CN110471112A - Dipping bed interval velocity exception inversion method based on stack velocity variation - Google Patents

Abstract

The core of the layer-by-layer velocity anomaly inversion method based on the stacking velocity change is to provide a global layer velocity inversion method based on the stacking slowness orthogonal function fitting. By deriving the weighted coefficients of the basis functions, the interlayer slowness anomaly is obtained, and the inversion method for directly obtaining the layer velocity of the inclined formation is obtained by superimposing the slowness anomaly and the background value, and a pioneering method for the layer velocity of the inclined formation The inversion method improves the accuracy of the velocity model.

Description

Velocity Anomaly Inversion Method Based on Stacking Velocity Variation in Inclined Layers

technical field

The invention relates to the technical field of seismic inversion layer velocity, and more particularly, relates to an anomalous inversion method of layer velocity anomalies in inclined layers based on stacking velocity changes.

Background technique

The longitudinal wave propagates in the anisotropic medium, and the properties of the longitudinal wave have certain changing rules. Using these changing rules, various parameters of the medium can be inverted. Lateral velocity variation is a special type of anisotropy, and the layer velocity of inclined formation can be inverted by using the variation law of P-wave attributes. The longitudinal wave attribute utilized in the present invention is mainly travel time difference.

Among them, the longitudinal wave travel time difference is the travel time difference caused by the change of velocity when the longitudinal wave passes through the abnormal body. We can obtain the impulse response function of the superimposed slowness change of the abnormal body by using the travel time difference generated by the longitudinal wave passing through the abnormal body.

It is well known that the anomaly of formation lateral velocity will cause the change of stacking velocity. When the anomalous body is within the coverage of CMP gathers, when the seismic wave passes through the anomalous body, different time differences will be caused due to the sudden change of velocity, which will lead to the distortion of stacking velocity. Using the Dix equation for horizontal formations or the Shah equation for inclined formations with superimposed velocity distortions will result in incorrect layer velocities. How accurate the slice velocity is, however, is critical for correct depth imaging. The linear impulse response function of the horizontal formation does not change with the change of the spatial position, so it can be inverted in the wavenumber domain. However, in the case of inclined formations, since the depth and thickness of each layer vary along the survey line, the path traveled by each P-wave ray in the CMP gather will also change. The change of the travel path leads to the change of the impulse response function of the formation when moving along the survey line. Since the calculated impulse response function is a feature that varies with space, the wave number domain inversion method based on SVD decomposition is no longer applicable.

For the tilt model, since the transverse layer slowness anomaly is finite, it can be approximated by a set of basis functions. Therefore, aiming at the spatial variation characteristics of the linear impulse response system of inclined formations, the present invention proposes a new method of inverting the weighting coefficients of the basis functions based on the least squares method to obtain the interlayer slowness anomaly.

The traditional method of retrieving layer velocity is based on the condition that the formation is horizontal, but most of the actual formations are inclined formations. Therefore, it is urgent to invent an inversion method for retrieving the layer velocity of inclined formations.

Contents of the invention

The present invention provides an abnormal inversion method of velocity anomalies in inclined layers based on the change of stacking velocity. The first step is to obtain the impulse response function of the abnormal change of CMP stacking slowness caused by the abnormal transverse velocity; the second step is to approximate the slowness anomaly function as The linear combination of a set of basis functions, the product of a set of basis functions and the impulse response function can be used to obtain the approximate function of the superimposed slowness change, and the weighted coefficient of the basis function is inverted based on the least square method to obtain the interlayer slowness anomaly. By superimposing the slowness anomaly and the background value, the layer velocity of the inclined formation can be obtained directly.

According to one aspect of the present invention, a method for inversion of velocity anomalies in inclined layers based on stacked velocity changes is provided, comprising the following steps:

Step S1, obtain the impulse response function of the model, and calculate the impulse response of the anomalous transverse velocity to the anomalous change of the CMP stacking slowness based on the change of the spatial position of the CMP gather along the survey line;

Step S2, assuming that the slowness anomaly function is approximated as a linear combination of a set of basis functions, and multiplying a set of basis functions with the impulse response function can obtain an approximate function of the superimposed slowness change, and inverting the weighted basis functions based on the least squares method The interlayer slowness anomaly is obtained by using the coefficient, and the layer velocity of the inclined formation is directly obtained by superimposing the slowness anomaly and the background value.

Preferably on the basis of the above scheme, the objective function is:

H·C=B; and,

C=(C ₁ ,C ₂ ,...,C _n ) ^T ;

in,

c ₁ =(c _1,0 ,c _1,1 ,...,c _1,k ) ^T ;

x _j represents the spatial position of the CMP in the lateral direction;

x _ji represents the spatial position of the abnormal body in the horizontal direction;

l represents the reflection horizon;

l' indicates the layer of the abnormal body;

k represents k basis function elements;

P represents the number of CMPs with superimposed slowness abnormalities;

M represents the number of CMP intervals from the x _j position to the leftmost side of the survey line;

p _k (x _ji ) means that the abnormal body is located in the kth basis function of x _ji ;

Indicates that the reflective layer is l, the approximate function of the superimposed slowness change of the CMP at x _j ;

Indicates the superposition of the impulse response function R _ll′ (x _ji , x _j ) and the basis function p _k (x _ji );

R _ll′ (x _ji , x _j ) represents the superimposed slowness variation impulse response function of the reflective layer at l, the spatial positions of the abnormal body at x _ji and l′, and the CMP at x _j ;

Description of drawings

Fig. 1 is that the present invention is used for seeking the model of inclined layer impulse response function;

Fig. 2 is the four-layer inclination model that the present invention is used for calculating;

Fig. 3 is the comparison that the present invention utilizes ray tracing (dotted line) and derivation (solid line) to obtain superposition velocity;

Fig. 4 is the comparison of the real (solid line) and the deduced (dotted line) layer velocity function of the four-layer tilt model of the present invention;

Fig. 5 is the comparison of the real (solid line) and deduced (dotted line) layer velocity functions of the four-layer tilt model when the fourth layer of Fig. 2 is assumed to have no velocity anomalies in the present invention;

Fig. 6 is a flow chart of the method for inversion of velocity anomalies in inclined layers based on stacking velocity changes according to the present invention.

Detailed ways

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

Please refer to Fig. 6, the present invention provides a method for inversion of velocity anomalies in inclined layers based on stacked velocity changes, including the following steps:

Step S1, obtain the impulse response function of the model, and calculate the impulse response of the anomalous transverse velocity to the anomalous change of the CMP stacking slowness based on the change of the spatial position of the CMP gather along the survey line;

Step S2, assuming that the slowness anomaly function is approximated as a linear combination of a set of basis functions, and multiplying a set of basis functions with the impulse response function can obtain an approximate function of the superimposed slowness change, and inverting the weighted basis functions based on the least squares method The interlayer slowness anomaly is obtained by using the coefficient, and the layer velocity of the inclined formation is directly obtained by superimposing the slowness anomaly and the background value.

In order to further illustrate the technical solution of the present invention, how to obtain the impulse response function of the model and how to use the least squares method to invert the weighting coefficients of the basis functions in steps S1 and S2 of the present invention will be described in detail below.

As shown in Figure 1, we assume that when there is a columnar anomalous body in the l-layer, the reflection of the m-th layer interface is recorded, let us study the effect of the anomalous body on the stacking slowness from the m-th layer interface. Assume again that in the CMP gather centered at point j, a slowness anomaly with unit value ω0 appears _at ji before point j, the width of the anomaly body is Δx, and the height of the anomaly body is the vertical thickness of layer l at ji. When the kth ray in the gather passes through the abnormal body, the length of the ray segment in the abnormal body is Therefore, there is a certain time delay, expressed as

This time delay causes a change in the superposition slowness, expressed as

Δω _k = μ _k s _k Δt _k,l (2)

μ _k is the linear model response of Lucas, expressed as

Since the k ₁ and k ₂ rays also pass through the anomalous body, and because of the unit slowness anomaly ω ₀ , the total change in superposition slowness at position j is

R _m,l (x _ji , x _j ) means that the reflection layer is the mth layer, the abnormal body space coordinates are x _ji and the lth layer, and the impulse response function of the superimposed slowness change of the CMP at x _j .

Similarly, the impulse response function at j+i is expressed as

Because R _m,l (x _ji ,x _j ) is not equal to R _m,l (x _j+i ,x _j ), so R _m,l (x _i ,x _j ) is an asymmetric function of position j, and because With the change of the position of j, the length of the ray passing through the abnormal body will also change accordingly, so R _m,l (x _ji ,x _j ) is a function that varies with space.

Assume that the slowness anomaly function of each layer is represented by a set of basis functions

Therefore, the approximate function of the stacking slowness change in layer l can be expressed as

Change the order of summation, which can be expressed as

is the approximate function of superposition slowness change, Indicates the superposition of the impulse response function R _ll′ (x _ji , x _j ) and the basis function p _k (x _ji ). For an n-level tilted model, the standard Q is written as

Among them, n represents the number of formation layers, and P represents the number of CMPs with superimposed slowness anomalies. Similarly, the coefficient c _l′,k is calculated by solving the minimum problem, expressed as

Then there is the partial derivative of standard Q to c _l′,k should be zero, expressed as

which is

thus get

k=0,1,2,...,m (12)

After certain processing, the coefficients c _l,k are obtained by solving the following linear equations

in, defined as

C ₁ is a vector defined as

c ₁ =(c _1,0 ,c _1,1 ,...,c _1,k ) ^T (15)

is a vector defined as

Equation (13) can be simplified as H·C=B (17)

and,

C=(C ₁ ,C ₂ ,…,C _n ) ^T (19)

If it is known or assumed that there is no abnormality in a certain layer (such as the lth layer), delete the lth column and lth row matrix in the super matrix H, and delete the lth vector in C and B at the same time.

Now to test the method given above, the present invention uses Chebyshev functions as basis functions. Fig. 2 is the four-layer tilting model used for calculation in the present invention, and the following comparative figures are results obtained by calculating the model. Fig. 3 is the comparison that utilizes ray-tracing technology (dotted line) and the inversion method (solid line) that the present invention proposes to obtain stacking velocity, compares two kinds of curves and can find that two curves fit very well in shallow layer, exist certain in deep layer and the error range is very small, which shows that it is advisable to use this inversion method to calculate the stacking velocity. Figure 4 is a comparison of the real (solid line) and derived (dotted line) layer velocity functions of the four-layer tilt model. Comparing the two curves, it can be found that the two curves fit well in the shallow layer, but there are certain errors in the deep layer, especially in the The large error in the fourth layer is because the information provided by the CMP in the fourth layer is very little, and it is affected by the first three layers, which produces a large error. It is observed that there is no abnormality in the real fourth layer speed, then you can directly delete the fourth column and fourth row matrix in H in the super matrix H, and delete the fourth vector in C and B at the same time, you can get the graph 5. It can be found that when it is known that there is no velocity anomaly in a certain layer, the matrix and vector of the layer can be directly obtained, which will improve the accuracy of layer velocity inversion. From the above analysis, the feasibility of the present invention can be well verified, and it is currently the best method for improving the velocity inversion of inclined layers.

Finally, the method of the present application is only a preferred embodiment, and is not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims (2)

1. The method for inverting velocity anomalies in inclined layers based on stacked velocity changes, is characterized in that it comprises the following steps: Step S1, obtain the impulse response function of the model, and calculate the impulse response of the anomalous transverse velocity to the anomalous change of the CMP stacking slowness based on the change of the spatial position of the CMP gather along the survey line; Step S2, assuming that the slowness anomaly function is approximated as a linear combination of a set of basis functions, and multiplying a set of basis functions with the impulse response function can obtain an approximate function of the superimposed slowness change, and inverting the weighted basis functions based on the least squares method The interlayer slowness anomaly is obtained by using the coefficient, and the layer velocity of the inclined formation is directly obtained by superimposing the slowness anomaly and the background value. 2. The layer-by-layer velocity anomaly inversion method based on stacking velocity changes as claimed in claim 1, wherein the objective function is: H·C=B; and, C = (C ₁ , C ₂ , . . . , C _n ) ^T ; in, c ₁ =(c _1,0 ,c _1,1 ,...,c _1,k ) ^T ; x _j represents the spatial position of the CMP in the lateral direction; x _ji represents the spatial position of the abnormal body in the horizontal direction; l represents the reflection horizon; l' indicates the layer of the abnormal body; k represents k basis function elements; P represents the number of CMPs with superimposed slowness abnormalities; M represents the number of CMP intervals from the x _j position to the leftmost side of the survey line; p _k (x _ji ) means that the abnormal body is located in the kth basis function of x _ji ; Indicates that the reflective layer is l, and the CMP is located at the approximate function of the superposition slowness change at x _j ; Indicates the superposition of impulse response function R _ll′ (x _ji , x _j ) and basis function p _k (x _ji ); R _ll′ (x _ji , x _j ) represents the superimposed slowness variation impulse response function where the reflective layer is l, the spatial positions of the abnormal body are x _ji and l′, and the CMP is located at x _j .