KR101459388B1 - Speed information derivation method of underground - Google Patents

Abstract

An objective of the present invention is to provide a method of deducing underground speed information, and more specifically to a method of deducing underground speed information, capable of rapidly and accurately deducing the speed information underground through a simple calculation process. In order to accomplish the objective of the present invention, provided is the method of deducing underground speed information, which includes: inputting an initial speed model to input an observed acoustic wave material and initial speed information (S100); creating a numeric modeling material by calculating a physical property of an underground medium based on the speed model and by estimating a sound source waveform from the observed acoustic wave material (S200); calculating an inclination direction using back-propagation based on the numeric modeling material and the observed acoustic wave material and configuring a pseudo Hessian matrix (S300); and calculating and updating the speed information using the inclination direction and the pseudo Hessian matrix (S400).

Description

[0001] SPEED INFORMATION DERIVATION METHOD OF UNDERGROUND [0002]

The present invention relates to a method of deriving an underground velocity information, and more particularly, to a method of deriving an underground velocity information using a back propagation method and a pseudo Hessian matrix in the inverse of an acoustic wave waveform in a time domain.

The development of underground resources such as minerals and crude oil buried underground requires a lot of cost and effort. In particular, the geological exploration of various methods directly or indirectly finds areas where underground resources are likely to be buried, and in some of them, direct drilling or indirect data analysis is conducted to determine the presence of underground resources and reserves It goes through the process of checking.

On the other hand, the existence and location of underground resources can be found by using seismic waves such as seismic waves. In other words, by seismically generating seismic waves and analyzing the seismic data received through the underground medium, the density of the underground medium can be determined. Through the structure of the underground medium, the existence of underground resources and the location . In this process, a general waveform inversion algorithm for obtaining a ground model that provides modeling data that minimizes the error with the measured data is applied.

Generally, waveform inversion is performed with the modeling data for the initial underground medium (initial model), which is assumed to be a combination of actual measured seismic data and preliminary information obtained through field geological survey or drill core analysis. We calculate the velocity of the seismic wave against the underground medium and the density of the underground medium together while iteratively updating the necessary parameters.

Seismic survey is a technique that can grasp underground structures and properties by artificially generating seismic waves in the surface or water and analyzing the propagation behavior of the generated seismic waves. In order to clearly understand the underground structure using such seismic waves, it is necessary to provide information on the propagation velocity of the underground medium.

In order to derive the velocity information of the underground medium, full wave form inversion is applied. However, there are many limitations in deriving subsurface velocity model using seismic wave inversion because it requires huge amount of computation and efficiency. In order to overcome this problem, a method using a back-propagation algorithm and a pseudo-Hessian matrix has been developed in the frequency domain or the Laplace domain.

However, the speed information derivation technique using the conventional waveform inversion is mainly performed in the frequency and Laplacian domain. To solve this problem, it is necessary to convert the time domain seismic data into the frequency or Laplacian domain, have.

In addition, since a large number of matrix calculations are required to perform waveform inversion in the frequency or Laplace domain, the calculation becomes complicated.

KR 10-0565773 B1 KR 10-1219746 B1 KR 10-1318994 B1 KR 10-1290332 B1

SUMMARY OF THE INVENTION An object of the present invention is to provide a method for quickly and accurately extracting underground speed information by simple calculation.

According to an embodiment of the present invention, there is provided a method of deriving an underground velocity using an acoustic wave, the method comprising: inputting an initial velocity model for inputting an observed velocity and an initial velocity information; (S200) calculating a physical property of the underground medium based on the velocity model and generating a numerical modeling data by estimating a sound source waveform from the observed acoustic wave data; (S300) calculating a slant direction using back propagation based on the numerical modeling data and the observed seismic wave data, and constructing a pseudo Hessian matrix; And (S400) calculating and updating the velocity information using the slant direction and a pseudo-Hessian matrix.

Preferably, in step (S100), the observed acoustic wave data is acquired in a time domain.

Preferably, in the step (S100), the initial velocity model is P wave velocity information of an underground medium set to an arbitrary value.

Preferably, in step S200, the physical properties of the underground medium are calculated using the Lame constant based on the P wave velocity information.

Preferably, in step (S200), the sound source waveform is deconvoluted,

(여기서, O(t)는 관측데이터, G(t)는 그린함수(green function), S(t)는 음원 파형을 나타낸다.)

(T) is the observation function, G (t) is the green function, and S (t) is the sound source waveform.

Based on the observed seismic wave data.

Preferably, in step (S200), the numerical modeling data is generated in the time domain,

(여기서, v_x,v_z는 속도, τ_ik(i,k=x,z)는 응력, f_x,f_z는 실제파에 의한 음원이며, r_ik(i,k=x,z)는 인장력에 의한 음원이다.)

(Wherein, v _x, v _z is the _{speed, τ ik (i, k =} x, z) is the stress, f _x, f _z is the source of the actual _{wave, r ik (i, k =} x, z) is a It is a sound source by tensile force.)

Is calculated on the basis of the relationship between the velocity and the stress.

Preferably, in step (S200), numerical modeling data generation is performed by using a lattice finite difference method.

Preferably, the step (S300) includes the steps of (S320) calculating a back propagated wave field based on the numerical modeling data and the observed seismic wave data,

(S340) The following equation

(여기서, 가상음원은

항과

항이다.)

(Here, the virtual sound source is

Section

.

Generating a virtual sound source vector using the virtual sound source vector,

(S360) Using the wave field and the virtual sound source vector, the following equation

(여기서,

은 영 지연 상호상관(zero-lag cross-correlation)을 나타낸다.)

(here,

Indicates a zero-lag cross-correlation.

And obtaining a similar Hessian matrix to the slope direction as shown in FIG.

Preferably, the wave length back propagated in the step (S320) is expressed by the following equation

(여기서, B(t)가 역전파된 파동장이며,T는 총 기록 시간, t는 시간 단계이다. )

(Where B (t) is the wave field back propagated, T is the total recording time, and t is the time step).

And is obtained as the residual of the observed acoustic wave data and the numerical modeling data.

Preferably, in the step (S400), the following equation

(Wherein, a ^{V ★ = [V, V,} ..., V], and V _n is a virtual sound source in the n-th lattice point vector, and p ⁱ is a step of calculating the i-th repetition, s is the speed change value, ns is Number of sound sources, w is white noise.)

The speed information is updated as shown in FIG.

According to the present invention, it is possible to quickly and accurately derive the underground velocity information through the inverse of the acoustic wave waveform in the time domain.

In addition, applying the back propagation method and the pseudo Hessian matrix to the inverse of the acoustic wave in the time domain has the effect of deriving the underground velocity model by simple calculation.

1 is a flowchart for explaining a method of deriving an underground speed information according to an embodiment of the present invention,
FIG. 2 is a block diagram specifically explaining the step S200 of FIG. 1,
3 is a block diagram specifically explaining the step S300 of FIG. 1,
4 is a graph showing a marmousi2 model according to an embodiment of the present invention,
5 is a graph illustrating an initial velocity model according to an embodiment of the present invention,
FIG. 6 is a graph illustrating a waveform inversed velocity model according to an embodiment of the present invention,
7 is a graph illustrating a result of sound source estimation according to an embodiment of the present invention,
8 is a graph showing an acoustic wave signal generated in a marmousi2 model according to an embodiment of the present invention,
9 is a graph showing an acoustic wave signal generated in a waveform-inversed velocity model according to an embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Brief Description of Drawings FIG. 1 is a block diagram of a computer system according to an embodiment of the present invention; FIG. 2 is a block diagram of a computer system according to an embodiment of the present invention; FIG.

Before describing the present invention in detail, the present invention will be described in further detail with reference to the accompanying drawings.

1) Similar to the back propagation technique in time domain, Hessian matrix

The objective function for waveform inversion in the time domain is expressed as Equation 1 below.

Here, E (p) is the objective function, v _o is the seismic data acquired in the field, and v _c is the data modeled from the arbitrarily assumed velocity model.

In order to obtain a velocity model that minimizes the objective function, the slope direction with respect to velocity is expressed as Equation (2) by differentiating Equation (1) with respect to velocity.

는 편미분 파동장을 나타낸다.here,

Indicates a partial derivative wave field.

The partial wave length field is expressed by the following equation (3) as a green function and a convolution of a virtual sound source, and a backward propagated wave field in the inverse time structure correction is expressed by Equation (4) below.

Here, G is a green function, V is a virtual sound source vector, * is a convolution operator, and d (T-t) is observation data.

To apply to the waveform inversion, d (Tt) in Equation (4) can be rewritten as the following Equation (5) by replacing with residual which is the difference between v _o and v _c .

Where B (t) is the wave field back propagated, T is the total recording time, and t is the time step.

When the equation (3) is applied to the equation (2), it is expressed as the following equation (6).

When the back propagated wave field defined by Equation (5) is applied to Equation (6), the oblique direction can be expressed as Equation (7) below.

은 영 지연 상호상관(zero-lag cross-correlation)을 나타낸다.here,

Represents a zero-lag cross-correlation.

In order to obtain the objective function, the direction of inclination at every lattice point is expressed by Equation (8) below.

Here, V ^* = [V, V, ... , V], and V _n is a virtual sound source vector at the nth lattice point. By using only the diagonal elements of the pseudo Hessian matrix using the virtual sound source vector, the maximum steepening direction can be constructed.

Therefore, the velocity value can be updated as shown in Equation (9) below using the back propagation method and the similar Hessian matrix.

Here, p ⁱ is an i-th iterative calculation step, s is a velocity change value, ns is the number of sound sources, and w is white noise.

2) Virtual sound source vector using 2-dimensional lattice modeling

In the present invention, a virtual sound source vector is constructed based on a two-dimensional time-domain excitation-lattice modeling technique. The relationship between the velocity and the stress in the time domain can be expressed by Equation (10), Equation (11), Equation (12), Equation (13), Equation (14).

Here, v _x, v _z is the _{speed, τ ik (i, k =} x, z) is the stress, f _x, f _z is the source of the actual _{wave, r ik (i, k =} x, z) is a tensile force .

The virtual sound source can be represented by the partial derivative of the wave field for each property variable. Accordingly, in the present invention, Equations (10) to (14) can be partially differentiated with respect to lambda (?) In the Lame constant and can be expressed as Equations (15) and (16) below.

항과

항이다.Here, the virtual sound source

Section

Respectively.

3) Sound source estimation in time domain

A seismic wave source waveform is obtained by using a deconvolution method for inversion of an acoustic wave waveform. The elastic wave observation data can be expressed by the following Equation (17).

Here, O (t) denotes observation data, G (t) denotes a green function, and S (t) denotes a sound source waveform. When the least squares deconvolution method is applied to obtain the sound source waveform, the least squared error is expressed by Equation (18) below.

When the least squares error is differentiated with respect to the source in order to calculate the sound source waveform, the cross correlation between the green function and the observation value and the autocorrelation of the green function are shown. It is possible to estimate the sound source waveform using the Levinson algorithm using the characteristics of the triplet matrix.

Hereinafter, detailed description will be made for the performance of the present invention with reference to the accompanying drawings based on the above-mentioned equations.

As shown in FIG. 1, a method of deriving an underground velocity information according to an embodiment of the present invention includes inputting data at step S100, generating a numerical modeling data at step S200, And generating a pseudo Hessian matrix (S400), and calculating and updating the velocity information.

First, the step (S100) will be described.

In operation S100, an initial velocity model for inputting the observed seismic wave data and the initial velocity information is input. Here, it is preferable that the observed acoustic wave data is acquired in a time domain. And, the initial velocity model is P wave velocity information of underground medium set to arbitrary value, and magnitude and velocity values are generated considering characteristics of exploration environment and underground medium. The P wave is a wave recorded first in the earthquake of the body wave passing through the inside of the earth, and it is well known to those skilled in the art, and thus a detailed description thereof will be omitted.

Next, the step (S200) will be described.

2, the physical property of the underground medium is calculated based on the velocity model, and a numerical modeling data is generated by estimating a sound source waveform from the observed acoustic wave data.

Here, it is preferable to calculate the physical properties of the underground medium using the Lame constant based on the P wave velocity information. At this time, the Lame constant is calculated by P wave velocity, S wave velocity and density according to the following equation (19), and S wave velocity and density are fixed constant values.

On the other hand, the sound source waveform is deconvoluted and derived from the observed acoustic wave data based on Equation (18), and the numerical modeling data is generated by using the calculated properties of the underground medium and the estimated sound source.

The numerical modeling data is generated in the time domain and is calculated on the basis of the relationship between the velocities and the stresses in Equations (10) to (14). Here, the numerical modeling data generation is characterized by numerical analysis using a lattice finite difference method.

Next, the step (S300) will be described.

In step S300, the gradient direction is calculated using the back propagation based on the numerical modeling data and the observed seismic data, and a pseudo Hessian matrix is constructed.

3, the step S300 includes calculating a backward propagation wave field based on the numerical modeling data and the observed seismic wave data S340, And generating a virtual sound source vector using Equation (16); and (S360) calculating a slanting direction and a pseudo Hessian matrix using Equation (7) using the wave field and the virtual sound source vector.

Meanwhile, the wave field back propagated in step S320 can be obtained as a residual of the observed acoustic wave data and the numerical modeling data as shown in Equation (5).

Next, the step (S400) will be described.

In operation S400, the velocity information is calculated and updated using the slanting direction and a similar Hessian matrix.

Here, in step S400, the velocity information may be updated by using a pseudo-Hessian matrix similar to the slant direction as in Equation (9).

Meanwhile, the execution step according to the embodiment of the present invention described above is repeatedly performed until the initial set repetition number is reached.

In the above-described embodiment of the present invention, first, the seismic wave data is generated for the marmousi2 velocity model as shown in FIG. 4, and the initial velocity model is generated as shown in FIG. 5 by smoothing the actual velocity model. The generated seismic wave data and the initial velocity model are used to carry out the present invention.

The waveform inversion results are shown in FIG. 6, and the result of the sound source estimation is shown in FIG. Referring to FIG. 7, it can be seen that the actual sound source waveform and the sound source waveform inversely matched each other. Figure 6, which is the inversion result, and Figure 4, the actual speed model, show that the two results are almost similar. 8, the artificial seismic data is generated using the marmousi2 model and the artificial seismic data is generated using the inversed velocity model as shown in FIG. Comparing FIG. 8 and FIG. 9, it can be seen that the two data are almost identical. The marmousi2 model applied to the embodiment of the present invention is widely used in the related art to verify related research and technology, and it is possible to confirm the performance and to secure the reliability of the present invention through the results of the present embodiment.

According to the above-described method of deriving the underground speed information according to the embodiment of the present invention, the following effects can be obtained.

First, it is possible to derive velocity information accurately and quickly through the inversion of seismic waves in time domain.

Second, it is possible to derive subsurface velocity model by simple calculation by applying the back propagation method and the similar Hessian matrix to the inverse of the seismic wave in the time domain.

Thirdly, it can be applied to the analysis of underground physical properties in geophysical field and to visualization of underground structures.

Fourth, it can be applied to the related fields such as ground survey, seismic survey, nondestructive survey, and historical site exploration.

The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the claims of the invention to be described below may be better understood. The embodiments described above are susceptible to various modifications and changes within the technical scope of the present invention by those skilled in the art. These various modifications and changes are also within the scope of the technical idea of the present invention and will be included in the claims of the present invention described below.

Claims (10)

A method for deriving an underground velocity information using an acoustic wave,
(S100) inputting an initial velocity model for inputting the observed acoustic wave data and the initial velocity information;
(S200) calculating a physical property of the underground medium based on the velocity model and generating a numerical modeling data by estimating a sound source waveform from the observed acoustic wave data;
(S300) calculating a slant direction using back propagation based on the numerical modeling data and the observed seismic wave data, and constructing a pseudo Hessian matrix; And
(S400) calculating and updating the velocity information using the slant direction and a pseudo-Hessian matrix,
In step S200, the numerical modeling data is generated in the time domain,
The following equation

(Wherein, v _x, v _z is the _{speed, τ ik (i, k =} x, z) is the stress, f _x, f _z is the source of the actual _{wave, r ik (i, k =} x, z) is a It is a sound source by tensile force.)
Wherein the calculation is based on the relationship between the velocity and the stress of the ground. The method according to claim 1,
Wherein the observed seismic wave data is acquired in a time domain in step (S100). The method according to claim 1,
Wherein the initial velocity model in the step (S100) is P wave velocity information of an underground medium set to an arbitrary value. The method of claim 3,
Wherein the physical properties of the underground medium are calculated using the Lame constant based on the P wave velocity information in step S200. The method according to claim 1,
In step S200, the sound source waveform is deconvoluted,

(T) is the observation function, G (t) is the green function, and S (t) is the sound source waveform.
And deriving from the observed seismic wave data based on the measured data. delete The method according to claim 1,
Wherein the generation of the numerical modeling data is performed by using a lattice finite difference method in the step (S200). A method for deriving an underground velocity information using an acoustic wave,
(S100) inputting an initial velocity model for inputting the observed acoustic wave data and the initial velocity information;
(S200) calculating a physical property of the underground medium based on the velocity model and generating a numerical modeling data by estimating a sound source waveform from the observed acoustic wave data;
(S300) calculating a slant direction using back propagation based on the numerical modeling data and the observed seismic wave data, and constructing a pseudo Hessian matrix; And
(S400) calculating and updating the velocity information using the slant direction and a pseudo-Hessian matrix,
The step (S300)
(S320) calculating a back propagated wave field based on the numerical modeling data and the observed seismic wave data;
(S340) The following equation

(Here, the virtual sound source is

Section

.
Generating a virtual sound source vector using the virtual sound source vector,
(S360) Using the wave field and the virtual sound source vector, the following equation

(here,

Indicates a zero-lag cross-correlation.
And obtaining a similar Hessian matrix to the slope direction as shown in FIG. 9. The method of claim 8,
The wave field back propagated in the above step (S320)

(Where B (t) is the wave field back propagated, T is the total recording time, and t is the time step).
And calculating the residual velocity of the observed acoustic wave and the numerical modeling data. A method for deriving an underground velocity information using an acoustic wave,
(S100) inputting an initial velocity model for inputting the observed acoustic wave data and the initial velocity information;
(S200) calculating a physical property of the underground medium based on the velocity model and generating a numerical modeling data by estimating a sound source waveform from the observed acoustic wave data;
(S300) calculating a slant direction using back propagation based on the numerical modeling data and the observed seismic wave data, and constructing a pseudo Hessian matrix; And
(S400) calculating and updating the velocity information using the slant direction and a pseudo-Hessian matrix,
In the step S400,

(Wherein, a ^{V ★ = [V, V,} ..., V], and V _n is a virtual sound source in the n-th lattice point vector, and p ⁱ is a step of calculating the i-th repetition, s is the speed change value, ns is Number of sound sources, w is white noise.)
And the speed information is updated as shown in FIG.

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