CN113466962A - Transverse wave prediction method and system based on Gaussian process regression - Google Patents
Transverse wave prediction method and system based on Gaussian process regression Download PDFInfo
- Publication number
- CN113466962A CN113466962A CN202110765085.2A CN202110765085A CN113466962A CN 113466962 A CN113466962 A CN 113466962A CN 202110765085 A CN202110765085 A CN 202110765085A CN 113466962 A CN113466962 A CN 113466962A
- Authority
- CN
- China
- Prior art keywords
- data set
- function
- gaussian process
- training data
- wave velocity
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 116
- 238000012549 training Methods 0.000 claims abstract description 70
- 238000009826 distribution Methods 0.000 claims abstract description 58
- 238000012360 testing method Methods 0.000 claims abstract description 48
- 238000010606 normalization Methods 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 abstract description 6
- 230000006870 function Effects 0.000 description 68
- 238000003860 storage Methods 0.000 description 14
- 238000004590 computer program Methods 0.000 description 9
- 238000010586 diagram Methods 0.000 description 9
- 230000005251 gamma ray Effects 0.000 description 8
- 239000011435 rock Substances 0.000 description 7
- 238000012545 processing Methods 0.000 description 6
- 238000011160 research Methods 0.000 description 6
- 238000010801 machine learning Methods 0.000 description 5
- 239000011148 porous material Substances 0.000 description 4
- 238000013528 artificial neural network Methods 0.000 description 3
- 239000011159 matrix material Substances 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 239000010459 dolomite Substances 0.000 description 2
- 229910000514 dolomite Inorganic materials 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 239000010440 gypsum Substances 0.000 description 2
- 229910052602 gypsum Inorganic materials 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 238000011002 quantification Methods 0.000 description 2
- 238000004445 quantitative analysis Methods 0.000 description 2
- 238000013076 uncertainty analysis Methods 0.000 description 2
- 229910021532 Calcite Inorganic materials 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000013398 bayesian method Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 229910052500 inorganic mineral Inorganic materials 0.000 description 1
- 239000011707 mineral Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000013139 quantization Methods 0.000 description 1
- 239000004576 sand Substances 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
- 230000001502 supplementing effect Effects 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
Landscapes
- Physics & Mathematics (AREA)
- Life Sciences & Earth Sciences (AREA)
- General Life Sciences & Earth Sciences (AREA)
- General Physics & Mathematics (AREA)
- Geophysics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Complex Calculations (AREA)
Abstract
本发明公开了一种基于高斯过程回归的横波预测方法及系统，根据测井参数岩性的复杂度将数据集划分为训练数据集和测试数据集；根据划分的训练数据集中的S波和P波的速度特征确定高斯过程中的均值函数和协方差函数，得到高斯过程回归模型；将划分的训练数据集输入到高斯过程回归模型中，通过最小化边际似然函数的负对数得到对应的超参数；根据先验定义，结合测试数据集中的纵波速度，建立训练数据集和测试数据集的联合高斯分布；根据联合高斯分布确定预测点的后验分布，将超参数代入得到预测井的横波速度。本发明计算中效率高、精度高、稳定性好。
The invention discloses a shear wave prediction method and system based on Gaussian process regression. According to the complexity of logging parameters and lithology, a data set is divided into a training data set and a test data set; The velocity characteristics of the wave determine the mean function and covariance function in the Gaussian process, and the Gaussian process regression model is obtained; the divided training data set is input into the Gaussian process regression model, and the corresponding negative logarithm of the marginal likelihood function is minimized. Hyperparameters: According to the prior definition, combined with the longitudinal wave velocity in the test data set, the joint Gaussian distribution of the training data set and the test data set is established; the posterior distribution of the predicted points is determined according to the joint Gaussian distribution, and the shear wave of the predicted well is obtained by substituting the hyperparameters speed. The calculation of the invention has high efficiency, high precision and good stability.
Description
Technical Field
The invention belongs to the technical field of exploration geophysical research, and particularly relates to a transverse wave prediction method and system based on Gaussian process regression.
Background
In seismic exploration, whether the collected data is accurate or not plays a crucial role in exploration results. The longitudinal wave velocity and the transverse wave velocity are key parameters in seismic exploration, and have important significance for underground structure explanation and reservoir description. The longitudinal wave velocity can be obtained by a conventional acoustic logging method, but because the exploration cost of the transverse wave velocity is too high, the information of the transverse wave velocity is often lacked in actual logging data.
In the process of identifying the lithology and the pore medium of the reservoir, the identification precision of the reservoir can be effectively improved by adding the transverse wave velocity information and the elastic parameter information. In order to be able to describe the complex lithologic reservoir more clearly, longitudinal and transverse wave velocities are indispensable parameter information. At present, prestack seismic inversion, prestack seismic attribute analysis AVA, AVO processing and the like become effective technical means for describing reservoirs and oil reservoirs, accurate longitudinal and transverse wave velocities are necessary basic data in logging data, and most of the logging data lack transverse wave velocity logging data at present, so that the significance of accurately calculating the transverse wave velocity in wells without transverse wave velocity logging data is great. The traditional shear wave velocity prediction method mainly comprises an empirical formula method and a rock physics modeling method. The traditional empirical formula method is to obtain a relation formula of the longitudinal wave velocity by using statistical analysis, and predict the corresponding transverse wave velocity by using the known longitudinal wave velocity. For example, in 1985, Castagna et al proposed a famous formula of "mudstone line" based on the velocity relationship between longitudinal and transverse waves in clastic rock. Xu et al in 2010 combined with Kuster's formula, differential effective medium theory (DEM) and Gassmann's equation, proposed a method for estimating longitudinal and transverse wave velocities using porosity, shale content, etc. The traditional empirical formula method is easy to implement and high in calculation efficiency, but the fitting relational expression only reflects the statistical rule of the logging data of specific rocks, and large errors exist in practical application.
The rock physical modeling method is mainly used for accurately calculating the elastic parameters of the rock by building a rock physical model and calculating the shear wave velocity based on the relationship between the elastic parameters and the shear wave velocity. And (3) performing deformation on the Pride model and the Lee model by Luohui and the like, providing a deformation P-L model, and predicting the transverse wave velocity by utilizing seismic inversion. In 2009, Xu et al established an Xu-Payne model by considering the influence of different pore types (inter-granular pores, holes and cracks) on the velocity of an elastic wave on the basis of an Xu-White model and combining a K-T theory and a differential effective medium theory. The volume parameters (mineral content, porosity and water saturation) input as the conventional petrophysical model and the petrophysical model parameters such as the pore aspect ratio are difficult to obtain, so that the conventional petrophysical modeling method cannot meet the technical requirement of shear wave prediction. The accuracy of predicting the shear wave velocity by using the rock physics modeling method is high, but the algorithm is complex, the needed parameters are more, and the calculation efficiency is low.
With the development of machine learning algorithms, a great deal of application is achieved in the prediction of well logging data. In 2014, Bagheripour et al proposed a fast and accurate method, namely the ACE neural network, which utilized existing well logging data to predict shear wave velocity. In the same year, Maleki et al estimated the shear wave velocity using empirical Correlation (Correlation coeffient) and two robust machine learning methods, Support Vector Regression (SVR) and BP neural network (BPNN). In 2017, Mehrgini et al propose an Elman-based artificial neural network method for predicting the transverse wave velocity. In 2020, Azadeport et al propose a transverse wave velocity prediction method combining petrophysics and machine learning. However, none of the above works provides uncertainty analysis of the shear wave prediction results and requires a large amount of training data to train the network.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method and a system for predicting shear wave based on gaussian process regression, which can predict the velocity of shear wave more effectively by using a smaller data set and provide uncertain quantitative analysis of the prediction result.
The invention adopts the following technical scheme:
a transverse wave prediction method based on Gaussian process regression comprises the following steps:
s1, dividing the data set into a training data set and a testing data set according to the complexity of the lithology of the logging parameters;
s2, determining a mean function and a covariance function in the Gaussian process according to the speed characteristics of the S wave and the P wave in the training data set divided in the step S1 to obtain a regression model of the Gaussian process;
s3, inputting the training data set divided in the step S1 into the Gaussian process regression model obtained in the step S2, and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function;
s4, establishing a combined Gaussian distribution of the training data set and the test data set according to prior definition and by combining the longitudinal wave velocity in the test data set divided in the step S1;
and S5, determining posterior distribution of the predicted points according to the combined Gaussian distribution obtained in the step S4, and substituting the hyperparameter obtained in the step S3 to obtain the transverse wave velocity of the predicted well.
Specifically, in step S2, first, a mean function and a covariance function are empirically selected, and then the velocities of the longitudinal wave and the transverse wave of the training data set are expressed in the form of gaussian process distribution, that is, the velocity v of the transverse wave is expressedSoFunction f (v) ofPo) Obeying a mean value of m (v)Po) Covariance of k (v)Po,v'Po) The gaussian process of (1).
Further, the mean function m (x) and the covariance function k (x, x') are defined as:
m(x)＝E[f(x)]
wherein f (x) is a latent function and represents the S-wave velocity corresponding to the P-wave velocity x, E is a mathematical expectation, sigma represents the signal variance, and liRepresenting the length scale, x, of the ith dimensioniD is the dimension of the variable x, which is known data of the ith dimension.
Specifically, step S3 specifically includes:
the longitudinal wave velocity v of the well log in the training data set TPoAnd transverse wave velocity vSoInputting the parameters into a Gaussian process regression model, and determining a hyperparameter initial value and iteration times in the Gaussian process regression model; the hyperparameter in the covariance function is determined by minimizing the negative logarithm of the marginal likelihood function.
Further, by minimizing the negative logarithm of the marginal likelihood function, the quasi-Newton optimizer L-BFGS is adopted to optimize to obtain the hyperparameters sigma and L as follows:
where-logp (f | x) is the negative logarithm of the marginal likelihood function,
for fitting training data;
is a penalty term;
is a normalization constant.
Specifically, step S4 specifically includes:
according to the prior definition, the mean value of the training data set and the test data set is established by combining the longitudinal wave velocity and the transverse wave velocity in the test data set
Covariance of
Combined Gaussian distribution of
K represents K (v)Po,vPo)。
Further, a joint Gaussian distribution
Comprises the following steps:
wherein, f (v)Po) Function values for training data sets，f(vP) For testing data set function values, N is a normal distribution.
Specifically, in step S5, the posterior distribution of the test data set includes a posterior mean and a posterior variance, the super-parameter obtained in step S3 is substituted into the posterior mean to obtain the transverse wave velocity of the predicted well, and the super-parameter obtained in step S3 is substituted into the posterior variance to obtain the point-by-point variance of the predicted point.
Further, the posterior distribution is specifically as follows:
f*|x*,x,f～N(k(x*,x)K-1f,k(x*,x*)-k(x*,x)K-1k(x,x*))
wherein f is*Test point x under the data x, f of the prior test*K denotes the square exponential kernel function defined above.
Another technical solution of the present invention is a transverse wave prediction system based on gaussian process regression, including:
the data module divides the data set into a training data set and a testing data set according to the complexity of the lithology of the logging parameter;
the regression module is used for determining a mean value and a covariance function in a Gaussian process according to the speed characteristics of S waves and P waves in the training data set divided by the data module to obtain a Gaussian process regression model;
the training module is used for inputting the training data set divided by the data module into a Gaussian process regression model obtained by the regression module and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function;
the joint module is used for establishing joint Gaussian distribution of the training data set and the test data set according to the prior definition and by combining the longitudinal wave speed in the test data set divided by the data module;
and the prediction module is used for determining posterior distribution of the predicted points according to the combined Gaussian distribution obtained by the combination module and substituting the hyper-parameters obtained by the training module into the predicted transverse wave velocity.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a transverse wave prediction method based on Gaussian process regression, which is characterized in that transverse wave velocity prediction is carried out by utilizing longitudinal wave velocity, and hyper-parameters suitable for logging data of a work area are obtained by training a Gaussian process regression model; because the logging data come from the same research area, the hyper-parameters obtained by training are suitable for the logging data of the work area; the invention does not need a large amount of training data, and can predict the transverse waves of other wells by only using the data of one well in the work area as a training data set. In addition, the invention can provide uncertainty quantification of the prediction result besides the prediction result of the transverse wave.
Further, the purpose of selecting the mean function and the covariance function is emphasized by supplementing the content set in step S2, and the purpose is to obtain the prior distribution of the training data, which is convenient for obtaining the posterior distribution subsequently. Because the relationship of the prior distribution, the posterior distribution and the likelihood function is:
where p (f) is the prior distribution, p (x | f) is the likelihood distribution, and p (f | x) is the posterior probability.
Furthermore, the selection of a mean function and a covariance function is determined, and the mean function is set as a zero mean function, so that the calculation is simple and convenient; the covariance function is set as a square exponential covariance function because this kernel is not only one of the commonly used kernels, but also has good stability.
Furthermore, the iteration times of the Gaussian process regression model suitable for the training data are determined by comparing the training effect and experience for many times, and then the hyperparameters in the covariance function are determined, so that the Gaussian process regression model of the training set is determined.
Furthermore, the adopted quasi-Newton optimizer L-BFGS has better convergence, the hyper-parameters can be quickly obtained by using the optimizer, and then a well-trained Gaussian process regression model is determined, so that the subsequent prediction is facilitated.
Further, f (v) is obtained by the definition of regression model and Gaussian processPo) And f (v)P) For the purpose of unionThe edge distribution property of the resultant probability distribution is further obtained as f (v)P) I.e. posterior distribution.
Further, a joint Gaussian distribution
Form of covariance matrix visually displaying joint probability distribution, combined with definition of square exponential covariance function
Making the computation of the covariance matrix simpler.
Further, the setting of step S5 specifies the mean and the posterior variance of the posterior distribution, facilitates the analysis of the prediction results from two angles, and it can be understood that the calculation of the mean and the posterior variance makes a relationship with the hyper-parameter.
Further, a specific expression of the posterior distribution is given, wherein the mean and the posterior variance are in the form of: k (x)*,x)K-1f and k (x)*,x*)-k(x*,x)K-1k(x,x*) It can be seen that either the mean or the a posteriori variance is related to the covariance function determined in this test, according to the definition of the squared exponential covariance function
Therefore, the hyper-parameters sigma and l obtained by optimization are substituted to calculate the posterior mean value and the posterior variance.
In conclusion, the Gaussian process regression model adopted by the invention is not only a probability model with universality and resolvability, but also can well complete the prediction of logging data by depending on a small data set and give uncertainty analysis of prediction results, and has high efficiency, high precision and good stability in calculation.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a scattergram of compressional and shear wave velocities;
FIG. 2 is a scatter plot of gamma ray vs. transverse wave velocity;
FIG. 3 is a scatter plot of density versus shear wave velocity;
FIG. 4 is a bar graph of the correlation coefficients of compressional velocity, gamma ray and density with shear velocity;
FIG. 5 is a plot of training data and lithology for three wells, where (a) is the compressional velocity for well C, (B) is the shear velocity for well C, (C) is the lithology for well A, (d) is the lithology for well B, and (e) is the lithology for well C;
FIG. 6 is a plot of the shear wave prediction for well A, where (a) is the measured compressional velocity, (b) is the shear velocity, (c) is the variance of the GPR prediction, (d) is the error of the prediction, (e) is the relative error of the prediction, and (f) is the lithology of well A;
FIG. 7 is a plot of the shear wave prediction for well B, where (a) is the measured compressional velocity, (B) is the shear velocity, (c) is the variance of the GPR prediction, (d) is the error of the prediction, (e) is the relative error of the prediction, and (f) is the lithology of well B;
FIG. 8 is a flow chart of the present invention;
FIG. 9 is a schematic diagram of the application of the Gaussian process regression method to well logging data.
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 some, not all, embodiments of the present invention. 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.
In the description of the present invention, it should be understood that the terms "comprises" and/or "comprising" indicate the presence of the stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The invention provides a transverse wave prediction method based on Gaussian process regression, which is a novel research approach for accurately predicting transverse wave velocity based on longitudinal wave velocity by testing logging data with complex lithology by adopting the Gaussian process regression method belonging to the machine learning category, and can provide not only a prediction result of the transverse wave velocity but also uncertainty quantitative analysis of the prediction result. This is of great significance for practical applications.
Referring to fig. 8 and 9, a method for predicting transverse waves based on gaussian process regression according to the present invention includes the following steps:
s1, determining a data set;
the research area is located at the front edge of the Longmen mountain in the Sichuan basin, and the target layer is an important marine exploration and development layer system in the area. Log data for the three wells used in the experiment were collected in the study area and are indicated at A, B and C, respectively.
The log data for each well includes 5 parameters: depth (Depth), Density (Density), Gamma ray (Gamma ray), longitudinal velocity (P-velocity), transverse velocity (S-velocity), and Lithology (Lithology).
By comparing lithological parameters of three wells, the logging data of a well C with more complex lithological properties is taken as a training data set T, and the longitudinal wave velocity and the transverse wave velocity of the well C are respectively expressed by vPo、vSoRepresents; the well log data of the well A, B is used as a test data set P, and the longitudinal and transverse wave velocities are respectively represented by vP、vSAnd (4) showing.
S2, determining a mean function and a covariance function in the Gaussian process;
a gaussian distribution describes a random variable, whereas a gaussian process is a collection of random variables, where any finite number has a joint gaussian distribution. Gaussian process regression is an important machine learning method based on probability and small data sets, and is actually a bayesian method relying on a gaussian process to learn.
Gaussian process f (x) is completely defined by the mean function and covariance function:
f(x)～GP(m(x),k(x,x')) (1)
wherein the mean function m (x) and the covariance function k (x, x') are defined as:
m(x)＝E[f(x)] (2)
k(x,x')＝E[(f(x)-m(x))(f(x')-m(x'))] (3)
generally, the mean function is set to a zero mean function; the covariance function is set as a squared exponential covariance function, one of the most commonly used covariance functions, and is expressed as follows:
where σ represents the signal variance, the hyperparameter liRepresenting the length scale of the ith dimension.
For predicting the transverse wave velocity, firstly, a mean value and a covariance function are selected according to experience, and then the longitudinal wave velocity and the transverse wave velocity (v) of a training data set are calculatedPo,vSo) Is expressed asThe form of the Gaussian process distribution (determined entirely by the mean and covariance functions), where x in equation (1) is used to represent the velocity v of the longitudinal wave in the training datasetPoDenotes the transverse wave velocity vSoFunction f (v) ofPo) Obeying a mean value of m (v)Po) Covariance of k (v)Po,v'Po) The Gaussian process of (a) is called a priori, and f (x), m (x), k (x, x') respectively represent f (v)Po),m(vPo),k(vPo,v'Po) (ii) a Accordingly, f (v)Po) Denotes vSo。
Typically, the mean function is set to a zero mean function; there are many choices of covariance functions, and one of the most widely used covariance functions is the squared exponential covariance function, which the present invention uses as the covariance function.
S3, training a Gaussian process regression model to obtain a hyperparameter;
the logging data (longitudinal and transverse wave velocity v of well C) in the training data set TPo、vSo) Inputting the initial value of the hyper-parameter and the iteration times in a model of Gaussian process regression; in order to make the function f (v)Po) More approximate to the actually measured transverse wave velocity vSoAnd determining a hyper-parameter in the covariance function.
The invention minimizes the negative logarithm of the marginal likelihood function-logP (f (v)Po)|vPo) For example, formula (7) shows that it is related to the covariance function, and the optimization formula (7) is to obtain the parameters σ and l in the covariance functioni。
Wherein K ═ K (x, x),
for fitting training data;
is a penalty term;
is a normalization constant.
In the invention, a quasi-Newton optimizer L-BFGS is adopted to optimize a formula (7) so as to obtain the hyperparameter suitable for the work area.
S4, establishing a combined Gaussian distribution of the training data set and the test data set;
the prior is defined, and the longitudinal wave velocity and the transverse wave velocity in the test data set P are combined to establish that the mean value of the training data set and the test data set is equal to
Covariance of
Combined Gaussian distribution of
Wherein K represents K (v)Po,vPo)。
In transverse wave prediction, x*Representing longitudinal wave velocity v in a test data setPThen, m (x)*),f(x*),k(x*,x*) Each using m (v)P),f(vP),k(vP,vP) Represents, the training data set function value f (v)Po) And a test data set function value f (v)P) The joint distribution of (a) is as follows:
and S5, predicting the transverse wave speed.
Obtaining the joint Gaussian distribution of the training data set and the test data set through the step S4 to obtain the posterior distribution f (v) of the test data setP)|vP,vPo,f(vPo) Including the posterior mean k (v)P,vPo)K-1f(vPo) And a posterior variance k (v)P,vP)-k(vP,vPo)K-1k(vPo,vP) (ii) a Substituting the hyper-parameters obtained by training in the step S3 into the posterior mean value to obtain the transverse wave velocity of the pre-logging well; and substituting the hyper-parameters into the corresponding posterior variances to obtain the point-by-point variances of the predicted points, wherein the point-by-point variances represent the reliability of the predicted results.
The posterior distribution is as follows:
f*|x*,x,f～N(k(x*,x)K-1f,k(x*,x*)-k(x*,x)K-1k(x,x*)) (6)
wherein K ═ K (v)Po,vPo). As seen from equation (6), the posterior mean and variance functions depend on the hyper-parameters σ and l in the covariance function (4). According to the formula (4), k (v) in the posterior mean value can be calculated by using the trained hyper-parametersP,vPo) And k (v)Po,vPo) And then obtaining a posterior mean k (v)P,vPo)K-1f(vPo) The posterior mean in this test is the predicted shear wave velocity. By the same token, a covariance matrix k (v) can be obtainedP,vP)、k(vP,vPo) And k (v)Po,vP) Further, the posterior variance k (v) is obtainedP,vP)-k(vP,vPo)K-1k(vPo,vP) Which characterizes the uncertainty of the predicted value.
The posterior variance function measures the reliability of the prediction result, and the smaller the posterior variance is, the higher the reliability of the prediction result is.
The invention provides a transverse wave prediction system based on Gaussian process regression, which can be used for realizing the transverse wave prediction method based on Gaussian process regression.
The data module determines a data set, and divides the data set into a training data set and a testing data set according to the complexity of lithology of logging parameters;
the regression module is used for determining a mean value and a covariance function in a Gaussian process according to characteristics of S waves and P waves in a training data set divided by the data module to obtain a Gaussian process regression model;
the training module is used for inputting the training data set divided by the data module into a Gaussian process regression model obtained by the regression module and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function;
the joint module is used for establishing joint Gaussian distribution of the training data set and the test data set according to the prior definition and by combining the longitudinal wave speed in the test data set divided by the data module;
and the prediction module is used for determining posterior distribution of the predicted points according to the combined Gaussian distribution obtained by the combination module and substituting the hyper-parameters obtained by the training module into the predicted transverse wave velocity.
The present invention provides, in one embodiment, a terminal device comprising a processor and a memory, the memory storing a computer program comprising program instructions, the processor being configured to execute the program instructions stored by the computer storage medium. The Processor may be a Central Processing Unit (CPU), or may be other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable gate array (FPGA) or other Programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, etc., which is a computing core and a control core of the terminal, and is adapted to implement one or more instructions, and is specifically adapted to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor provided by the embodiment of the invention can be used for the operation of the transverse wave prediction method based on the Gaussian process regression, and comprises the following steps:
dividing a data set into a training data set and a testing data set according to the complexity of lithology of logging parameters; determining a mean function and a covariance function in a Gaussian process according to the speed characteristics of S waves and P waves in the divided training data set to obtain a regression model of the Gaussian process; inputting the divided training data sets into a Gaussian process regression model, and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function; according to prior definition, combined with longitudinal wave velocity in the test data set, establishing combined Gaussian distribution of the training data set and the test data set; and determining posterior distribution of the predicted points according to the combined Gaussian distribution, and substituting the hyper-parameters to obtain the transverse wave velocity of the predicted well.
In an embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a Memory device in the terminal device and is used for storing programs and data. It is understood that the computer readable storage medium herein may include a built-in storage medium in the terminal device, and may also include an extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space storing an operating system of the terminal. Also, one or more instructions, which may be one or more computer programs (including program code), are stored in the memory space and are adapted to be loaded and executed by the processor. It should be noted that the computer-readable storage medium may be a high-speed RAM memory, or may be a non-volatile memory (non-volatile memory), such as at least one disk memory.
One or more instructions stored in the computer-readable storage medium may be loaded and executed by the processor to implement the corresponding steps of the method for shear wave prediction based on gaussian process regression in the above embodiments; one or more instructions in the computer-readable storage medium are loaded by the processor and perform the steps of:
dividing a data set into a training data set and a testing data set according to the complexity of lithology of logging parameters; determining a mean function and a covariance function in a Gaussian process according to the speed characteristics of S waves and P waves in the divided training data set to obtain a regression model of the Gaussian process; inputting the divided training data sets into a Gaussian process regression model, and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function; according to prior definition, combined with longitudinal wave velocity in the test data set, establishing combined Gaussian distribution of the training data set and the test data set; and determining posterior distribution of the predicted points according to the combined Gaussian distribution, and substituting the hyper-parameters to obtain the transverse wave velocity of the predicted well.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. 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.
Examples
The method comprises the steps of taking the front edge of a gantry of the Sichuan basin as a research area, collecting logging data of three wells in the research area, wherein the logging data comprise Depth (Depth), Density (Density), Gamma ray (Gamma ray), longitudinal wave velocity (P-velocity), transverse wave velocity (S-velocity) and Lithology (Lithology) parameters. The scatter plots of gamma ray, density, longitudinal wave velocity and transverse wave velocity are shown in fig. 1, 2 and 3. Simultaneously, a histogram of the correlation of the three is drawn, as shown in fig. 4. As can be seen from the observation of fig. 1, 2, and 3, the correlation between the longitudinal wave velocity and the transverse wave velocity is more significant than the correlation between the gamma ray, the density, and the longitudinal wave velocity, and the histogram of the correlation coefficient in fig. 4 also shows that the correlation between the longitudinal wave velocity and the transverse wave velocity is strong, and therefore, the transverse wave velocity is predicted only by using the longitudinal wave velocity.
With respect to the selection of the data set, the study determined the well log data for well C as the training data set and the well log data for well A, B as the testing data set by comparing the lithology parameters of the three wells. The longitudinal and transverse wave velocities of the training data and the lithology of the wells A, B and C are shown in FIG. 5, the labels on the right side of the figure represent different types of lithologic media, wherein SS, Cal, SH, Siltstone, Dol and Gyp represent sandstone, calcite, shale, sandstone, dolomite and gypsum, respectively, and Gyp-Dol represents a mixed medium of dolomite and gypsum, and it can be seen that the lithology of the logging data used in the experiment is very complex.
The results of the shear wave prediction of well a using the shear wave velocity prediction based on the gaussian process regression method are shown in fig. 6, in which (a) - (f) show in sequence: measured compressional velocity, shear velocity (blue line represents measured shear velocity, red line represents shear velocity predicted by GPR method, green line represents shear velocity predicted by mudstone line formula method), prediction variance, error between predicted shear and measured shear, relative error, and lithology of well A. As seen from fig. 6(b), the GPR method is closer to the trend and the value of the variation of the measured shear wave velocity than the results predicted by the well-known mudstone line formula. In fig. 6, (c) shows the variance curve changes, which are all small, indicating that the reliability of the shear velocity prediction of the well a is high. This is also demonstrated by the mean variance of the well a predictions shown in table 8, and the values of the mean error and the mean relative error also indicate that the predictions for the gaussian process regression are more accurate.
The predicted shear wave results for well B are shown in fig. 7. FIGS. 7(B) and 7(c) illustrate that the GPR method is more accurate in predicting the shear velocity of well B, and the quantization results in Table 8 also illustrate that the error of this prediction is smaller.
Table 8 average error, average variance and average relative error of predicted shear wave velocity
In summary, the transverse wave prediction method and system based on the gaussian process regression have high transverse wave prediction accuracy and provide uncertainty quantification for the prediction result.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (10)
1. A transverse wave prediction method based on Gaussian process regression is characterized by comprising the following steps:
s1, dividing the data set into a training data set and a testing data set according to the complexity of the lithology of the logging parameters;
s2, determining a mean function and a covariance function in the Gaussian process according to the speed characteristics of the S wave and the P wave in the training data set divided in the step S1 to obtain a regression model of the Gaussian process;
s3, inputting the training data set divided in the step S1 into the Gaussian process regression model obtained in the step S2, and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function;
s4, establishing a combined Gaussian distribution of the training data set and the test data set according to prior definition and by combining the longitudinal wave velocity in the test data set divided in the step S1;
and S5, determining posterior distribution of the predicted points according to the combined Gaussian distribution obtained in the step S4, and substituting the hyperparameter obtained in the step S3 to obtain the transverse wave velocity of the predicted well.
2. The method of claim 1, wherein in step S2, the mean function and the covariance function are selected empirically, and then the velocity of the compressional and shear waves of the training data set is expressed in the form of gaussian process distribution, i.e. the velocity of the shear wave v is expressedSoFunction f (v) ofPo) Obeying a mean value of m (v)Po) Covariance of k (v)Po,v'Po) The gaussian process of (1).
3. The method of claim 2, wherein the mean function m (x) and the covariance function k (x, x') are defined as:
m(x)＝E[f(x)]
wherein f (x) is a latent function and represents the S-wave velocity corresponding to the P-wave velocity x, E is a mathematical expectation, sigma represents the signal variance, and liRepresenting the length scale, x, of the ith dimensioniD is the dimension of the variable x, which is known data of the ith dimension.
4. The method according to claim 1, wherein step S3 is specifically:
the longitudinal wave velocity v of the well log in the training data set TPoAnd transverse wave velocity vSoInputting the parameters into a Gaussian process regression model, and determining a hyperparameter initial value and iteration times in the Gaussian process regression model; the hyperparameter in the covariance function is determined by minimizing the negative logarithm of the marginal likelihood function.
5. The method of claim 4, wherein the hyperparameters σ and L are optimized using a quasi-Newtonian optimizer L-BFGS by minimizing the negative logarithm of the marginal likelihood function as follows:
where-logp (f | x) is the negative logarithm of the marginal likelihood function,
for fitting training data;
is a penalty term;
is a normalization constant.
6. The method according to claim 1, wherein step S4 is specifically:
according to the prior definition, the mean value of the training data set and the test data set is established by combining the longitudinal wave velocity and the transverse wave velocity in the test data set
Covariance of
Combined Gaussian distribution of
K represents K (v)Po,vPo)。
7. The method of claim 6, wherein the joint Gaussian distribution
Comprises the following steps:
wherein, f (v)Po) For the training data set function value, f (v)P) For testing data set function values, N is a normal distribution.
8. The method of claim 1, wherein in step S5, the posterior distribution of the test dataset comprises posterior mean and posterior variance, the hyper-parameters obtained in step S3 are substituted into the posterior mean to obtain the predicted transverse wave velocity of the well, and the hyper-parameters obtained in step S3 are substituted into the posterior variance to obtain the point-by-point variance of the predicted points.
9. The method according to claim 8, characterized in that the posterior distribution is in particular:
f*|x*,x,f～N(k(x*,x)K-1f,k(x*,x*)-k(x*,x)K-1k(x,x*))
wherein f is*Test point x under the data x, f of the prior test*K denotes the square exponential kernel function defined above.
10. A system for shear wave prediction based on gaussian process regression, comprising:
the data module divides the data set into a training data set and a testing data set according to the complexity of the lithology of the logging parameter;
the regression module is used for determining a mean value and a covariance function in a Gaussian process according to the speed characteristics of S waves and P waves in the training data set divided by the data module to obtain a Gaussian process regression model;
the training module is used for inputting the training data set divided by the data module into a Gaussian process regression model obtained by the regression module and obtaining corresponding hyper-parameters by minimizing the negative logarithm of the marginal likelihood function;
the joint module is used for establishing joint Gaussian distribution of the training data set and the test data set according to the prior definition and by combining the longitudinal wave speed in the test data set divided by the data module;
and the prediction module is used for determining posterior distribution of the predicted points according to the combined Gaussian distribution obtained by the combination module and substituting the hyper-parameters obtained by the training module into the predicted transverse wave velocity.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110765085.2A CN113466962B (en) | 2021-07-06 | 2021-07-06 | Transverse wave prediction method and system based on Gaussian process regression |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110765085.2A CN113466962B (en) | 2021-07-06 | 2021-07-06 | Transverse wave prediction method and system based on Gaussian process regression |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113466962A true CN113466962A (en) | 2021-10-01 |
| CN113466962B CN113466962B (en) | 2023-03-28 |
Family
ID=77878677
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110765085.2A Active CN113466962B (en) | 2021-07-06 | 2021-07-06 | Transverse wave prediction method and system based on Gaussian process regression |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113466962B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114510817A (en) * | 2021-12-27 | 2022-05-17 | 中国航天空气动力技术研究院 | Wind field sensing algorithm for planning gliding path of unmanned aerial vehicle |
| TWI856496B (en) * | 2023-01-19 | 2024-09-21 | 衛波科技股份有限公司 | A method for predicting an on-site earthquakes using artificial intelligence and seismic p-wave parameters |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104516015A (en) * | 2013-09-27 | 2015-04-15 | 中国石油天然气集团公司 | Method for determining longitudinal wave speed and transverse wave speed of coalbed gas |
| CN111751878A (en) * | 2020-05-21 | 2020-10-09 | 中国石油天然气股份有限公司 | Method and device for predicting transverse wave velocity |
| EP3779808A1 (en) * | 2019-08-13 | 2021-02-17 | Robert Bosch GmbH | Device and method for training a gaussian process regression model |
| CN112922582A (en) * | 2021-03-15 | 2021-06-08 | 西南石油大学 | Gas well wellhead choke tip gas flow analysis and prediction method based on Gaussian process regression |
-
2021
- 2021-07-06 CN CN202110765085.2A patent/CN113466962B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104516015A (en) * | 2013-09-27 | 2015-04-15 | 中国石油天然气集团公司 | Method for determining longitudinal wave speed and transverse wave speed of coalbed gas |
| EP3779808A1 (en) * | 2019-08-13 | 2021-02-17 | Robert Bosch GmbH | Device and method for training a gaussian process regression model |
| CN111751878A (en) * | 2020-05-21 | 2020-10-09 | 中国石油天然气股份有限公司 | Method and device for predicting transverse wave velocity |
| CN112922582A (en) * | 2021-03-15 | 2021-06-08 | 西南石油大学 | Gas well wellhead choke tip gas flow analysis and prediction method based on Gaussian process regression |
Non-Patent Citations (3)
| Title |
|---|
| 伍顺伟 等: "玛湖地区横波预测方法优选及其对岩石力学参数计算的影响", 《特种油气藏》 * |
| 赵旭阳 等: "基于测井横波预测的地应力场及岩石力学参数建模", 《断块油气田》 * |
| 逄硕等: "基于岩石物理模型的页岩孔隙结构反演及横波速度预测", 《吉林大学学报(地球科学版)》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114510817A (en) * | 2021-12-27 | 2022-05-17 | 中国航天空气动力技术研究院 | Wind field sensing algorithm for planning gliding path of unmanned aerial vehicle |
| CN114510817B (en) * | 2021-12-27 | 2024-07-12 | 中国航天空气动力技术研究院 | Wind field sensing algorithm for unmanned aerial vehicle glide path planning |
| TWI856496B (en) * | 2023-01-19 | 2024-09-21 | 衛波科技股份有限公司 | A method for predicting an on-site earthquakes using artificial intelligence and seismic p-wave parameters |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113466962B (en) | 2023-03-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP3894907B1 (en) | Machine learning-augmented geophysical inversion | |
| US11320551B2 (en) | Training machine learning systems for seismic interpretation | |
| CN110031896B (en) | Seismic random inversion method and device based on multi-point geostatistics prior information | |
| US11693139B2 (en) | Automated seismic interpretation-guided inversion | |
| CN102353989B (en) | Method for estimating velocity of transverse waves based on inversion of equivalent elastic modulus for self-adapting matrix minerals | |
| CN104749624B (en) | A kind of seismic facies identification and its uncertain quantitative assessment synchronization realizing method | |
| Martin et al. | Iterative refinement of implicit boundary models for improved geological feature reproduction | |
| CN107203005A (en) | A kind of method that quantification calculates crack characterising parameter | |
| CN112965103B (en) | Multi-pore reservoir prestack seismic probability multi-channel inversion method | |
| Ball et al. | Relative rock physics | |
| EP2956804B1 (en) | Method of modelling a subsurface volume | |
| CN113466962A (en) | Transverse wave prediction method and system based on Gaussian process regression | |
| CN115130529A (en) | A prestack seismic inversion method and device | |
| CN103760600A (en) | Gas saturation inversion method | |
| US10324206B2 (en) | Method of modelling a subsurface volume | |
| CN112796738A (en) | A method for calculating formation permeability combining array acoustic logging and conventional logging | |
| CN114114414A (en) | Artificial intelligence prediction method for 'dessert' information of shale reservoir | |
| Brisson et al. | Estimating uncertainties in 3-D models of complex fold-and-thrust belts: a case study of the Eastern Alps triangle zone | |
| CN114075973A (en) | Stratum element logging curve reconstruction method and device | |
| Goovaerts | Geostatistical modeling of the spaces of local, spatial, and response uncertainty for continuous petrophysical properties | |
| CN118378319B (en) | Three-dimensional unit body attribute modeling method and system based on multi-source heterogeneous information fusion | |
| CN114861515A (en) | Calculation method, device, device and medium for layer velocity data volume | |
| CN111751882A (en) | Method and device for generating sensitive rock physical parameters | |
| CN114488301B (en) | A method for predicting the porosity of tight sandstone reservoirs | |
| CN110135112A (en) | A Shale Anisotropy Estimation Method Based on Particle Filter Algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |