A multi-scale integrated well logging data super-resolution method based on fractal theory

Abstract

The application provides a well logging data super-resolution method, in particular to a multi-scale integrated well logging data super-resolution method based on fractal theory, in order to realize accurate and reliable characterization of a target reservoir and solve the problem that the traditional super-resolution method does not consider geological heterogeneity. The method excavates the structural fractal characteristics of the well logging data through the fractal theory, fully plays the time sequence information of the well logging data in the process of constructing a large-scale nonlinear mapping model under different scales by using an LSTM network, and then integrates and optimizes the super-resolution results of each scale through the LSTM network to obtain a final super-resolution result. In the super-resolution process, the multi-scale fractal shape and time sequence information of the well logging data are excavated as much as possible, and compared with the traditional single fractal interpolation method, the robustness and accuracy of the super-resolution result are greatly improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of petroleum engineering, and particularly relates to a multi-scale integrated well logging data super-resolution method based on fractal theory. BACKGROUND

[0002] Oil and gas resources, as the most important primary energy in the world, play an increasingly important role in the world's energy consumption. Unconventional oil and gas resources have become the main target of global exploration and development. However, unconventional oil and gas reservoirs have the disadvantage of poor flowability due to low porosity and low permeability, which brings new difficulties to the development process. In order to realize the effective production of unconventional oil and gas resources, the requirement for fine-scale characterization of oil and gas reservoirs is getting higher and higher. Therefore, the research on improving the accuracy of oil and gas resource characterization has always been the focus of the relevant field.

[0003] In order to realize the accurate and reliable characterization of the target reservoir, multi-scale geological data such as core, logging and seismic are usually used. Among these geological data, the economic cost of obtaining sufficient core data with the highest vertical resolution is very expensive, and the vertical resolution of seismic data is too low to meet the fine-scale reservoir characterization. The vertical resolution of logging data is relatively higher than that of seismic data, and the cost is much lower than that of core data, and it is an important data for fine-scale reservoir characterization. Therefore, improving the vertical resolution of logging can directly improve the accuracy and reliability of reservoir characterization. In the literature, there are two methods to improve the vertical resolution of logging: one is to improve the hardware performance of logging instrument; the other is to use some signal super-resolution technology on the original logging data. The former is the most effective in principle, but in practice it needs a lot of manpower, material resources and financial cost; on the contrary, the latter can significantly reduce the cost by using advanced signal processing and deep learning technology to improve the vertical resolution of logging.

[0004] The conventional logging resolution enhancement method, such as vertical resolution matching method, spline function interpolation, deconvolution and other techniques, usually regards the formation as a homogeneous body. However, in fact, any formation is heterogeneous, and the formation of unconventional reservoirs is more complex, so using a homogeneous model will inevitably produce a large error. Therefore, people have proposed different kinds of machine learning techniques, such as neural network, CNN, to improve the vertical resolution enhancement characterization performance of logging data. In these methods, the multi-scale fractal shape and time sequence information in the target logging curve are far from being fully utilized. Therefore, a new method is needed to fully utilize the fractal information and time sequence information of logging data to achieve a super-resolution result that is more in line with the geological conditions. SUMMARY

[0005] The purpose of the present application is to solve the problem that the existing super-resolution method does not fully consider the heterogeneous geology, and fully utilizes the fractal information and time sequence information of the logging data, and the present application provides a logging data super-resolution method based on multi-scale integration of fractal theory, which comprises the following steps:

[0006] Step one: judging the self-similarity of the logging data to obtain a parameter that can measure the degree of self-similarity of the logging data;

[0007] Step two: selecting a method for mining self-similarity information according to the parameter of the degree of self-similarity of the logging data obtained in step one, judging whether the logging data has strict similarity, if the logging data is strictly self-similar, using the traditional fractal interpolation method, if it is not strictly self-similar, using the piecewise interpolation method;

[0008] Step three: establishing an iterative function system of the corresponding method, determining the parameter values and the fractal interpolation function;

[0009] Step four: fractal interpolation of the logging data set according to the function iterative system of step three, obtaining an interpolation result with large-scale difference from the original data;

[0010] Step five: using a multi-view multi-scale integrated machine learning method to perform large-scale difference nonlinear mapping on the result obtained in step four and the original data, and establishing a logging data super-resolution machine learning model;

[0011] Step six: using the machine learning model to perform logging data super-resolution on unknown wells and evaluating the results.

[0012] The present application has the following beneficial results:

[0013] The present application proposes a new multi-scale integrated logging super-resolution method, which combines fractal interpolation and LSTM network. Specifically, fractal interpolation technology is used to mine the nonlinear self-similarity information of the logging data, and then LSTM is used to reveal the corresponding time sequence information. Finally, the final super-resolution result is obtained by performing multi-view and multi-scale integrated regression mapping. In the super-resolution process, the geological heterogeneity is considered, the multi-scale fractal shape and time sequence information of the logging data are mined as much as possible, and the accuracy of the super-resolution result is greatly improved compared with the traditional single fractal interpolation method. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 The flowchart of the logging data super-resolution method based on multi-scale integration of fractal theory described in the present application;

[0015] Figure 2 The fractal interpolation result diagram of the GR curve of a certain experimental well of the logging data super-resolution method based on multi-scale integration of fractal theory described in the fifth embodiment of the present application;

[0016] Figure 3 The schematic diagram of the super-resolution result of the GR curve of well Gu 204 in the local neighborhood of 6 scales based on the fractal theory multi-scale integrated well logging data super-resolution method described in embodiment six of the present application;

[0017] Figure 4 The schematic diagram of the super-resolution result of the GR curve of well Gu 204 in the local neighborhood of 12 scales based on the fractal theory multi-scale integrated well logging data super-resolution method described in embodiment six of the present application;

[0018] Figure 5 The schematic diagram of the super-resolution result of the GR curve of well Gu 204 in the local neighborhood of 18 scales based on the fractal theory multi-scale integrated well logging data super-resolution method described in embodiment six of the present application;

[0019] Figure 6 The schematic diagram of the super-resolution result of the GR curve of well Gu 204 in the local neighborhood of 24 scales based on the fractal theory multi-scale integrated well logging data super-resolution method described in embodiment six of the present application;

[0020] Figure 7 The schematic diagram of the final super-resolution result of the GR curve of well Gu 204 based on the fractal theory multi-scale integrated well logging data super-resolution method described in embodiment six of the present application;

[0021] Figure 8 The schematic diagram of the super-resolution result comparison of the GR curve of well Gu 204 based on the fractal theory multi-scale integrated well logging data super-resolution method described in the present application and the methods of sparse representation, bicubic linear interpolation, SRCNN network and random forest network;

[0022] Figure 9 The schematic diagram of the super-resolution result comparison of the low-resolution data obtained by 4 times down-sampling of the original well logging data and the original data and the high-frequency information recovery based on the fractal theory multi-scale integrated well logging data super-resolution method described in the present application;

[0023] Figure 10 The schematic diagram of the super-resolution result comparison of the GR, DEN, AC and LLD curves of well Gu 203 based on the fractal theory multi-scale integrated well logging data super-resolution method described in the present application and the original data. EMBODIMENT

[0024] Embodiment one:

[0025] In combination with Figure 1To illustrate the embodiments, the fractal theory-based multi-scale integrated well logging data super-resolution method of the embodiments includes the following steps:

[0026] Step one: judging self-similarity of the well logging data to obtain a parameter that can measure the self-similarity degree of the well logging data;

[0027] Step two: selecting a method for mining self-similarity information according to the parameter of the self-similarity degree of the well logging data obtained in step one, if the well logging data is strictly self-similar, a traditional fractal interpolation method is used, if not strictly self-similar, a piecewise interpolation method is used;

[0028] Step three: establishing an iterative function system of the corresponding method, determining parameter values and a fractal interpolation function;

[0029] Step four: fractal interpolating the well logging data set according to the function iterative system of step three to obtain an interpolation result that has a large-scale difference from the original data;

[0030] Step five: using a multi-view multi-scale integrated machine learning method to perform a large-scale difference nonlinear mapping on the result obtained in step four and the original data, and establishing a well logging data super-resolution machine learning model;

[0031] Step six: using the machine learning model to perform well logging data super-resolution on an unknown well and evaluating the well.

[0032] Embodiment two:

[0033] The embodiment is a further limitation on the fractal theory-based multi-scale integrated well logging data super-resolution method of embodiment one,

[0034] The method for judging self-similarity of the well logging data in step one is as follows:

[0035] The range analysis method (R / S analysis method) is used to calculate the Hurst index, and the specific calculation formula is shown in formula (1):

[0036]

[0037] Wherein, SubsequenceLengthL is the length of the subsequence after reorganizing the well logging data, R a (SubsequenceLengthL) is the range of the first SubsequenceLengthL numbers, S(SubsequenceLengthL) is the standard deviation, E() represents the expected value, C represents a constant, and H is the Hurst index. Using the R / S analysis method, the well logging data with a length of N is divided into subsequences with lengths of Short sequence, for each Subsequence Length L, calculate its re-label difference Draw The slope of the straight line fitted to the plot of ln(Subsequence Length L) is the value of the Hurst exponent H.

[0038] Embodiment Three:

[0039] The embodiment is a further limitation of the multi-scale integrated well logging data super-resolution method based on fractal theory of the specific embodiment one,

[0040] The method for mining self-similarity information of well logging data in step two is:

[0041] The Hurst exponent H obtained according to step one can reflect the autocorrelation of the sequence. When H=0.5, it indicates that the sequence is random and unrelated. When H≠0.5, the sequence has fractal characteristics. When 0

[0042] When the well logging data has strong self-similarity, traditional fractal interpolation can be used to mine self-similarity information. When the Hurst exponent of the well logging data is close to 0.5, it is considered that the well logging data has weak self-similarity. If a traditional fractal interpolation is used to mine self-similarity information of the well logging data, only one iteration function system is used for the whole well logging curve, and the influence of the vertical scaling factor is not considered, which will cause a large error. Therefore, for well logging curves with small self-similarity, a segmented fractal interpolation method is used.

[0043] Embodiment Four:

[0044] The embodiment is a further limitation of the multi-scale integrated well logging data super-resolution method based on fractal theory of the specific embodiment one,

[0045] The iteration function system for constructing the fractal interpolation function in step three is as follows:

[0046] For a set of well logging data where Index I and M are constants, x IndexI is the logging depth, y IndexI is the well logging data corresponding to the corresponding depth, represents a two-dimensional space. The fractal interpolation function f(x) based on this data set needs to satisfy f(x IndexI )=y IndexI , Index I=0, 1,..., M, and the iteration function system needs to be constructed to determine f(x), ω IndexIThe function in the iterative function system is represented, and each function in the iterative function system is an affine transformation, represented as:

[0047]

[0048] and satisfies the end point condition

[0049]

[0050] The parameter a IndexI , c IndexI , e IndexI , f IndexI is obtained from the formula (2), (3)

[0051]

[0052] In the formula, aIndexI is a standard parameter of adjacent depth, c IndexI is a standard parameter of adjacent sampling points, eIndexI is a standard parameter of depth intersection, fIndexI is a standard parameter of adjacent sampling points on the depth interval, and dIndexI is a free parameter, referred to as a vertical scale factor. Since the fractal dimension D and the Hurst index H satisfy a linear relationship D = 2 - H, there is

[0053]

[0054] When the interpolation point and the vertical scale factor are determined, the corresponding coefficients a IndexI , c IndexI , e IndexI , f IndexI are obtained according to the formula (4), and the corresponding iterative function system is determined.d IndexI The size of d can be calculated according to the formula (5) after the Hurst index is obtained. Thus, the iterative function system (IFS) and the fractal interpolation function are determined.

[0055] Embodiment Five

[0056] The embodiment is a further limitation of the multi-scale integrated well logging data super resolution method based on fractal theory in the specific embodiment one,

[0057] Step four: fractal interpolation of the well logging data set according to the iterative function system in step three:

[0058] The original well logging data set is regarded as an interpolation point for fractal interpolation, and each parameter of the iterative function system and the fractal interpolation function obtained in step three is used to perform fractal interpolation on the original well logging data set, so as to obtain an interpolation result based on the data set.

[0059] Embodiment Six

[0060] The embodiment is further limitation of the multi-scale integrated logging data super-resolution method based on fractal theory in the specific embodiment one,

[0061] The multi-view multi-scale integrated machine learning method for establishing the large-scale difference nonlinear mapping model in step five is:

[0062] The fractal interpolation result will have a large-scale difference with the original data amount, and additional high-frequency information is brought, so it is necessary to establish a nonlinear mapping model, and the application proposes to establish a multi-view multi-scale nonlinear mapping model Indicated as:

[0063]

[0064] Among them, The nonlinear multi-view multi-scale model is realized by using a long short-term memory network (LSTM), DepthD represents the target depth, and NPoint represents a local neighborhood point set, L is a local neighborhood point set of high-resolution data obtained by fractal interpolation of low-resolution logging data with a depth of DepthD points, and L SR is a logging data super-resolution value with a target depth of DepthD at the current scale, ScaleS=1, 2, 3,... represents signals of different scales, and ViewV=1, 2, 3,... represents different views, i.e., filtering high-dimensional data by different methods.

[0065] Next, a depth-to-multi-scale estimation integration method is used to optimize the model to ensure the accuracy and reliability of the model, i.e.:

[0066]

[0067] Among them, H SR is a logging data super-resolution result of the target depth DepthD, and G represents a multi-scale integrated model. is a logging data super-resolution result of DepthD at the ScaleS scale, and the model is realized by using an LSTM network.

[0068] The LSTM network is a special recurrent neural network that can solve the long-term dependence of sequence deep learning models. It can not only extract information from sequence data like a standard recurrent neural network, but also retain information with long-term correlation from previous steps. Therefore, the application uses the longitudinal (i.e., depth) semantic information mining capability of LSTM to establish a logging data super-resolution machine learning model.

[0069] Embodiment seven:

[0070] The embodiment is further limited to the fractal theory-based multi-scale integrated well logging data super-resolution method of the specific embodiment one,

[0071] The method for super-resolving and quantitatively evaluating unknown wells in step six by using the machine learning model established in step five is:

[0072] The structural information of the well logging data is mined through the fractal theory, the interpolation results are optimized by using various filtering methods, the corresponding well logging data of the test well is super-resolved at different scales, the final super-resolution results are obtained by integrating the regression results, and the super-resolution effect is quantitatively evaluated by using the root mean square error (RMSE), the mean absolute error (MAE), the peak signal-to-noise ratio (PSNR) and the Pearson correlation coefficient, and the calculation formula is as follows:

[0073]

[0074] wherein, is a maximum value in the depth sampling vector y IndexI , H(x IndexI ) represents the super-resolution result of the IndexIth depth sampling point on the depth axis, and Corr Pearson is the Pearson correlation coefficient, Cov(y IndexI , y IndexI-1 ) represents the covariance of adjacent depth sampling vectors, and sigma (y IndexI ) represents the standard deviation of the depth sampling vector y IndexI .

[0075] In order to verify the effectiveness of the method, the logging data of five wells randomly selected in the Qijia-Gulong sag in the western region of Changyuan in Daqing, north of Songliao Basin, are taken as the research objects, and the logging super-resolution method is directly verified by 4 times super-resolution experiment. The experimental results show that the method can fuse the structural information of the logging data, realize high accuracy super-resolution effect and effective high-frequency information, and has certain practical value.

[0076] In the logging curve selection, four logging conventional curves of GR, DEN, AC and LLD are selected, Figure 7 a schematic diagram of the super-resolution result and the original data is given.

[0077] However, the experimental results also reflect that the method needs to be improved. Since the vertical scaling factor d is related to the Hurst coefficient, the optimal value is not obtained, resulting in the existence of pseudo-peak in the fractal interpolation and the final result. Therefore, in the subsequent research, the calculation method of d needs to be further optimized to make the error of the fractal interpolation result smaller and realize the further enhancement of the super-resolution effect.

[0078] The present application aims at the problem of insufficient consideration of geological heterogeneity and self-similarity of logging data in the classical logging data super-resolution research, and proposes a multi-view multi-scale logging data super-resolution method based on fractal theory. Through direct 4 times super-resolution experiment on different wells and different logging curves, it is found that the self-similarity of most logging curves is not particularly significant, so the fractal interpolation is mainly used to mine the self-similarity of logging data. After fractal interpolation of the original data, the interpolation results combined with the structure information of the logging data are obtained, which have large-scale differences with the original data. Due to the large difference in data quantity, it is necessary to establish a nonlinear mapping model. In order to fully utilize the rich high-resolution context information of specific depth logging data, the multi-view multi-scale nonlinear mapping method is used to map the high-resolution data to the target resolution data, and the results at each scale are integrated and optimized by using LSTM network to obtain the final super-resolution result.

[0079] The method of the present application fully utilizes the rich high-resolution context information of specific depth logging data by using LSTM network while considering the structure information of logging data. Compared with the traditional single fractal interpolation method and bicubic interpolation, sparse representation and random forest method, the method of the present application has better accuracy and robustness. Referring to the higher resolution imaging resistivity data, it is found that the super-resolution result of the present application has effective high-frequency information, as shown in the following figure. Figure 6

[0080] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can understand and think of the transformation or replacement within the technical scope of the present application, which should be covered in the protection scope of the claims of the present application.​

Claims

1. A multi-scale integrated super-resolution method for well logging data based on fractal theory, characterized in that, It comprises the following steps: Step one: self-similarity judgment is made on the logging data to obtain a parameter capable of measuring the degree of self-similarity of the logging data; The method for judging the self-similarity of the logging data is to calculate the Hurst index by using the weighted range analysis method: where SubsequenceLengthL is the length of the subsequence after reorganization of the well logging data, R a is the range of the first SubsequenceLengthL numbers, S(SubsequenceLengthL) is their standard deviation, denotes the expected value, C denotes a constant, and H is the Hurst exponent; using the R / S analysis method, a well logging data of length N is divided into short sequences of lengths For each SubsequenceLengthL, the re-scaled range is calculated, and a plot of ln(SubsequenceLengthL) is drawn, and the slope of the straight line fitted to the plot is the value of the Hurst exponent H. Step two: the method for mining self-similarity information is selected according to the parameter of the degree of self-similarity of the logging data obtained in step one, if the logging data is strictly self-similar, the traditional fractal interpolation method is used, if it is not strictly self-similar, the piecewise fractal interpolation method is used; Step three: an iterative function system of the corresponding method is established, and the parameter values and the fractal interpolation function are determined; Constructing iterated function systems where IndexI is a constant, denotes a two-dimensional space, ω IndexI denotes a function in the iterated function system, is given by And the end point data satisfy Wherein, x IndexI is the logging depth, y IndexI is the logging data corresponding to the corresponding depth, parameters a IndexI , c IndexI , e IndexI , f IndexI are obtained from formulas (2), (3), and the calculation formula is: where a IndexI is a standard parameter of adjacent depth, c IndexI is a standard parameter of adjacent sampling points, e IndexI is a standard parameter of depth crossing, f IndexI is a standard parameter of adjacent sampling points in depth interval, d IndexI is a free parameter, called vertical scale factor, and |d IndexI | < 1; when and the interpolation points are not collinear, the fractal dimension D of the fractal interpolation function f(x) image satisfies Since the fractal dimension D and the Hurst index H satisfy the linear relationship D = 2 - H, there is When the interpolation point and vertical scaling factor are determined, the corresponding coefficient a is obtained according to equation (4). IndexI c IndexI e IndexI f IndexI Determine the corresponding iterative function system, d IndexI The size can be calculated according to equation (5) after obtaining the Hurst exponent; Step four: fractal interpolation is made on the logging data set according to the iterative function system of step three, and an interpolation result with large-scale difference from the original data is obtained; Step five: a multi-view multi-scale integrated machine learning method is used to make large-scale difference nonlinear mapping on the result obtained in step four and the original data, and a logging data super-resolution machine learning model is established; Step six: the machine learning model is used to make logging data super-resolution on unknown wells and make quantitative evaluation.

2. The method of claim 1, wherein the method is based on fractal theory of multiscale integration of well logging data super-resolution. The method for mining self-similarity information in step two: According to the Hurst index H obtained in step one, the self-correlation of the sequence can be reflected, when H=0.5, it indicates that the sequence is random and unrelated; when H≠0.5, the sequence has fractal characteristics, wherein: 0 When the logging data has strong self-similarity, the traditional fractal interpolation is selected to mine self-similarity information, when the logging data has weak self-similarity, the piecewise fractal interpolation method is selected to mine self-similarity information of the logging data.

3. The method of claim 2, wherein the method is based on fractal theory of multiscale integration of well logging data super-resolution. The multi-view multi-scale integrated machine learning method for establishing the large-scale difference nonlinear mapping model in step five is: wherein g is a nonlinear multi-view multi-scale model, which is implemented by using a long short-term memory network (LSTM); DepthD represents a target depth; NPoint represents a local neighborhood point set of high-resolution data with the depth of DepthD obtained by fractal interpolation on low-resolution well logging data, NPoint represents a local neighborhood point set of high-resolution data with the depth of DepthD obtained by fractal interpolation on low-resolution well logging data, SR ScaleS=1, 2, 3,... represents signals at different scales; and ViewV=1, 2, 3,... represents different views, i.e., filtering of high-dimensional data by using different methods. Next, the deep multi-scale estimation integration method is used to optimize the model to ensure the accuracy and reliability of the model, that is: wherein H SR is the logging data super-resolution result of the target depth DepthD, and G represents the multi-scale integrated model; represents the logging data super-resolution result of DepthD at the ScaleS-th scale, and the model is implemented using an LSTM network.

4. The method of claim 3, wherein the method is based on fractal theory of multiscale integration of well logging data super-resolution. The evaluation indexes for evaluating the super-resolution effect in step six are root mean square error RMSE, mean absolute error MAE, peak signal-to-noise ratio PSNR, and Pearson correlation coefficient, and the calculation formulas are as follows: in, For the depth sampling vector y IndexI The maximum value in, H(x) IndexI () represents the super-resolution result of the IndexI-th depth sampling point on the depth axis; Corr Pearson Let Pearson correlation coefficient be denoted as Cov(y). IndexI ,y IndexI-1 ) represents the covariance of adjacent depth sampling vectors; σ(y IndexI ) represents the depth sampling vector y IndexI The standard deviation.

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