CN112394396A - Random inversion method, equipment and system for earthquake - Google Patents
Random inversion method, equipment and system for earthquake Download PDFInfo
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Abstract
The invention provides a method, a system, computer equipment and a computer readable storage medium for seismic stochastic inversion, and relates to the technical field of seismic exploration. The method comprises the steps of obtaining seismic data and a low-frequency model; constructing prior information of model parameters; constructing a likelihood function fused into low-frequency information by using the seismic data and the low-frequency model; and sampling the posterior probability according to the prior information and the likelihood function to obtain an inversion result. The method overcomes the limitation of the conventional simulation method, then constructs the likelihood function fused with the low-frequency information, enables the inversion result to be more stable and reliable, accelerates the search of solution space, and then combines the sequential Gibbs resampling operator and the improved Metropolis algorithm to realize the sampling of posterior probability to obtain the inversion result with high resolution.
Description
Technical Field
The invention relates to the technical field of seismic exploration, in particular to an inversion technology of a seismic, and specifically relates to a seismic random inversion method, a seismic random inversion system, computer equipment and a computer readable storage medium.
Background
The deterministic inversion method loses small-scale heterogeneity of a reservoir, has low vertical resolution, and is suitable for reservoir prediction with thick horizon, so that the method is applied more in the early stage of oil and gas exploration. Compared to deterministic inversion, stochastic inversion has a higher vertical resolution and is more suitable for uncertainty estimation.
The high frequency components of the stochastic inversion originate mainly from two points, the first point being the small scale variability and the second point being that it integrates high frequency log data. Bortoli et al (1993) and Haas and Dubrule (1994) originally applied geostatistics to seismic inversion, and a method for performing channel-by-channel simulation re-optimization based on Sequential Gaussian Simulation (SGS) is provided, belongs to a single-channel inversion method, and has the problem of low calculation efficiency. To overcome this problem, debye et al (1996), Sams et al (1999) and conteras (2005) introduced methods of simulated annealing and markov monte carlo (MCMC) to improve computational efficiency; ravalec et al (2000) propose a Fourier moving average simulation algorithm (FFT-MA), which is an algorithm for performing rapid simulation in a frequency domain and can rapidly construct prior information of model parameters; hu (2000), Hu and Ravalec (2004) propose a step-by-step deformation algorithm (GDM) to perturb the prior information. In recent years, YIN and the like (2014), Wangbaoli and the like (2015), Sun Ruiying and the like (2015) and Zhao morning and the like (2018) are combined with FFT-MA spectral simulation and a step-by-step deformation algorithm to carry out fast stochastic inversion, so that the calculation efficiency of the stochastic inversion is improved.
At present, the methods achieve better effect in practical application, but still have some problems:
1. both sequential gaussian simulation and fourier moving average simulation algorithms require model parameters to obey gaussian distribution, data which do not conform to gaussian distribution need to be subjected to normal transformation, and then the data are transformed back to the original data space through inverse gaussian transformation, which usually results in that a variation function cannot be reproduced.
2. Each model generated by the step-by-step deformation algorithm perturbation may be consistent with the observed values and the prior information, but it cannot be guaranteed that the variability of the models matches the variability of the posterior probability distribution, and therefore, the generated model cannot provide sampling of the posterior probability distribution.
3. The MCMC method still requires high computational cost because it needs to calculate the prior probability of the high-dimensional distribution when searching the solution space.
Therefore, how to provide a new solution, which can solve the above technical defects, is a technical problem to be solved in the art.
Disclosure of Invention
In view of this, embodiments of the present invention provide a method, a system, a computer device, and a computer readable storage medium for seismic stochastic inversion, in which sequential gibbs resampling is used to perturb prior information constructed, a sequential gibbs resampling operator combines sequential simulation and gibbs sampling, can rapidly perturb prior information, and combines sequential gibbs resampling and improved Metropolis sampling to obtain a posterior solution of a model parameter, without calculating prior probability of high-dimensional distribution, and at the same time, improve accuracy and stability of inversion.
One of the objectives of the present invention is to provide a seismic stochastic inversion method, comprising:
acquiring seismic data and a low-frequency model;
constructing prior information of model parameters;
constructing a likelihood function fused into low-frequency information by using the seismic data and the low-frequency model;
and sampling the posterior probability according to the prior information and the likelihood function to obtain an inversion result.
In a preferred embodiment of the present invention, the a priori information of the parameters of the constructed model includes:
constructing prior information of the model parameters by using a direct sequential simulation algorithm;
a histogram of the prior information is reproduced.
In a preferred embodiment of the invention, the likelihood function is constructed as:
wherein L (m) is a likelihood function, m is a model parameter, d is observation data, g is a positive operator, σeIs Gaussian noise variance, alpha is an adjustable factor, mLFMIs a low frequency model.
In a preferred embodiment of the present invention, the sampling a posterior probability according to the prior information and the likelihood function to obtain an inversion result includes:
gibbs sampling and sequential simulation are combined to form a sequential Gibbs resampling operator;
perturbing the prior information using the sequential Gibbs resampling operator;
constructing an improved Metropolis algorithm;
and (4) sampling the posterior probability by combining the sequential Gibbs resampling operator and an improved Metropolis algorithm to obtain an inversion result.
In a preferred embodiment of the present invention, the acceptance criteria of the improved Metropolis operator are:
wherein m iscurrentAs an initial model, mproposeTo suggest a model, L (m)current) As a likelihood function of the initial model, L (m)propose) Is a likelihood function of the proposed model.
In a preferred embodiment of the present invention, the sampling a posterior probability according to the prior information and the likelihood function to obtain an inversion result further includes:
and selecting data in the neighborhood range of the sequential simulation as conditional data to perform the sequential simulation and the sequential Gibbs resampling.
One of the objects of the present invention is a seismic stochastic inversion system, the system comprising:
the seismic data acquisition module is used for acquiring seismic data and a low-frequency model;
the prior information construction module is used for constructing the prior information of the model parameters;
the likelihood function construction module is used for constructing a likelihood function fused into low-frequency information by using the seismic data and the low-frequency model;
and the inversion result determining module is used for realizing the sampling of the posterior probability according to the prior information and the likelihood function so as to obtain the inversion result.
In a preferred embodiment of the present invention, the prior information constructing module includes:
the prior information determining module is used for constructing the prior information of the model parameters by using a direct sequential simulation algorithm;
and the histogram reproduction module is used for reproducing the histogram of the prior information.
In a preferred embodiment of the present invention, the inversion result determination module includes:
the sampling operator forming module is used for combining Gibbs sampling and sequential simulation to form a sequential Gibbs resampling operator;
the prior information disturbance module is used for disturbing the prior information by using the sequential Gibbs resampling operator;
the improved algorithm construction module is used for constructing an improved Metropolis algorithm;
and the posterior probability acquisition module is used for sampling the posterior probability by combining the sequential Gibbs resampling operator and the improved Metropolis algorithm so as to obtain an inversion result.
In a preferred embodiment of the present invention, the inversion result determining module further includes:
and the neighborhood range selection module is used for selecting data in the neighborhood range of the sequential simulation as conditional data, and performing the sequential simulation and the sequential Gibbs resampling.
One of the objects of the present invention is to provide a computer apparatus comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a method of seismic stochastic inversion.
It is an object of the present invention to provide a computer-readable storage medium storing a computer program for performing a seismic stochastic inversion method.
The invention has the beneficial effects that the invention provides a random inversion method, a system, computer equipment and a computer readable storage medium for earthquake, firstly, the prior information of model parameters is constructed by utilizing a direct sequential simulation algorithm is explored under a Bayesian framework, the direct sequential simulation algorithm does not need the model parameters to obey Gaussian distribution, the limitation of the conventional simulation method is overcome, then a likelihood function fused with low-frequency information is constructed, the inversion result is more stable and reliable, the search of a solution space is accelerated, and then the sampling of posterior probability is realized by combining a sequential Gibbs resampling operator and an improved Metropolis algorithm, so that the inversion result with high resolution is obtained.
In order to make the aforementioned and other objects, features and advantages of the invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of a seismic stochastic inversion system according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a prior information construction module in a seismic stochastic inversion system according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of a first embodiment of an inversion result determination module in a seismic stochastic inversion system according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a second implementation manner of an inversion result determination module in a seismic stochastic inversion system according to an embodiment of the present invention;
FIG. 5 is a flow chart of a seismic stochastic inversion method according to an embodiment of the present invention;
fig. 6 is a detailed flowchart of step S102 in fig. 5;
fig. 7 is a detailed flowchart of a first embodiment of step S104 in fig. 5;
fig. 8 is a detailed flowchart of a second embodiment of step S104 in fig. 5;
FIG. 9 is a graph showing the comparison of 50 inversion results (gray curves) with model data (black curves) in an embodiment of the present invention;
FIG. 10 is a schematic diagram showing a comparison of a seismic record synthesized by 50 inversion results (gray curves) with an actual seismic record (black curves) in an embodiment provided by the invention;
FIG. 11 is a schematic diagram of constrained sparse pulse inversion in an embodiment provided by the present invention;
FIG. 12 is a schematic diagram of random inversion in an embodiment provided by 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.
As will be appreciated by one skilled in the art, embodiments of the present invention may be embodied as a system, apparatus, method or computer program product. Accordingly, the present disclosure may be embodied in the form of: entirely hardware, entirely software (including firmware, resident software, micro-code, etc.), or a combination of hardware and software.
The principles and spirit of the present invention are explained in detail below with reference to several representative embodiments of the invention.
The existing deterministic inversion method loses small-scale heterogeneity of a reservoir, has low vertical resolution and is suitable for reservoir prediction with thick horizon, so that the method is more applied in the early stage of oil and gas exploration. Compared with deterministic inversion, stochastic inversion has higher vertical resolution and is more suitable for uncertainty estimation, and therefore has greater advantages in identifying thin reservoirs.
The invention aims to develop a seismic random inversion method based on a sequential Gibbs resampling algorithm, which utilizes a direct sequential simulation algorithm to construct prior information of model parameters, gets rid of the limitation that the model parameters obey Gaussian distribution hypothesis, and is suitable for prior distribution in any shape. Because the model generated by the disturbance of the gradual deformation algorithm can not provide the sampling of posterior probability distribution, the invention disturbs the constructed prior information by utilizing the sequential Gibbs resampling, and the sequential Gibbs resampling operator combines the sequential simulation and the Gibbs sampling, thereby being capable of quickly disturbing the prior information. The MCMC method still requires high computational cost because it needs to calculate the prior probability of the high-dimensional distribution when searching the solution space. The invention combines sequential Gibbs resampling and improved Metropolis sampling to obtain the posterior solution of the model parameters, does not need to calculate the prior probability of high-dimensional distribution, and simultaneously improves the accuracy and the stability of inversion.
Specifically, fig. 1 is a schematic structural diagram of a seismic stochastic inversion system provided in the invention, please refer to fig. 1, where the seismic stochastic inversion system includes:
a seismic data acquisition module 100 for acquiring seismic data and a low frequency model;
and a priori information constructing module 200 for constructing the priori information of the model parameters. Fig. 2 is a schematic structural diagram of a prior information constructing module 200 according to an embodiment of the present invention, please refer to fig. 2, where the prior information constructing module 200 includes:
a priori information determining module 210, configured to construct the priori information of the model parameters by using a direct sequential simulation algorithm;
a histogram reproduction module 220 for reproducing a histogram of the prior information.
That is, in one embodiment of the invention, prior information for the model parameters is constructed using direct sequential simulation under a Bayesian framework. Aiming at the problems existing in the process of constructing prior information by a direct sequential simulation algorithm: the method can ensure the reproduction of the mean value, the variance and the variation function of the prior information and cannot ensure the reproduction of the histogram of the prior information, so that the prior information of the model parameters is constructed by adopting a modified direct sequential simulation algorithm. Specifically, the method comprises the following steps:
(1) bayesian framework
Consider a forward problem:
d＝g(m)+e (1)
in the formula: d represents the observed data, m represents the model parameters, e represents the noise, and g is a forward operator representing the mapping of the model parameters m to the observed data d. The corresponding inverse problem is expressed as: and under the condition of given observation data d, positive operator g and prior information of the model parameter, the model parameter m is deduced. In the bayesian approach, all information states are represented in the form of probability density functions, and the solution to inversion is a posterior probability density function, which is a combination of all information states and can be written in the form:
σM(m)＝kρM(m)L(m) (2)
in the formula: k is a normalization constant, pM(m) is the prior information of the model parameters, and L (m) is a likelihood function describing the degree of matching of the model data with the observed data. Under the assumption of linear gaussians, an analytical solution of the posterior probability can be obtained. However, in practical cases, the model parameters usually do not follow a gaussian distribution and the forward operator is non-linear, so that no analytic solution for the posterior probability can be obtained, and therefore, the posterior probability can be sampled later by using the improved Metropolis operator.
(2) Prior information for constructing model parameters using direct sequential simulation
To construct a priori information on the model parameters, a geostatistical simulation method is used. Since most simulation algorithms can only simulate Gaussian random fields, model parameters are required to obey Gaussian distribution, otherwise normal transformation is required, and the problem that the variation function cannot be reproduced is usually caused.
Therefore, Direct Sequential Simulation (DSS) is adopted to construct prior information of model parameters, and the algorithm is a popularization of Sequential Gaussian Simulation (SGS) and can be suitable for prior distribution of any shape. However, this algorithm has a problem: the mean value, the variance and the variation function of the prior information can be ensured to be reproduced, and the histogram reproduction of the prior information can not be ensured. To address this problem, the histogram of prior information is reproduced using the method proposed by Oz et al. The only difference between this method and sequential gaussian simulation is that the shape of the conditional distribution is modified from one simulation node to another to ensure the reproduction of the histogram, so that the kriging system solved in each step of the simulation is the same as for sequential gaussian simulation.
Referring to fig. 1, the seismic stochastic inversion system further comprises:
and a likelihood function constructing module 300, configured to construct a likelihood function fused into the low-frequency information by using the seismic data and the low-frequency model.
In one embodiment of the invention, the likelihood function fused into the low-frequency information is constructed by utilizing the seismic data and the low-frequency model, and the introduction of the low-frequency model not only can make the inversion result more stable and reliable, but also can accelerate the search of a solution space.
The likelihood function is constructed as follows:
in the formula: sigmaeIs the variance of Gaussian noise, alpha is a tunable factor, mLFMIs a low frequency model.
And an inversion result determining module 400, configured to implement sampling of a posterior probability according to the prior information and the likelihood function to obtain an inversion result.
Fig. 3 is a schematic structural diagram of a first implementation of the inversion result determining module 400 according to an embodiment of the present invention, please refer to fig. 3, where the inversion result determining module 400 includes:
a sampling operator formation module 410 for combining gibbs sampling with sequential simulation to form a sequential gibbs resampling operator;
a priori information perturbation module 420 for perturbing the priori information using the sequential gibbs resampling operator;
an improved algorithm construction module 430, configured to construct an improved Metropolis algorithm;
and the posterior probability acquisition module 440 is configured to perform posterior probability sampling by combining the sequential gibbs resampling operator and the improved Metropolis algorithm to obtain an inversion result.
That is, in an embodiment of the present invention, sequential gibbs resampling operator and improved Metropolis algorithm are combined to realize sampling of posterior probability, the sequential gibbs resampling operator is a sampling mode combining gibbs sampling and sequential simulation, and is a re-simulation algorithm, which can perform rapid disturbance sampling on prior information and keep the spatial structure consistent, and then the improved Metropolis algorithm is combined to realize sampling of posterior probability, so as to avoid calculating complex high-dimensional prior distribution, and ensure the calculation efficiency of inversion, specifically:
(1) improved Metropolis operator
The classical Metropolis algorithm needs to calculate the prior information rho at the same timeM(m) and likelihood functions L (m), however for some complex a priori information ρ is calculatedM(m) can be difficult. To this end, an improved Metropolis algorithm is used to sample the posterior probability distribution.
Suppose mcurrentIs an initial model, representing the current prior distribution pM(m) a first realization ofproposeIs a proposed model, representing the initial model mcurrentIs also an implementation of the prior distribution. The likelihood functions of these two realizations are simultaneously calculated according to equation (3), which is respectively expressed as: l (m)current)，L(mpropose). Improved Metropolis algorithmThe acceptance criteria for the child are as follows:
the sampling operator does not need to calculate the prior probability rho of a high dimension relative to the classical Metropolis operatorM(m) that can be applied to complex a priori information, but must be able to perturb the sampling of the a priori information.
(2) Sequential Gibbs resampling
The implementation of the prior information can be obtained by a Direct Sequential Simulation (DSS) method, but when a modified Metropolis operator is used, it is necessary to be able to make the current model gradually perturbed to other models, and the perturbed model needs to be consistent with the spatial structure of the prior information.
The method comprises the steps of using sequential Gibbs resampling to quickly disturb prior information, using a sequential Gibbs resampling operator as a sampling mode for combining Gibbs sampling and sequential simulation, selecting a subset S of model parameters, performing conditional re-simulation on the subset in a sequential simulation mode, repeating the conditional re-simulation on the subset to quickly disturb sampling on the prior information, and keeping the spatial structure consistent. The sequential Gibbs resampling can disturb prior information by only re-simulating part of model parameters each time, the calculation efficiency is high, the receiving rate of the improved Metropolis operator can be adjusted by controlling the size of the subset, and the receiving rate is usually maintained between 25% and 50%. The posterior probability sampling can be realized by combining an improved Metropolis sampling operator, and the method comprises the following steps:
1) firstly, an initial model m is generated through a DSS algorithmcurrentAnd calculating its likelihood function L (m)current)。
2) A subset S of the model parameters, i.e. the re-simulation region, is randomly selected.
3) Carrying out condition simulation on the re-simulation area to obtain a proposed model mproposeCalculating a likelihood function L (m) of the proposed modelpropose)。
4) According to (4)) Is receiving or rejecting mproposeIf received, let mcurrent＝mproposeElse mcurrentRemain unchanged.
5) Repeating the steps 2) to 4) by using random seeds, and finally realizing the sampling of the posterior probability distribution of the model parameters.
Fig. 4 is a schematic structural diagram of a second implementation of the inversion result determining module 400 according to an embodiment of the present invention, please refer to fig. 4, where the inversion result determining module 400 further includes:
and a neighborhood range selection module 450, configured to select data in a neighborhood range of the sequential simulation as conditional data, and perform the sequential simulation and the sequential gibbs resampling.
In one embodiment of the present invention, during sequential simulation (DSS, SGS, etc.) and sequential gibbs resampling, previously simulated points are added to the condition data, in addition to the initial condition data, and then the condition data is progressively increased as the simulation progresses. If all the condition data is considered, a very large kriging equation needs to be solved, which is very time and memory consuming.
Thus, consider selecting data within a certain neighborhood as conditional data, rather than all conditional data points. For the two-dimensional case, the neighborhood shape may be rectangular, circular, elliptical, etc., and the neighborhood size may be limited to twice the range of the variation function. The calculation efficiency can be greatly improved by selecting the proper simulation neighborhood, and the simulation precision can not be greatly influenced.
In the Bayes framework, (1) firstly, the prior information of the model parameters is constructed by utilizing a direct sequential simulation algorithm which does not need the model parameters to obey Gaussian distribution, so that the limitation of the conventional simulation method is overcome; (2) then, a likelihood function fused with low-frequency information is constructed, so that an inversion result is more stable and reliable, and the search of a solution space is accelerated; (3) and then, sampling of posterior probability is realized by combining a sequential Gibbs resampling operator and an improved Metropolis algorithm, and a high-resolution inversion result is obtained.
Furthermore, although in the above detailed description several unit modules of the system are mentioned, this division is not mandatory only. Indeed, the features and functions of two or more of the units described above may be embodied in one unit, according to embodiments of the invention. Also, the features and functions of one unit described above may be further divided into embodiments by a plurality of units. The terms "module" and "unit" used above may be software and/or hardware that realizes a predetermined function. While the modules described in the following embodiments are preferably implemented in software, implementations in hardware, or a combination of software and hardware are also possible and contemplated.
Having described the seismic stochastic inversion system of an exemplary embodiment of the present invention, a method of an exemplary embodiment of the present invention is described next with reference to the accompanying drawings. The implementation of the method can be referred to the above overall implementation, and repeated details are not repeated.
The invention aims to develop a high-resolution seismic stochastic inversion method, which utilizes prior information of model parameters constructed by direct sequential simulation, can get rid of the dependence of conventional seismic stochastic inversion on Gaussian prior distribution hypothesis, and better conforms to the real situation of the model parameters; a likelihood function fused with low-frequency information is constructed, so that the inversion result is more stable and reliable, and the search of a solution space can be accelerated; the posterior solution of the model parameters is obtained by combining sequential Gibbs resampling and improved Metropolis sampling, the prior probability of high-dimensional distribution does not need to be calculated, and the accuracy and the stability of inversion are improved; compared with the conventional deterministic inversion method, the inversion result with high vertical resolution can be obtained.
Specifically, fig. 5 is a schematic flow chart of a seismic stochastic inversion method provided in the invention, please refer to fig. 5, where the seismic stochastic inversion method includes:
s101: acquiring seismic data and a low-frequency model;
s102: and constructing prior information of the model parameters. Fig. 6 is a schematic flow chart of the step, please refer to fig. 6, which includes:
s201: constructing prior information of the model parameters by using a direct sequential simulation algorithm;
s202: a histogram of the prior information is reproduced.
That is, in one embodiment of the invention, prior information for the model parameters is constructed using direct sequential simulation under a Bayesian framework. Aiming at the problems existing in the process of constructing prior information by a direct sequential simulation algorithm: the method can ensure the reproduction of the mean value, the variance and the variation function of the prior information, and cannot ensure the reproduction of the histogram of the prior information, so that the prior information of the model parameters is constructed by adopting a modified direct sequential simulation algorithm, and the method specifically comprises the following steps:
(1) bayesian framework
Consider a forward problem:
d＝g(m)+e (1)
in the formula: d represents the observed data, m represents the model parameters, e represents the noise, and g is a forward operator representing the mapping of the model parameters m to the observed data d. The corresponding inverse problem is expressed as: and under the condition of given observation data d, positive operator g and prior information of the model parameter, the model parameter m is deduced. In the bayesian approach, all information states are represented in the form of probability density functions, and the solution to inversion is a posterior probability density function, which is a combination of all information states and can be written in the form:
σM(m)＝kρM(m)L(m) (2)
in the formula: k is a normalization constant, pM(m) is the prior information of the model parameters, and L (m) is a likelihood function describing the degree of matching of the model data with the observed data. Under the assumption of linear gaussians, an analytical solution of the posterior probability can be obtained. However, in practical cases, the model parameters usually do not follow a gaussian distribution and the forward operator is non-linear, so that no analytic solution for the posterior probability can be obtained, and therefore, the posterior probability can be sampled later by using the improved Metropolis operator.
(2) Prior information for constructing model parameters using direct sequential simulation
To construct a priori information on the model parameters, a geostatistical simulation method is used. Since most simulation algorithms can only simulate Gaussian random fields, model parameters are required to obey Gaussian distribution, otherwise normal transformation is required, and the problem that the variation function cannot be reproduced is usually caused.
Therefore, Direct Sequential Simulation (DSS) is adopted to construct prior information of model parameters, and the algorithm is a popularization of Sequential Gaussian Simulation (SGS) and can be suitable for prior distribution of any shape. However, this algorithm has a problem: the mean value, the variance and the variation function of the prior information can be ensured to be reproduced, and the histogram reproduction of the prior information can not be ensured. To address this problem, the histogram of prior information is reproduced using the method proposed by Oz et al. The only difference between this method and sequential gaussian simulation is that the shape of the conditional distribution is modified from one simulation node to another to ensure the reproduction of the histogram, so that the kriging system solved in each step of the simulation is the same as for sequential gaussian simulation.
Referring to fig. 5, the seismic stochastic inversion method further includes:
s103: and constructing a likelihood function fused into the low-frequency information by using the seismic data and the low-frequency model.
In one embodiment of the invention, the likelihood function fused into the low-frequency information is constructed by utilizing the seismic data and the low-frequency model, and the introduction of the low-frequency model not only can make the inversion result more stable and reliable, but also can accelerate the search of a solution space.
The likelihood function is constructed as follows:
in the formula: sigmaeIs the variance of Gaussian noise, alpha is a tunable factor, mLFMIs a low frequency model.
S104: and sampling the posterior probability according to the prior information and the likelihood function to obtain an inversion result.
Fig. 7 is a flowchart illustrating a first implementation manner of step S104 in the embodiment of the present invention, please refer to fig. 7, where step S104 includes:
s301: gibbs sampling and sequential simulation are combined to form a sequential Gibbs resampling operator;
s302: perturbing the prior information using the sequential Gibbs resampling operator;
s303: constructing an improved Metropolis algorithm;
s304: and (4) sampling the posterior probability by combining the sequential Gibbs resampling operator and an improved Metropolis algorithm to obtain an inversion result.
That is, in an embodiment of the present invention, sequential gibbs resampling operator and improved Metropolis algorithm are combined to realize sampling of posterior probability, the sequential gibbs resampling operator is a sampling mode combining gibbs sampling and sequential simulation, and is a re-simulation algorithm, which can perform rapid disturbance sampling on prior information and keep the spatial structure consistent, and then the improved Metropolis algorithm is combined to realize sampling of posterior probability, so as to avoid calculating complex high-dimensional prior distribution, and ensure the calculation efficiency of inversion, specifically:
(1) improved Metropolis operator
The classical Metropolis algorithm needs to calculate the prior information rho at the same timeM(m) and likelihood functions L (m), however for some complex a priori information ρ is calculatedM(m) can be difficult. To this end, an improved Metropolis algorithm is used to sample the posterior probability distribution.
Suppose mcurrentIs an initial model, representing the current prior distribution pM(m) a first realization ofproposeIs a proposed model, representing the initial model mcurrentIs also an implementation of the prior distribution. The likelihood functions of these two realizations are simultaneously calculated according to equation (3), which is respectively expressed as: l (m)current)，L(mpropose). The acceptance criteria for the improved Metropolis operator are as follows:
the sampling operator does not need to calculate the prior probability rho of a high dimension relative to the classical Metropolis operatorM(m) that can be applied to complex a priori information, but must be able to perturb the sampling of the a priori information.
(2) Sequential Gibbs resampling
The implementation of the prior information can be obtained by a Direct Sequential Simulation (DSS) method, but when a modified Metropolis operator is used, it is necessary to be able to make the current model gradually perturbed to other models, and the perturbed model needs to be consistent with the spatial structure of the prior information.
The method comprises the steps of using sequential Gibbs resampling to quickly disturb prior information, using a sequential Gibbs resampling operator as a sampling mode for combining Gibbs sampling and sequential simulation, selecting a subset S of model parameters, performing conditional re-simulation on the subset in a sequential simulation mode, repeating the conditional re-simulation on the subset to quickly disturb sampling on the prior information, and keeping the spatial structure consistent. The sequential Gibbs resampling can disturb prior information by only re-simulating part of model parameters each time, the calculation efficiency is high, the receiving rate of the improved Metropolis operator can be adjusted by controlling the size of the subset, and the receiving rate is usually maintained between 25% and 50%. The posterior probability sampling can be realized by combining an improved Metropolis sampling operator, and the method comprises the following steps:
1) firstly, an initial model m is generated through a DSS algorithmcurrentAnd calculating its likelihood function L (m)current)。
2) A subset S of the model parameters, i.e. the re-simulation region, is randomly selected.
3) Carrying out condition simulation on the re-simulation area to obtain a proposed model mproposeCalculating a likelihood function L (m) of the proposed modelpropose)。
4) Receiving or rejecting m according to equation (4)proposeIf received, let mcurrent＝mproposeElse mcurrentRemain unchanged.
5) Repeating the steps 2) to 4) by using random seeds, and finally realizing the sampling of the posterior probability distribution of the model parameters.
Fig. 8 is a flowchart illustrating a second implementation manner of step S104 in the embodiment of the present invention, please refer to fig. 8, where step S104 further includes:
s305: and selecting data in the neighborhood range of the sequential simulation as conditional data, and performing the sequential simulation and the sequential Gibbs resampling.
In one embodiment of the present invention, during sequential simulation (DSS, SGS, etc.) and sequential gibbs resampling, previously simulated points are added to the condition data, in addition to the initial condition data, and then the condition data is progressively increased as the simulation progresses. If all the condition data is considered, a very large kriging equation needs to be solved, which is very time and memory consuming.
Thus, consider selecting data within a certain neighborhood as conditional data, rather than all conditional data points. For the two-dimensional case, the neighborhood shape may be rectangular, circular, elliptical, etc., and the neighborhood size may be limited to twice the range of the variation function. The calculation efficiency can be greatly improved by selecting the proper simulation neighborhood, and the simulation precision can not be greatly influenced.
In the Bayesian framework, (1) firstly, the prior information of the model parameters is constructed by utilizing a direct sequential simulation algorithm which does not need the model parameters to obey Gaussian distribution, so that the limitation of the conventional simulation method is overcome; (2) then, a likelihood function fused with low-frequency information is constructed, so that an inversion result is more stable and reliable, and the search of a solution space is accelerated; (3) and then, sampling of posterior probability is realized by combining a sequential Gibbs resampling operator and an improved Metropolis algorithm, and a high-resolution inversion result is obtained.
It should be noted that while the operations of the method of the present invention are depicted in the drawings in a particular order, this does not require or imply that the operations must be performed in this particular order, or that all of the illustrated operations must be performed, to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions.
The present invention also provides a computer device comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a method of seismic stochastic inversion.
The present invention also provides a computer-readable storage medium storing a computer program for executing a seismic stochastic inversion method.
The technical solution of the present invention will be described in detail with reference to specific examples. Fig. 9 is a schematic diagram illustrating comparison between 50 inversion results (gray curves) and model data (black curves) in an embodiment provided by the present invention, fig. 10 is a schematic diagram illustrating comparison between seismic records synthesized by 50 inversion results (gray curves) and real seismic records (black curves) in an embodiment provided by the present invention, fig. 11 is a schematic diagram illustrating inversion of constrained sparse pulses in an embodiment provided by the present invention, and fig. 12 is a schematic diagram illustrating random inversion in an embodiment provided by the present invention. As can be seen from fig. 9 to 12, in the bayesian framework of the invention, (1) the prior information of the model parameters is first constructed by using the direct sequential simulation algorithm, and the direct sequential simulation algorithm does not need the model parameters to obey gaussian distribution, thereby overcoming the limitation of the conventional simulation method; (2) the likelihood function fused into the low-frequency information is constructed by utilizing the seismic data and the low-frequency model, and the introduction of the low-frequency model not only can enable the inversion result to be more stable and reliable, but also can accelerate the search of a solution space; (3) the prior information of the model parameters is disturbed by utilizing a sequential Gibbs resampling operator, and the sequential Gibbs resampling is an algorithm of sequential resampling and can quickly disturb the prior information. (4) And finally, the improved Metropolis algorithm is combined to realize the sampling of the posterior probability, and the improved Metropolis operator can avoid calculating the high-dimensional prior probability and is suitable for complex prior information. Compared with the conventional deterministic inversion method, the inversion result with high vertical resolution can be obtained.
Improvements to a technology can clearly be distinguished between hardware improvements (e.g. improvements to the circuit structure of diodes, transistors, switches, etc.) and software improvements (improvements to the process flow). However, as technology advances, many of today's process flow improvements have been seen as direct improvements in hardware circuit architecture. Designers almost always obtain the corresponding hardware circuit structure by programming an improved method flow into the hardware circuit. Thus, it cannot be said that an improvement in the process flow cannot be realized by hardware physical modules. For example, a Programmable Logic Device (PLD), such as a Field Programmable Gate Array (FPGA), is an integrated circuit whose Logic functions are determined by programming the Device by a user. A digital system is "integrated" on a PLD by the designer's own programming without requiring the chip manufacturer to design and fabricate application-specific integrated circuit chips. Furthermore, nowadays, instead of manually making an Integrated Circuit chip, such Programming is often implemented by "logic compiler" software, which is similar to a software compiler used in program development and writing, but the original code before compiling is also written by a specific Programming Language, which is called Hardware Description Language (HDL), and HDL is not only one but many, such as abel (advanced Boolean Expression Language), ahdl (alternate Language Description Language), traffic, pl (core unified Programming Language), HDCal, JHDL (Java Hardware Description Language), langue, Lola, HDL, laspam, hardbyscript Description Language (vhr Description Language), and the like, which are currently used by Hardware compiler-software (Hardware Description Language-software). It will also be apparent to those skilled in the art that hardware circuitry that implements the logical method flows can be readily obtained by merely slightly programming the method flows into an integrated circuit using the hardware description languages described above.
The controller may be implemented in any suitable manner, for example, the controller may take the form of, for example, a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro) processor, logic gates, switches, an Application Specific Integrated Circuit (ASIC), a programmable logic controller, and an embedded microcontroller, examples of which include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicone Labs C8051F320, the memory controller may also be implemented as part of the control logic for the memory.
Those skilled in the art will also appreciate that, in addition to implementing the controller as pure computer readable program code, the same functionality can be implemented by logically programming method steps such that the controller is in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Such a controller may thus be considered a hardware component, and the means included therein for performing the various functions may also be considered as a structure within the hardware component. Or even means for performing the functions may be regarded as being both a software module for performing the method and a structure within a hardware component.
The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions.
For convenience of description, the above devices are described as being divided into various units by function, and are described separately. Of course, the functionality of the units may be implemented in one or more software and/or hardware when implementing the present application.
From the above description of the embodiments, it is clear to those skilled in the art that the present application can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present application may be essentially or partially implemented in the form of software products, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and include instructions for causing a computer system (which may be a personal computer, a server, or a network system, etc.) to execute the methods described in the embodiments or some parts of the embodiments of the present application.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The application is operational with numerous general purpose or special purpose computing system environments or configurations. For example: personal computers, server computers, hand-held or portable systems, tablet-type systems, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics systems, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or systems, and the like.
The application may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The application may also be practiced in distributed computing environments where tasks are performed by remote processing systems that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage systems.
While the present application has been described with examples, those of ordinary skill in the art will appreciate that there are numerous variations and permutations of the present application without departing from the spirit of the application, and it is intended that the appended claims encompass such variations and permutations without departing from the spirit of the application.
Claims (14)
1. A method of seismic stochastic inversion, the method comprising:
acquiring seismic data and a low-frequency model;
constructing prior information of model parameters;
constructing a likelihood function fused into low-frequency information by using the seismic data and the low-frequency model;
and sampling the posterior probability according to the prior information and the likelihood function to obtain an inversion result.
2. The method of claim 1, wherein the prior information for the constructed model parameters comprises:
constructing prior information of the model parameters by using a direct sequential simulation algorithm;
a histogram of the prior information is reproduced.
3. The method of claim 2, wherein the likelihood function is constructed by:
wherein L (m) is a likelihood function, m is a model parameter, d is observation data, g is a positive operator, σeIs Gaussian noise variance, alpha is an adjustable factor, mLFMIs a low frequency model.
4. The method of claim 3, wherein sampling a posterior probability based on the prior information and a likelihood function to obtain an inversion result comprises:
gibbs sampling and sequential simulation are combined to form a sequential Gibbs resampling operator;
perturbing the prior information using the sequential Gibbs resampling operator;
constructing an improved Metropolis algorithm;
and (4) sampling the posterior probability by combining the sequential Gibbs resampling operator and an improved Metropolis algorithm to obtain an inversion result.
5. The method as in claim 4, wherein the acceptance criteria of the modified Metropolis operator is:
wherein m iscurrentAs an initial model, mproposeTo suggest a model, L (m)current) As a likelihood function of the initial model, L (m)propose) Is a likelihood function of the proposed model.
6. The method of claim 4, wherein sampling a posterior probability based on the prior information and a likelihood function to obtain an inversion result further comprises:
and selecting data in the neighborhood range of the sequential simulation as conditional data to perform the sequential simulation and the sequential Gibbs resampling.
7. A seismic stochastic inversion system, the system comprising:
the seismic data acquisition module is used for acquiring seismic data and a low-frequency model;
the prior information construction module is used for constructing the prior information of the model parameters;
the likelihood function construction module is used for constructing a likelihood function fused into low-frequency information by using the seismic data and the low-frequency model;
and the inversion result determining module is used for realizing the sampling of the posterior probability according to the prior information and the likelihood function so as to obtain the inversion result.
8. The system of claim 7, wherein the prior information construction module comprises:
the prior information determining module is used for constructing the prior information of the model parameters by using a direct sequential simulation algorithm;
and the histogram reproduction module is used for reproducing the histogram of the prior information.
9. The system of claim 7, wherein the likelihood function is constructed by:
wherein L (m) is a likelihood function, m is a model parameter, d is observation data, g is a positive operator, σeIs the variance of Gaussian noise, alpha is a tunable factor, mLFMIs a low frequency model.
10. The system of claim 7, wherein the inversion result determination module comprises:
the sampling operator forming module is used for combining Gibbs sampling and sequential simulation to form a sequential Gibbs resampling operator;
the prior information disturbance module is used for disturbing the prior information by using the sequential Gibbs resampling operator;
the improved algorithm construction module is used for constructing an improved Metropolis algorithm;
and the posterior probability acquisition module is used for sampling the posterior probability by combining the sequential Gibbs resampling operator and the improved Metropolis algorithm so as to obtain an inversion result.
11. The system as in claim 10, wherein the acceptance criteria of the improved Metropolis operator is:
wherein m iscurrentAs an initial model, mproposeTo suggest a model, L (m)current) As a likelihood function of the initial model, L (m)propose) Is a likelihood function of the proposed model.
12. The system of claim 10, wherein the inversion result determination module further comprises:
and the neighborhood range selection module is used for selecting data in the neighborhood range of the sequential simulation as conditional data, and performing the sequential simulation and the sequential Gibbs resampling.
13. A computer device, comprising: a processor adapted to implement instructions and a storage device storing instructions adapted to be loaded by the processor and to perform a method of seismic stochastic inversion according to any of claims 1 to 6.
14. A computer-readable storage medium, in which a computer program is stored, the computer program being adapted to perform a method of seismic stochastic inversion according to any of the claims 1 to 6.
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