CN110471112A - Dipping bed interval velocity exception inversion method based on stack velocity variation - Google Patents
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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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- G01V1/303—Analysis for determining velocity profiles or travel times
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- G—PHYSICS
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Abstract
Dipping bed interval velocity exception inversion method based on stack velocity variation, its core is to provide a kind of dipping bed overall situation Interval Velocity Inversion method based on the fitting of stacking slowness orthogonal function, this method is to obtain the weighting coefficient of basic function by the orthogonal function inverting of fitting, it is abnormal to find out interlayer slowness, it is superimposed using slowness is abnormal with background value, to directly find out the inversion method of tilted stratum interval velocity, the initiative inversion method proposed for tilted stratum interval velocity, improves the order of accuarcy of rate pattern.
Description
Technical Field
The invention relates to the technical field of seismic inversion layer velocity, in particular to a method for inverting the abnormal velocity of a dip layer based on stacking velocity change.
Background
Longitudinal waves propagate in an anisotropic medium, the properties of the longitudinal waves have certain change rules, and various parameters of the medium can be inverted by using the change rules. The transverse velocity change is a special type of anisotropy, and the layer velocity of the inclined stratum can be inverted by using the change rule of the longitudinal wave attribute. The longitudinal wave attribute utilized by the invention is mainly travel time difference.
The travel time difference of the longitudinal wave is generated due to the change of the velocity when the longitudinal wave passes through the velocity anomaly, and the impulse response function of the superposition slowness change of the anomaly can be obtained by utilizing the travel time difference of the longitudinal wave generated when the longitudinal wave passes through the anomaly.
It is well known that formation lateral velocity anomalies can cause variations in the stacking velocities. When the abnormal body is within the coverage range of the CMP gather, seismic waves pass through the abnormal body to cause different time differences due to sudden speed changes, so that the superposition speed is distorted. Using the Dix equation for horizontal formations or the Shah equation for dipping formations in the case of stacked velocity distortions will yield the wrong layer velocities. However, the accuracy of the slice velocity is critical for proper depth imaging. The linear impulse response function of the horizontal formation is invariant to spatial position and thus can be inverted in the wavenumber domain. However, in the case of a dipping formation, the path followed by each longitudinal wave ray within the CMP gather will also vary as the depth and thickness of each layer varies along the line. The change of the travel path causes the impulse response function of the stratum to change when the stratum moves along the measuring line, and the wave number domain inversion method based on the SVD is not suitable any more because the calculated impulse response function is the characteristic changing along with the space.
For the tilt model, since the lateral layer slowness anomaly is finite, it can be approximated with a set of basis functions. Therefore, aiming at the space change characteristic of a linear impulse response system of the inclined stratum, the invention provides a new method for inverting the weighting coefficient of the basis function based on the least square method so as to solve the interlayer slowness abnormity.
The traditional method for inverting the stratum velocity is established under the condition that the stratum is horizontal, but the stratum under the actual condition is mostly an inclined stratum, so that the invention of the inversion method for inverting the stratum velocity of the inclined stratum is urgently needed.
Disclosure of Invention
The invention provides a method for inverting the abnormal speed of a sloping layer based on the change of stacking speed, which comprises the steps of solving an impulse response function of the abnormal change of CMP stacking slowness caused by the abnormal transverse speed in the first step; and the second step is to approximate the slowness abnormality function to a linear combination of a group of basis functions, to multiply the group of basis functions and the impulse response function to obtain an approximate function of the superposition slowness change, to invert the weighting coefficient of the basis functions based on the least square method to obtain the interlayer slowness abnormality, and to superpose the slowness abnormality and the background value, thereby directly obtaining the velocity of the inclined stratum.
According to one aspect of the invention, a method for inverting the anomaly of the layer velocity of a dip layer based on the change of the stacking velocity is provided, which comprises the following steps:
step S1, obtaining an impulse response function of the model, and solving the impulse response of the transverse speed abnormity to the CMP superposition slowness abnormity change based on the change of the CMP gather along the measuring line space position;
and step S2, assuming that the slowness anomaly function is approximate to a linear combination of a group of basis functions, multiplying the group of basis functions with the impulse response function to obtain an approximate function of the change of the superposition slowness, inverting the weighting coefficient of the basis functions based on the least square method to obtain the interlayer slowness anomaly, and superposing the slowness anomaly and a background value to directly obtain the velocity of the inclined stratum.
On the basis of the above scheme, preferably, the objective function is:
h, C ═ B; and,
C＝(C1,C2,…,Cn)T；
wherein,
c1＝(c1,0,c1,1,…,c1,k)T；
xjrepresenting the spatial position of the CMP in the lateral direction;
xj-irepresenting the spatial position of the anomaly in the transverse direction;
l represents a reflection horizon;
l' represents the horizon of the anomaly;
k represents k basis function elements;
p represents the number of CMP with abnormal stacking slowness;
m represents from xjThe number of CMP intervals from the position to the leftmost side of the measuring line;
pk(xj-i) Indicating that the anomaly is located at xj-iThe kth basis function of (1);
indicating that the reflective layer is l and CMP is located at xjA superimposed slowness change approximation function of (a);
representing an impulse response function Rll′(xj-i,xj) And a basis function pk(xj-i) Superposition of (2);
Rll′(xj-i,xj) The spatial position of the abnormal body is xj-iAnd l', CMP is located at xjA superimposed slowness change impulse response function of (a);
drawings
FIG. 1 is a model for determining a tilted horizon impulse response function according to the present invention;
FIG. 2 is a four-layer tilt model for the calculation of the present invention;
FIG. 3 is a comparison of the present invention using ray tracing (dashed line) and derivation (solid line) to find the stacking velocity;
FIG. 4 is a comparison of the true (solid line) and derived (dashed line) slice velocity functions of the four-slice tilt model of the present invention;
FIG. 5 is a comparison of the true (solid line) and derived (dashed line) slice velocity functions of the four-slice tilt model of FIG. 2 assuming no velocity anomaly for the fourth slice of FIG. 2;
FIG. 6 is a flow chart of an inversion method of the anomaly of the velocity of the inclined layer based on the change of the stacking velocity.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Referring to fig. 6, the present invention provides a method for inverting an anomaly of a layer velocity of a dip layer based on a change in a stacking velocity, including the following steps:
step S1, obtaining an impulse response function of the model, and solving the impulse response of the transverse speed abnormity to the CMP superposition slowness abnormity change based on the change of the CMP gather along the measuring line space position;
and step S2, assuming that the slowness anomaly function is approximate to a linear combination of a group of basis functions, multiplying the group of basis functions with the impulse response function to obtain an approximate function of the change of the superposition slowness, inverting the weighting coefficient of the basis functions based on the least square method to obtain the interlayer slowness anomaly, and superposing the slowness anomaly and a background value to directly obtain the velocity of the inclined stratum.
For further explanation of the technical solution of the present invention, how to obtain the impulse response function of the model and how to invert the weighting coefficients of the basis functions by the least square method in steps S1 and S2 of the present invention will be described in detail below.
As shown in FIG. 1, we assumeWhen the columnar abnormal body exists in the ith layer, the reflection of the interface of the mth layer is recorded, and the influence of the abnormal body on the superposition slowness is researched from the interface of the mth layer. Assuming again that the CMP gather centered at point j, the unit value ω appears at j-i before point j0The anomaly width is deltax and the anomaly height is the vertical thickness of the l-th layer at j-i. When the kth ray in the gather passes through the abnormal body, the length of the ray segment in the abnormal body is asThere is therefore a certain time delay, denoted as
This time delay results in a change in the superimposed slowness, denoted as
Δωk＝μkskΔtk,l (2)
μkIs a linear model response of Lucas, expressed as
Due to k1And k2The ray also passes through the anomaly and is due to unit slowness anomaly omega0The total variation of the superimposed slowness at the j position is
Rm,l(xj-i,xj) The reflecting layer is represented as the m-th layer, and the spatial coordinate of the abnormal body is xj-iAnd the l layer, CMP being at xjThe impulse response function of the superimposed slowness change.
Similarly, the impulse response function at j + i is expressed as
Because R ism,l(xj-i,xj) Is not equal to Rm,l(xj+i,xj) So that Rm,l(xi,xj) Is an asymmetric function of the j position, and the length of the ray passing through the anomaly changes due to the change of the j position, so that the R is said to bem,l(xj-i,xj) Is a spatially varying function.
It is assumed that the slowness abnormality functions of the respective layers are represented by a set of basis functions
Thus, the superposition slowness change approximation function of the l-th layer can be expressed as
Changing the summation order can be expressed as
To superimpose the slowness-change approximation function,representing an impulse response function Rll′(xj-i,xj) And a basis function pk(xj-i) And (3) superposition. For the n-layer tilt model, the standard Q is written as
Where n represents the number of formation layers and P represents the number of CMP with superimposed slowness anomalies. Similarly, the coefficient c is calculated by solving the minimum value probleml′,kIs shown as
Then there is a standard Q pair cl′,kThe derivation should be zero, expressed as
Namely, it is
Thus obtaining
k＝0,1,2,……,m (12)
After certain treatment, the coefficient c is obtained by solving the following linear equation systeml,k
Wherein,is defined as
C1Is a vector, defined as
c1＝(c1,0,c1,1,…,c1,k)T (15)
Is a vector, defined as
Equation (13) can be simplified to H · C ═ B (17)
And,
C＝(C1,C2,…,Cn)T (19)
if it is known or assumed that there is no anomaly in a certain layer (e.g., the l-th layer), the l-th column and l-th row matrices in the super matrix H are deleted, and the l-th vectors in C and B are deleted.
The method given above is now tested and the present invention uses the Chebyshev function as the basis function. FIG. 2 is a diagram of a four-layer tilt model for calculation according to the present invention, and the subsequent comparison diagram is a diagram of the results obtained by calculating the model. Fig. 3 is a comparison of the ray tracing technique (dotted line) and the inversion method (solid line) proposed by the present invention to find the stacking velocity, and comparing the two curves shows that the two curves fit well in the shallow layer, and have a certain error and a small error range in the deep layer, which indicates that it is advisable to find the stacking velocity by using the inversion method. Fig. 4 is a comparison of the real (solid line) and derived (dashed line) layer velocity functions of the four-layer tilt model, and comparing the two curves shows that the two curves fit well in the shallow layer, and that a certain error exists in the deep layer, particularly a large error occurs in the fourth layer, because the information provided by the CMP in the fourth layer is little, and the large error occurs only under the influence of the first three layers. If it is found that there is no abnormality in the true layer-by-layer speed of the fourth layer, the 4 th column and the 4 th row in the H matrix can be removed directly from the super matrix H, and the 4 th vectors in C and B can be removed at the same time, so that fig. 5 can be obtained. It has been found that the accuracy of inverting the velocity of a layer can be improved by directly mapping the matrix and vector of the layer when it is known that no velocity anomaly exists in the layer. The feasibility of the method can be well verified from the analysis, and the method is the optimal method for improving the inversion of the layer-by-layer velocity of the inclined layer at present.
Finally, the method of the present application is only a preferred embodiment and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. The method for inverting the anomaly of the velocity of the inclined layer based on the change of the stacking velocity is characterized by comprising the following steps of:
step S1, obtaining an impulse response function of the model, and solving the impulse response of the transverse speed abnormity to the CMP superposition slowness abnormity change based on the change of the CMP gather along the measuring line space position;
and step S2, assuming that the slowness anomaly function is approximate to a linear combination of a group of basis functions, multiplying the group of basis functions with the impulse response function to obtain an approximate function of the change of the superposition slowness, inverting the weighting coefficient of the basis functions based on the least square method to obtain the interlayer slowness anomaly, and superposing the slowness anomaly and a background value to directly obtain the velocity of the inclined stratum.
2. The method for inverting the anomaly of the layer-by-layer velocity of the dip based on the change of the stacking velocity according to claim 1, wherein the objective function is as follows:
h, C ═ B; and,
C＝(C1，C2，…，Cn)T；
wherein,
c1＝(c1，0，c1，1，…，c1，k)T；
xjrepresenting the spatial position of the CMP in the lateral direction;
xj-irepresenting the spatial position of the anomaly in the transverse direction;
l represents a reflection horizon;
l' represents the horizon of the anomaly;
k represents k basis function elements;
p represents the number of CMP with abnormal stacking slowness;
m represents from xjThe number of CMP intervals from the position to the leftmost side of the measuring line;
pk(xj-i) Indicating that the anomaly is located at xj-iThe kth basis function of (1);
indicating that the reflective layer is l and CMP is located at xjA superimposed slowness change approximation function of (a);
representing an impulse response function Rll′(xj-i，xj) And a basis function pk(xj-i) Superposition of (2);
Rll′(xj-i，xj) The spatial position of the abnormal body is xj-iAnd l', CMP is located at xjOf a stack ofThe slowness change impulse response function is added.
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| JP2006349491A (en) * | 2005-06-15 | 2006-12-28 | Central Res Inst Of Electric Power Ind | Identifying method of inclined base structure using micromotion array exploration method |
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| WO2017196718A1 (en) * | 2016-05-12 | 2017-11-16 | Baker Hughes Incorporated | Geosteering by adjustable coordinate systems and related methods |
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| CN109459790A (en) * | 2017-09-06 | 2019-03-12 | 中国石油化工股份有限公司 | For coal measure strata seismic velocity field method for building up and system |
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