structure output unit
An underground imaging apparatus for color imaging underground structures from the calculated modeling parameters.
A measurement data processing step of converting the measurement data input from the receivers into data substantially equivalent to the resultant data of the Laplace transform by multiplying a gain in the form of a p power of time;
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.
The method of claim 12, wherein the measuring data processing step
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.
The method of claim 12, wherein the measuring data processing step
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.
15. The method of claim 13 or 14, wherein the underground modeling step
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.
16. The objective function of claim 15, wherein

(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.
16. The method of claim 15, wherein updating the modeling parameter
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.
16. The method of claim 15, wherein updating the modeling parameter
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.
The method of claim 18,
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) 19. The method of claim 18, wherein the updating of the modeling parameter comprises adding a plurality of white noises having different magnitudes to the Hessian or approximated Hessian matrix to obtain an increment of the modeling parameters, normalizing each increment, and then adding up to a final increment. Underground structure imaging method.

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