CN111399045B - Post-stack density inversion method based on statistical constraint - Google Patents
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Abstract
The invention discloses a statistical constraint-based post-stack density inversion method, which adopts post-stack data with relatively high signal-to-noise ratio, takes a convolution model as a basis, and adopts a step-by-step iteration mode to obtain a global optimal density inversion result. The method comprises the following specific steps: the method comprises the following steps: obtaining a statistical regression coefficient of longitudinal waves and density on the well by using a statistical regression method; step two: establishing a density and longitudinal wave statistical relationship as a constrained objective function; step three: and (5) inverting the longitudinal wave and the density by adopting an iterative optimization algorithm. The invention utilizes the post-stack earthquake to carry out density inversion, the signal-to-noise ratio of post-stack earthquake data relative to pre-stack gather data is much higher, and inversion can be directly carried out without excessive preprocessing. The method adopts the simultaneous inversion of the longitudinal waves and the density, balances the contribution degree of different parameter magnitudes to the post-stack earthquake by taking the statistical relationship between the longitudinal waves and the density as a regular constraint condition, and can still obtain a more reliable density inversion result when the regression correlation degree of the longitudinal waves and the density is lower.
Description
Technical Field
The invention relates to the technical field of oil-gas exploration, in particular to a post-stack density inversion method based on statistical constraints.
Background
In the field of geophysical exploration, density is an inherent attribute for characterizing a reservoir, and can be used for judging lithology, analyzing components of minerals, and directly calculating porosity for evaluating the reservoir if the mineral components and the fluid density are known. Therefore, the density of the subsurface medium is one of the important parameters for geophysical exploration.
The core of reservoir prediction is seismic inversion, a reservoir inversion method taking post-stack seismic data as basic data is an important method for reservoir prediction, and when the post-stack seismic attribute analysis and inversion are carried out, only the relation between amplitude and longitudinal wave velocity or one parameter can be generally concerned. The inversion of the post-stack seismic data cannot give parameters of the physical properties and the fluid characteristics of reactants such as Poisson ratio, longitudinal and transverse wave velocity ratio and the like, and research on the physical properties and the fluid characteristics of reservoirs is limited. With the increasing difficulty of exploration and development, the task of completing the oil-gas exploration of lithologic strata by using the post-stack seismic reservoir prediction technology is more and more difficult.
At present, the main method for acquiring density parameters from seismic data is to utilize AVO inversion, and the theoretical basis of the AVO inversion is the Zoeppritz equation and the approximate expression thereof. When the AVO approximation formula is used for three-parameter inversion, the longitudinal wave velocity in the inversion is usually more accurate, but the accuracy of the transverse wave velocity and the density is poorer. Because the amplitude data of small offset is mainly controlled by the seismic longitudinal wave velocity, the medium-distance and far-distance offset amplitude is sensitive to the density parameter, and the large-offset seismic data is needed for obtaining the density parameter by AVO inversion. The AVO inversion method is high in resolution and relatively mature, but the inversion uncertainty is high, the result cannot be accurately predicted, the inversion parameters are not reliable enough, and the inversion effect is not ideal.
Disclosure of Invention
The invention aims to provide a post-stack density inversion method based on statistical constraint to solve the problems in the background technology.
In order to solve the technical problems, the invention provides the following technical scheme:
a post-stack density inversion method based on statistical constraint comprises the following steps:
the method comprises the following steps: obtaining statistical regression coefficients of the data of the Vp and the rho of the longitudinal wave on the well by using a statistical regression method, wherein the statistical regression relationship of the density and the longitudinal wave is as follows: p AVpBA, B is a statistical regression relation coefficient, and A is a, B is B calculated by using a least square method;
step two: establishing an objective function taking the statistical relationship between the density and the longitudinal wave as a regular constraint, and adopting the following formula:
the formula: l ═ d (WR-d)T(WR-d)+λ(ρ-aVpb)T(ρ-aVpb) (2-1)
The formula:
a and b in the formula (2-1) are statistical regression relation coefficients a and b in the step one; w is the wavelet matrix and R is the reflection coefficient;
thirdly, inverting the longitudinal wave Vp and the density rho by adopting an iterative optimization algorithm:
solving the objective function formula (2-1) to obtain the solution of the objective function as:
the formula:
where m is [ Vp, ρ ]]，G＝W[JacobiVp,Jacobiρ]，C＝[aCe b,Ce]，CeThe method comprises the steps that a variance matrix with normalized density inversion variation is adopted, lambda is a coefficient of a regular constraint condition, d is post-stack seismic observation data, d is WR, W is a wavelet matrix, and R is a reflection coefficient;
the formula:
the formula:
the formula:
the formula:
the formula:
the formula:
the Jacobi matrix is a partial derivative matrix of the reflection coefficient R relative to the longitudinal wave and the density, formulas (3-2) to (3-7) are specifically used for calculating the Jacobi matrix, the length of the post-stack seismic observation data is n, wherein the superscript "-" refers to an upper interface, and the superscript "+" refers to a lower interface;
the operation process of the algorithm is explained by utilizing the artificially synthesized data as follows:
step 301: inputting data by an algorithm, wherein the data input by the algorithm comprises post-stack seismic observation data, a longitudinal wave model, a density model and statistical regression relation coefficients a and b of longitudinal waves and density on a well;
step 302: d-WR (d-WR) difference value between forward result of convolution of the primary values of longitudinal waves and density and the wavelets and post-stack seismic observation data is obtained0；
Step 303: calculating a Jacobi matrix of reflection coefficients to the longitudinal waves and the density according to formulas (3-2) to (3-7), combining the Jacobi matrices of the longitudinal waves and the density by using G ═ W [ JacobiVp, Jacobi rho ], indirectly obtaining the change rate of the earthquake about the longitudinal waves and the density, combining statistical regression relation coefficients a and b of the longitudinal waves and the density, substituting the coefficients into a formula (3-1), and solving the change quantity DeltaVp and Deltarho of the longitudinal waves and the density corresponding to the difference value of the forward-evolution earthquake observation data and the post-stack earthquake observation data;
step 304: updating the inversion longitudinal wave and density results: vp is defined as Vp0+△Vp，ρ＝ρ0+△ρ；
Step 305: substituting the longitudinal wave and density inversion results obtained in the step 304 into a formula (2-2) and a convolution model d-WR to be subjected to forward modeling to synthesize new post-stack seismic observation data;
step 306: judging whether accumulated errors between forward seismic data and post-stack seismic observation data meet a set magnitude, if so, stopping iterative disturbance, ending inversion, and outputting a result; and if the accumulated error between the forward seismic data and the post-stack seismic observation data does not reach the set magnitude, traversing steps 302-305 to continue iterative perturbation.
In the above, in step 301, the reflection coefficient of the post-stack seismic data is calculated by using the formula (2-2) for the longitudinal wave velocity and the density, and the post-stack seismic data d is convolved with the wavelets to synthesize the post-stack seismic observation data d.
In the above, in step 301, the longitudinal wave model and the density model respectively use the low-frequency portions of the longitudinal wave and the density on the well as the initial values of the disturbance of the iterative algorithm.
In the above step 301, the coefficients of the uphole longitudinal waves and the density satisfy an exponential statistical regression relationship, and are A, B, and a is a, and B is B calculated by a least square method.
Compared with the prior art, the invention has the following beneficial effects: the method adopts a step-by-step iteration method for solving, firstly, a longitudinal wave model and a density model are used as initial models for inversion, the error between the convolution forward record and the post-stack seismic observation data d is calculated, the variable quantity of the longitudinal wave and the density is calculated by using a formula (3-1), the inversion result of the longitudinal wave and the density is updated, if the error between the convolution forward record and the post-stack seismic observation data is small enough, the iteration disturbance is stopped, and the inversion process is ended.
The method is different from the traditional pre-stack gather AVO density inversion which is limited by inversion accuracy and parameter contribution degree, the method utilizes post-stack seismic observation data to perform density inversion, the signal-to-noise ratio of post-stack seismic observation data relative to pre-stack gather data is high, and inversion can be directly performed without excessive preprocessing. The method adopts two-dimensional simultaneous inversion of longitudinal waves and density, balances the contribution degree of different parameter magnitudes to observation data by taking the statistical relationship between the longitudinal waves and the density as a regular constraint condition, and can still obtain a more reliable density inversion result when the regression correlation degree of the longitudinal waves and the density is lower on the basis of a convolution model.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a graph showing experimental data in an example of the present invention, wherein FIG. 1(a) is a theoretical synthetic record; fig. 1(b) is a theoretical synthetic record plus noise.
FIG. 2 is a cross-plot of longitudinal wave Vp and density ρ of the test data in the embodiment of the present invention.
FIG. 3 is a graph of wavelet test data in an embodiment of the present invention.
FIG. 4 is a second example of experimental data according to the present invention, wherein FIG. 4(a) is a longitudinal wave model; fig. 4(b) is a density model.
Fig. 5 is a result of experimental inversion in the example of the present invention, in which fig. 5(a) is a longitudinal wave inversion comparison and fig. 5(b) is a density inversion comparison.
FIG. 6 is an algorithmic flow chart of the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a statistical constraint-based post-stack density inversion method, which adopts post-stack seismic observation data with relatively high signal-to-noise ratio, takes a convolution model as a basis, and adopts a step-by-step iteration mode to obtain a global optimal density inversion result. The method comprises the following specific steps:
the method comprises the following steps: obtaining a statistical regression coefficient of the data of the longitudinal waves and the density on the well by using a statistical regression method;
step two: establishing a density and longitudinal wave statistical relationship as a target function of regular constraint;
step three: and (5) inverting the longitudinal wave and the density by adopting an iterative optimization algorithm.
The method comprises the following specific steps:
the method comprises the following steps of firstly, obtaining statistical regression coefficients of data of the aboveground longitudinal wave Vp and the density rho by using a statistical regression method: the density and the longitudinal wave accord with an exponential statistical regression relation: p AVpB。
And performing least square regression calculation by using the longitudinal wave (reciprocal of acoustic wave time difference) and the density measured on the well, and obtaining statistical regression relation coefficients A, B and B.
Step two, establishing an objective function with the statistical relationship between the density rho and the longitudinal wave Vp as constraints, wherein the formula is as follows:
the formula: l ═ d (WR-d)T(WR-d)+λ(ρ-aVpb)T(ρ-aVpb) (2-1)
The formula:
in the above formula (2-1), a and b are coefficients of statistical regression relationship between Vp and ρ obtained by statistical regression over the well, W is a wavelet matrix, and R is a reflection coefficient. The regression relation between the longitudinal waves and the density is added into the objective function so as to balance the magnitude of the longitudinal waves and the density and the contribution degree to the stacked seismic observation data, and the objective is obtained by optimizing and inverting.
Thirdly, inverting the longitudinal wave Vp and the density rho by adopting an iterative optimization algorithm:
solving the objective function formula (2-1) to obtain the solution of the objective function as:
the formula:
where m is [ Vp, ρ ]]，G＝W[JacobiVp,Jacobiρ]，C＝[aCe b,Ce]，CeThe method is characterized in that the method is a variance matrix of density inversion variation normalization, lambda is a coefficient of a regular constraint condition, d is post-stack seismic observation data, d is WR, W is a wavelet matrix, and R is a reflection coefficient.
The Jacobi matrix is a partial derivative matrix of the reflection coefficient R with respect to the longitudinal wave and the density, formulas (3-2) to (3-7) are specifically calculated Jacobi matrices, the length of post-stack seismic observation data is n, wherein the superscript "-" refers to an upper interface, and the superscript "+" refers to a lower interface.
The algorithm design flow chart according to fig. 6 shows: the operation process of the algorithm is explained by utilizing artificially synthesized data: the method comprises algorithm input data and an algorithm iterative inversion process. The algorithm input data includes: the method comprises the steps of post-stack seismic recording, a longitudinal wave model, a density model and statistical regression relation coefficients a and b of longitudinal waves and density on a well. The iterative inversion process of the algorithm comprises the following steps: (1) calculating the difference Deltad between the forward result of convolution of the initial values of the longitudinal wave and the density and the wavelet convolution shown in figure 3 and the post-stack seismic observation data figure 1(b)0(ii) a (2) Calculating the Jacobian matrix of the reflection coefficient to the longitudinal wave and the density according to the formula (3-2) to the formula (3-7), and using G ═ W [ JacobiVp, Jacobi rho [ ]]Combining the Jacobian matrixes of the longitudinal waves and the density to indirectly obtain the change rate of the post-stack seismic observation data about the longitudinal waves and the density, substituting the change rate into a formula (3-1) by combining the statistical relation parameters (a and b) of the longitudinal waves and the density on the well, and solving the variable quantity delta Vp and delta rho of the longitudinal waves and the density corresponding to the difference value of the forward evolution seismic observation data and the post-stack seismic observation data; (3) updating the inversion longitudinal wave and density results: vp is defined as Vp0+△Vp，ρ＝ρ0+ DELTAρ; (4) substituting the longitudinal wave and density inversion results obtained in the step (3) into a formula (2-2) and a convolution model d ═ WR, forward-computing to synthesize new post-stack seismic observation data, stopping iterative disturbance if the accumulated error between the forward-computing seismic data and the post-stack seismic observation data is small enough or meets a set magnitude, finishing inversion, and outputting results, wherein the graph 5 is the comparison between the inversion results and accurate values; if the accumulated error does not reach the satisfactory level, traversing (1)And (4) continuing iterative perturbation.
Post-stack seismic observation data: the reflection coefficient is calculated by using the formula (2-2) according to the velocity and the density of the longitudinal wave, the reflection coefficient and the wavelet convolution are synthesized into the post-stack seismic observation data d as shown in figure 1(a), and random noise is added to the post-stack seismic observation data for testing the robustness of the algorithm as shown in figure 1 (b). Longitudinal wave model and density model: respectively adopting the low-frequency parts of the uphole longitudinal wave and the solid lines with the density shown in fig. 5(a) and 5(b), wherein fig. 5(a) is longitudinal wave inversion comparison, the solid line is accurate longitudinal wave speed, and the dotted line is inverted longitudinal wave; fig. 5(b) is a density inversion comparison, the solid line is the exact density, and the dotted line is the inverted density.
As an initial value for the iterative algorithm perturbation, as shown in fig. 4. Statistical relation coefficient of the uphole longitudinal wave and the density: and (3) calculating to obtain statistical regression relation coefficients a and b by using a least square method, wherein the figure 2 is an intersection graph of the longitudinal wave and the density on the well.
The method adopts a step-by-step iteration method for solving, firstly, a longitudinal wave model and a density model are used as initial models for inversion, the error between the convolution forward record and the post-stack seismic observation data d is calculated, the variable quantity of the longitudinal wave and the density is calculated by using a formula (3-1), the inversion results of the longitudinal wave and the density are updated, if the error between the convolution forward record and the observation data is small enough, the iteration disturbance is stopped, and the inversion process is ended.
The method is different from the traditional pre-stack gather AVO density inversion which is limited by inversion accuracy and parameter contribution degree, the method utilizes post-stack earthquake to perform density inversion, the signal-to-noise ratio of post-stack earthquake data to pre-stack gather data is high, and inversion can be directly performed without excessive preprocessing. The method adopts two-dimensional simultaneous inversion of longitudinal waves and density, balances the contribution degree of different parameter magnitudes to observation data by taking the statistical relationship between the longitudinal waves and the density as a regular constraint condition, and can obtain a more reliable density inversion result on the basis of a convolution model.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the 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 (4)
1. A post-stack density inversion method based on statistical constraint is characterized by comprising the following steps:
the method comprises the following steps: obtaining statistical regression coefficients of the data of the Vp and the rho of the longitudinal wave on the well by using a statistical regression method, wherein the statistical regression relationship of the density and the longitudinal wave is as follows: p AVpBA, B is a statistical regression relation coefficient, and A is a, B is B calculated by using a least square method;
step two: establishing an objective function taking the statistical relationship between the density and the longitudinal wave as a regular constraint, and adopting the following formula:
the formula: l ═ d (WR-d)T(WR-d)+λ(ρ-aVpb)T(ρ-aVpb) (2-1)
The formula:
a and b in the formula (2-1) are statistical regression relation coefficients a and b in the step one; w is the wavelet matrix and R is the reflection coefficient;
thirdly, inverting the longitudinal wave Vp and the density rho by adopting an iterative optimization algorithm:
solving the objective function formula (2-1) to obtain the solution of the objective function as:
the formula:
where m is [ Vp, ρ ]]，G＝W[JacobiVp,Jacobiρ]，C＝[aCe b,Ce]，CeIs a variance matrix with normalized density inversion variation, lambda is a coefficient of a regular constraint condition, d is post-stack seismic observation data, d is WR, W is a wavelet matrix, and R is the inverseA coefficient of radiation;
the formula:
the formula:
the formula:
the formula:
the formula:
the formula:
the Jacobi matrix is a partial derivative matrix of the reflection coefficient R relative to the longitudinal wave and the density, formulas (3-2) to (3-7) are specifically used for calculating the Jacobi matrix, the length of the post-stack seismic observation data is n, wherein the superscript "-" refers to an upper interface, and the superscript "+" refers to a lower interface;
the operation process of the algorithm is explained by utilizing the artificially synthesized data as follows:
step 301: inputting data by an algorithm, wherein the data input by the algorithm comprises post-stack seismic observation data, a longitudinal wave model, a density model and statistical regression relation coefficients a and b of longitudinal waves and density on a well;
step 302: d-WR (distance between the initial value of the longitudinal wave and the density) and the forward result of the wavelet convolution and the difference between the post-stack seismic observation data0；
Step 303: calculating a Jacobi matrix of reflection coefficients to the longitudinal waves and the density according to formulas (3-2) to (3-7), combining the Jacobi matrices of the longitudinal waves and the density by using G ═ W [ JacobiVp, Jacobi rho ], indirectly obtaining the change rate of the earthquake about the longitudinal waves and the density, substituting the change rate into the formula (3-1) by combining the statistical regression relation coefficients a and b of the longitudinal waves and the density, and solving the change quantities delta Vp and delta rho of the longitudinal waves and the density corresponding to the difference value of the forward-modeling and the post-stack earthquake observation data;
step 304: updating the inversion longitudinal wave and density results: vp is defined as Vp0+ΔVp，ρ＝ρ0+Δρ；
Step 305: substituting the longitudinal wave and density inversion results obtained in the step 304 into a formula (2-2) and a convolution model d-WR to be subjected to forward modeling to synthesize new post-stack seismic observation data;
step 306: judging whether accumulated errors between forward seismic data and post-stack seismic observation data meet a set magnitude, if so, stopping iterative disturbance, ending inversion, and outputting a result; and if the accumulated error between the forward seismic data and the post-stack seismic observation data does not reach the set magnitude, traversing steps 302-305 to continue iterative perturbation.
2. The method of claim 1, wherein in step 301, the post-stack seismic data is convolved with wavelets to form post-stack seismic survey data d by calculating a reflection coefficient using the formula (2-2) for the longitudinal wave velocity and the density.
3. The method according to claim 2, wherein in step 301, the compressional wave model and the density model respectively use the low frequency parts of the compressional wave and the density on the well as initial values of the perturbation of the iterative algorithm.
4. The method as claimed in claim 2, wherein in step 301, the longitudinal wave and the density on the well satisfy an exponential statistical regression relationship, the coefficient is A, B, and a and B are calculated by a least square method.
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