A method for characterizing and assessing well integrity using acoustic data using unsupervised machine learning

Abstract

A method and system for characterizing and evaluating the integrity of a cased well using unsupervised machine learning of acoustic data is provided. Acoustic waveform data of acoustic signals received by a receiver array of an acoustic logging tool are collected and processed to determine a high-dimensional representation of the acoustic waveform data. The high-dimensional representation is input into an unsupervised machine learning system to determine a low-dimensional representation of the acoustic waveform data. A clustering method is applied to the low-dimensional representation to identify a set of clusters therein. Based on the set of clusters, the integrity characteristics of at least one well of a depth interval of the cased well are determined. In an embodiment, at least one well integrity characteristic can characterize the cement condition in the annulus of the cased well as a function of azimuth and depth, and can be used to evaluate the cement integrity in the depth interval of the cased well.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 62 / 682,249, filed on June 8, 2018; the contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates to well logging in oil and gas fields. In particular, the present disclosure relates to characterizing and assessing well integrity using acoustic data. Background Art

[0004] With the recent advent of stricter government regulations requiring oil and gas operators to deliver and maintain wells with qualified pressure seals, effective characterization and assessment of well integrity has become important. The goal is to prevent uncontrolled flow of underground formation fluids from causing leaks to the surface (e.g., atmosphere or ocean) or other formations. Characterization and assessment of well integrity can be performed after cementing operations or during the service life of the well or at the end of its service life before plugging and / or abandoning the well. Summary of the invention

[0005] This summary is provided to introduce some concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used to help limit the scope of the claimed subject matter.

[0006] In one embodiment, a method for characterizing the well integrity of a cased well is described. The method includes: i) collecting acoustic waveform data of acoustic signals received by a receiver array of an acoustic logging tool for depth intervals of the cased well; ii) determining a high-dimensional representation of the acoustic waveform data collected in i); iii) inputting the high-dimensional representation of ii) into an unsupervised machine learning system to determine a low-dimensional representation of the acoustic waveform data; iv) applying a clustering method to the low-dimensional representation of iii) to identify a set of clusters in the low-dimensional representation of iii); and v) determining at least one characteristic related to the well integrity of the depth interval of the cased well based on the set of clusters identified in iv).

[0007] Other features and advantages of the present disclosure will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] In the following detailed description, the present disclosure is further described by way of non-limiting examples of the present disclosure with reference to the several accompanying drawings mentioned, wherein like reference numerals refer to like parts throughout the several views of the drawings, in which:

[0009] Figure 1It is an acoustic logging tool (such as SONICSCANNER TM Tool) schematic diagram;

[0010] Figure 2 It can be Figure 1 Schematic diagram of an acoustic logging measurement performed by an acoustic logging tool;

[0011] Figure 3 yes Figure 1 and Figure 2 A schematic diagram of an acoustic logging tool deployed in a cased well using a multi-string casing;

[0012] Figure 4 A workflow for characterizing and assessing well integrity is shown, the workflow employing unsupervised machine learning of acoustic data acquired by an acoustic logging tool; the workflow can determine the well integrity of a cased well, such as cementing properties of at least one annulus that is part of the cased well;

[0013] Figures 5A-5C It is a slowness-time-coherence (STC) image derived from the acoustic waveform obtained from a single receiver combined with bandpass filtering at different center frequencies;

[0014] Figures 6A-6H Depicted is the STC image derived from the sound waveform obtained by eight azimuth receivers combined with bandpass filtering with a center frequency of 20 kHz;

[0015] Figure 7 Schematic diagram of the neural network structure used for a two-dimensional self-organizing map (SOM) machine learning system, which can be used for acoustic wave data compression as a Figure 4 part of the workflow;

[0016] Figure 8 Depicted by Figure 7 The U matrix of 1800 compressed STC images, each with dimensions of 72 × 240 × 3, generated by the 2D Self-Organizing Map (SOM) machine learning system from 1800 input STC images acquired by synthetic acoustic waveforms in cased wells using multi-tube casings;

[0017] Fig. 9 and Fig.10 is a schematic diagram of an autoencoder (AE) machine learning system that can be used for acoustic wave data compression as Figure 4 Part of the workflow;

[0018] Fig.11 yes Fig. 9 and Fig.10 An illustration of the encoder structure of an AE machine learning system, which can be used for acoustic wave data compression, as Figure 4Part of the workflow;

[0019] Fig.12 Depicted by Fig.11 The encoder structure of the AE machine learning system generates a U matrix of 1800 compressed STC images, each of size 9 × 30 × 8, from the original STC image of size 72 × 240 × 3. The original STC image is generated from a synthetic acoustic waveform in a cased well using multiple string casings;

[0020] Fig.13A is a diagram illustrating a naive or incorrect implementation of a variational autoencoder (VAE) machine learning system;

[0021] Fig. 13B is a diagram showing the correct implementation of a variational autoencoder (VAE) machine learning system using a reparameterized system, which can be used for acoustic wave data compression as Figure 4 part of the workflow;

[0022] Fig.14A Is Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder portion of a VAE machine learning system, where TKO data derived from monopolar acoustic waveforms are used as input to the VAE machine learning system;

[0023] Fig. 14B Is Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder portion of a VAE machine learning system, where the TKO data derived from the dipole acoustic waveform is used as input to the VAE machine learning system;

[0024] Fig. 14C Is Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder portion of a VAE machine learning system, where STC image data derived from a monopolar acoustic waveform is used as input to the VAE machine learning system;

[0025] Fig.14D Is Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder part of the VAE machine learning system, where the STC image data derived from the dipole acoustic waveform is used as the input to the VAE machine learning system;

[0026] Fig.15A yes Fig.14A Vertical bar charts of t-SNE visualization and clustering results are shown;

[0027] Fig. 15B yes Fig. 14BVertical bar charts of t-SNE visualization and clustering results are shown;

[0028] Fig. 15C yes Fig. 14C Vertical bar charts of t-SNE visualization and clustering results are shown;

[0029] Fig.15D yes Fig.14D Vertical bar charts of t-SNE visualization and clustering results are shown;

[0030] Fig.16 Depicted by Fig. 13B the compressed (low-dimensional) STC images produced by the encoder portion of the VAE machine learning system; in producing these compressed STC images, the VAE machine learning system is trained on STC images of size 101×86 (8686-dimensional) to generate new similar STC images by decoding from the 128-dimensional latent variable z; and

[0031] Fig.17 is a schematic diagram of a computer system that can be used to implement the methods and systems described herein. DETAILED DESCRIPTION

[0032] The details shown herein are merely examples and are presented only for the purpose of illustratively discussing examples of the present disclosure and for the purpose of providing what is believed to be the most useful and understandable description of the principles and conceptual aspects of the present disclosure. In this regard, no attempt is made to show the details in more detail than necessary, and the description in conjunction with the accompanying drawings makes it clear to those skilled in the art how several forms of the subject disclosure can be implemented in practice. In addition, the same reference numerals and designations in the various drawings represent the same elements.

[0033] Embodiments of the present disclosure relate to methods and systems for characterizing and assessing the well integrity of a cased well using unsupervised machine learning of acoustic data. The methods and systems employ an acoustic logging tool that transmits one or more transmitter excitations within a depth interval in a cased well. The transmitter excitations may be monopole, dipole, and / or quadrupole excitations. Acoustic waveform data generated by a receiver array of the acoustic logging tool in response to the transmitter excitations over the depth intervals are collected and processed to determine a high-dimensional representation of the acoustic waveform data. The high-dimensional representation of the acoustic waveform data is input into an unsupervised machine learning system to determine a low-dimensional representation of the acoustic waveform data. A clustering method is applied to the low-dimensional representation to identify a set of clusters in the low-dimensional representation. Based on the identified set of clusters, at least one characteristic related to the well integrity of the depth interval of the cased well is determined.

[0034] In an embodiment, the at least one characteristic relates to well integrity as a function of azimuth and depth in a cased well.For example, the at least one characteristic may characterize cement conditions in the annulus of a cased well as a function of azimuth and depth.

[0035] Acoustic measurements performed by acoustic logging tools are widely used to characterize and assess the integrity of wells, including the condition of cement placed in cased wells. Proper well integrity can inhibit and prevent fluid leakage into the subsurface formation or surface by using cement as part of the casing string. These acoustic measurements typically include acoustic (low frequency) measurements in the signal frequency range of hundreds of Hz to 20kHz.

[0036] For example, A wireline downhole tool that can be configured to perform many different sonic measurements as a function of azimuth (direction in direction) and depth (axial depth) in a cased hole. Azimuth is typically specified by an azimuth between 0 and 360 degrees about the axis of the cased hole, which corresponds to the axis of the tool when properly centered. Figure 1 Shows the SONICSCANNER TM Schematic diagram of tool 101.

[0037] Figure 2 Showing the SONICSCANNER in a cased hole TM Tools 101. SONICSCANNER TM The tool includes multiple transmitters and receivers in axial and azimuthal arrays that can be configured to excite and detect multiple drilling modes. These modes include monopole modes that can be excited at low and high frequencies and far and near (relative to the receiver array) monopole sources, dipole modes that can be excited in two orthogonal directions to produce cross-dipole excitations, and quadrupole modes for excitation in four orthogonal directions. The acoustic waveforms or arrival waves detected by the tool's receiver array at depth intervals in the cased well can be processed to determine logs related to the characteristics of the cased well environment as a function of azimuth and depth in the cased well. The depth intervals of the acoustic waveforms detected by the tool's receiver array depend on the axial position of the tool in the cased well. Near-monopole excitation can provide cement bonded log signals (CBL) as well as variable density log curves (VDL) signals, which are measurements that can be made with older generation cement bonded log curve tools. Typically, the amplitude of the early arrival portion of the CBL signal is related to the presence of cement in the annulus, and the signal is high whenever there is a lack of cement or a lack of good cementation with the casing. The VDL signal may indicate whether there is formation reach. The presence of formation reach may indicate coupling to the formation through cement attached to the formation, or vice versa.

[0038] Figure 3Tool 101 is shown positioned in a plugged well 350 penetrating a formation 360. Well 350 is shown as being equipped with a multi-column casing 370. As described herein, multi-column casing employs two or more casings whose longitudinal extents within the well overlap each other over at least a portion of the longitudinal extents of the two or more casings. Along the longitudinal extents of the overlapping casings, the multi-column casing forms a plurality of annuli, including an innermost annulus disposed within at least one outer annulus (or multiple outer annuli). The innermost annulus is the annulus between the first and second casings (in order of the formation from the center axial direction of the well). At least one outer annulus (or multiple outer annuli) is the annulus (multiple annuli) outside the second casing. For purposes of illustration, a particular section of the well is shown as having a first casing 380a and a second casing 380b, wherein the first casing 380a is surrounded by an annulus 390a, and the second casing 380b is surrounded by an annulus 390b. For a portion of its length, annulus 390a is located between casing 380a and formation 360, and for a portion of its length, annulus 390a is located between casing 380a and casing 380b. For a portion of its length, annulus 390b is located between casing 380b and formation 360. It should be understood that Figure 3 The annuli 390a, 390b may individually present various conditions or states (eg, annulus is hard cement, annulus is light cement, annulus is water) or other conditions or states that may affect the integrity of the well.

[0039] Recently, when plugging and / or abandoning cased wells, the use of multi-string casing (e.g. Figure 3 Characterizing and evaluating well integrity in cased wells (multi-string casing) is of increasing interest. In such applications, the data received from acoustic measurements are high-dimensional and often contain multiple modalities, and currently no deterministic inversion methods exist to automatically interpret the wellbore integrity / cementing properties of cased wells from such data.

[0040] According to the present disclosure, an unsupervised machine learning system can be used to provide a data-driven method to characterize and evaluate well integrity (including cementing characteristics of the annulus (multiple annuli) of a cased well) from high-dimensional acoustic data. Unlike supervised machine learning systems that require input signals and labeled output characteristics as a training set, unsupervised machine learning systems use high-dimensional acoustic data as input without any labels. In addition, due to the "curse of dimensionality" phenomenon, applying clustering algorithms to high-dimensional data is more challenging than applying them to low-dimensional data. The unsupervised machine learning system can provide a low-dimensional representation of unlabeled high-dimensional acoustic data for clustering, and therefore, it is applicable to many subsurface data with knowledge discovery potential, thereby releasing untapped value.

[0041] In an embodiment, the unsupervised machine learning system may employ one or more of the following: a self-organizing map (SOM) machine learning system, a SOM with an autoencoder (SOM-AE) machine learning system, a variational auto-encoder (VAE) machine learning system, and / or a generative adversarial network (GAN) machine learning system. Each of these four options is based on a neural network and has good generalization capabilities to generate a low-dimensional representation of high-dimensional acoustic wave data.

[0042] The SOM machine learning system employs a two-layer neural network that is trained using a competitive learning method (a form of unsupervised learning) to generate a representation graph of high-dimensional input data that is not more than 3 dimensions and discretized. Each network neuron of the two-layer neural network with no more than three coordinates is fully connected to the input layer, which has the same number of neurons as the input dimension, and no neurons are connected to each other. Once the SOM machine learning system is trained using the input data, the weight vectors of all neurons constitute a codebook. The Euclidean distance between the codebook vectors of adjacent neurons approximates the topological structure of the input data, that is, data samples that are close to each other in the high-dimensional input space are mapped to nearby SOM neurons and can therefore be used for adaptive clustering. As a powerful tool for interpreting results, the unified distance matrix (U-matrix) can be used to visualize the trained SOM machine learning system by depicting the Euclidean distance between the codebook vectors of adjacent neurons in the image.

[0043] The SOM-AE machine learning system extends the SOM machine learning system by reducing the high dimensionality of input data to an intermediate dimension using the encoder of an autoencoder (AE), and then feeding the compressed result (intermediate dimension) generated by the encoder part of AE to a single-layer neural network (the same as in the SOM machine learning system). AE uses a multi-layer neural network structure having an input layer, an output layer having the same number of neurons as the input layer, and one or more hidden layers connecting them. AE includes an encoder part as the first half and a decoder part as the second half, which are designed as a bottleneck topology in which the number of neurons in the encoder part decreases and the number of neurons in the decoder part increases.

[0044] The VAE machine learning system is different from other unsupervised learning systems, such as SOM and AE, because it can not only reduce the dimensionality of high-dimensional data to a low-dimensional latent variable space, but also generate unforeseen new samples, such as those in the training set, but not exactly the same. Such ability depends on its understanding of the input data space. The ability to approximate the probability distribution p(x) of a given input. However, due to the curse of dimensionality, modeling a high-dimensional space of inputs is difficult. Instead, we can assume that there is a latent space So each given input data Latent variables It is generated by complex projection f(z). Once p(z) and f(z) are known, p(x) can be simply obtained as p(x) = ∫p(x|z)p(z)dz. The VAE machine learning system assumes that p(z) is normally distributed and uses a multi-layer neural network similar to AE via an encoder-decoder structure from the training data space. f(z) is learned from the kernel, resulting in the optimal network parameters and the corresponding latent variables for further clustering. In addition, new samples x can be generated by randomly sampling from the normal distribution p(z) and passing p(x|z) as a decoder.

[0045] The GAN machine learning system employs two neural networks (a generator and a discriminator) that compete with each other in a zero-sum game framework. The generator generates candidate data distributions, while the discriminator evaluates the candidate data distributions. Typically, the generator learns to map from a latent space to the data distribution of interest, while the discriminator distinguishes the candidates generated by the generator from the real data distribution. The training goal of the generator network is to improve the error rate of the discriminator network (i.e., by generating novel candidates that "fool" the discriminator network into thinking are not synthetic and are part of the real data distribution).

[0046] In an embodiment, one or more waveform processing methods may be applied to acoustic waveform data representing acoustic signals received by a receiver array of an acoustic logging tool for a range of depth values ​​(or depth intervals) in a cased well to derive high-dimensional input data for input into an unsupervised machine learning system.

[0047] For example, a first waveform processing method, referred to as the TKO method or the matrix pencil (MP) method, can be applied to acoustic waveform data representing acoustic signals received by a receiver array of an acoustic logging tool for a range of depth values ​​in a cased well to generate data representing the dispersion relationship between slowness and frequency in the acoustic waveform data. The details of the TKO method are described in: M. P. Ekstrom, "Dispersion estimation from borehole acoustic arrays using a modified matrix pencil algorithm," in Conference Record of The Twenty-Ninth Asian Conference on Signals, Systems and Computers, Pacific Grove, CA, 1995, and Y. Hua and T. K. Sarkar, "Matrix pencil method for estimating parameters of exponentially damped / undamped sinusoids in noise," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 38, no. 5, pp. 814-824, 1990.

[0048] In another example, a second waveform processing method, referred to as the STC method, can be applied to acoustic waveform data representing acoustic signals received by a receiver array of an acoustic logging tool for a range of depth values ​​in a cased borehole to derive data representing a slowness-time-coherence (STC) image corresponding to the acoustic waveform data. The STC method calculates a coherence map of the received acoustic waveform within a time window and a moveout angle range. Details of the STC method are described in: JB Haldorsen, DL Johnson, T. Plona, ​​B. Sinha, H.-P. Valero and K. Winkler, "Borehole acoustic waves," Oilfield Review, 2006.

[0049] The unsupervised machine learning system determines a low-dimensional representation of the input data directly from the input data itself. The unsupervised machine learning system can be trained using high-dimensional input data (e.g., TKO data and / or STC images) derived from simulated acoustic waveforms that cover and correspond to different cased hole situations associated with a range of well integrity / cementing properties that can be determined from the workflow. Alternatively or additionally, the unsupervised machine learning system can be trained with high-dimensional input data (e.g., TKO data and / or STC images) obtained from measured acoustic waveforms in different known cased hole environments that cover and correspond to a range of well integrity / cementing properties that can be determined from the workflow.

[0050] The low-dimensional representation produced by the unsupervised machine learning system can be processed by one or more clustering methods to identify multiple clusters (classes) in the low-dimensional representation and discover identifiers (labels) for the multiple clusters directly from the data itself. A cluster is a group or class of data elements in the low-dimensional representation. Characteristics for characterizing and assessing well integrity can be determined from the cluster identifiers produced by the clustering method and the corresponding acoustic data. For example, such characteristics may be related to cementing of annulus(s) in a cased well as a function of azimuth and depth.

[0051] Workflow

[0052] Go to Figure 4 , a workflow is presented that collects data representative of acoustic logging tools (e.g., Figure 1 Acoustic waveform data of an acoustic signal received by a plurality of receivers of a receiver array of an acoustic logging tool (block 401). The transmitter excitation may be monopole, dipole and / or quadrupole excitation. In an embodiment, the cased well may have a Figure 3 Multi-string casing shown. In other embodiments, the cased well may adopt other casing configurations.

[0053] In block 403, the acoustic waveform data collected in block 401 is processed to determine a geophysical representation of the acoustic waveform data (e.g., a slowness that varies with time, a slowness that varies with frequency, a slowness that varies with time and frequency, and / or a slowness that varies with time and space). In an embodiment, the processing of block 403 may employ one or more waveform processing methods (e.g., a TKO method and / or an STC method) on the collected acoustic waveform data to determine a geophysical representation of the acoustic waveform data as described herein.

[0054] In box 405, the geophysical representation of the acoustic waveform data of box 403 is input to an unsupervised machine learning system, which determines a compressed (low-dimensional) data set of the geophysical representation of the acoustic waveform data. In this operation, the geophysical representation of the acoustic waveform data of box 403 is used as high-dimensional input data of the unsupervised machine learning system. The unsupervised machine learning system determines the low-dimensional representation of the input data directly from the input data itself. The unsupervised machine learning system used in box 405 can be trained using high-dimensional input data (e.g., TKO data and / or STC image data) obtained from simulated acoustic waveforms, which cover and correspond to different cased well situations related to the range of well integrity / cementing characteristics that can be determined from the workflow. Alternatively or additionally, the unsupervised machine learning system used in box 405 can be trained using high-dimensional input data (e.g., TKO data and / or STC image data) obtained from measured acoustic waveforms in different known cased well environments, wherein the measured acoustic waveforms cover and correspond to the range of well integrity / cementing characteristics that can be determined from the workflow.

[0055] A number of clusters may be selected or estimated in block 407. For example, the number of clusters may be selected from predefined values ​​or estimated through data processing.

[0056] In block 409, a clustering method (e.g., k-means clustering or agglomerative clustering) can be applied to the compressed (low-dimensional) data set output by the unsupervised learning system in block 405. The clustering method processes the compressed (low-dimensional) data set to identify a set of clusters and corresponding cluster identifiers (or labels) in the compressed (low-dimensional) data set. The number of clusters in the identified set of clusters can be based on the number of clusters selected or estimated in block 407.

[0057] In box 411, cluster identifiers (or labels) for the set of clusters identified in box 409 can be output as a function of the receiver azimuth position and depth in the cased hole. The cluster identifiers (or labels) obtained by the clustering method on the compressed (low-dimensional) data are initially collapsed one-dimensional vectors in which the labels of all depth and azimuth positions are flattened together. By reshaping (rearranging the indexes) the one-dimensional vector represented by the labels into a two-dimensional matrix, a two-dimensional map of the labels can be obtained, in which one dimension (y-axis, from top to bottom) represents the depth position and the other dimension (x-axis, from left to right) represents the depth position.

[0058] In box 413, the geophysical representation of the acoustic waveform data (or modeling data) at the receiver azimuth position and depth of the cluster identifier output in box 411 can be analyzed to select one or more cluster identifiers identified by the clustering method. Such analysis can include expert analysis of the selected frame corresponding to each cluster / cluster identifier output in box 411. In a non-limiting example, the frame of the acoustic wave data is the acoustic wave data at a specific depth. In general, the frame and depth can be used interchangeably. Such analysis can also use modeling to understand and interpret the data from these selected frames.

[0059] The number of cluster identifiers selected in block 413 may also be selected through such analysis. Alternatively, an objective function may be defined and used in machine learning and clustering operations to estimate and determine the number of clusters and the corresponding cluster identifiers selected in block 413.

[0060] In block 415, at least one well integrity characteristic as a function of azimuth and depth in the cased wellbore may be determined using the one or more cluster identifiers selected in block 413. For example, the at least one well integrity characteristic may be related to the condition of cement (presence of hard cement or soft cement or water) in at least one annulus of the cased wellbore as a function of azimuth and depth in the cased wellbore.

[0061] Different well integrity / cement properties (hard cement / soft cement / fluid) can change the received acoustic waveform and then change the acoustic data features (e.g., STC, TKO) accordingly. Therefore, their low-dimensional representations have different distributions in the latent space, and after clustering methods are applied, their surrounding areas (in depth and azimuth) produce different cluster labels.

[0062] In a non-limiting example, one may review the depth and azimuth of the entire processing to understand the overall distribution of well integrity / cement properties, and / or select certain areas in depth / azimuth with certain specific tags of interest, which may be different from their surrounding areas, to quickly understand that such areas are different from their surrounding areas, which may then guide experts with domain knowledge to further study other auxiliary measurements acquired / processed from ultrasonic, seismic, electromagnetic equipment, etc., for better understanding of the properties.

[0063] In an embodiment, the at least one characteristic related to well integrity determined in block 415 may be stored in a computer memory and output for display and assessment of well integrity at depth intervals in a cased well.

[0064] In an embodiment, the operations of blocks 401 to 415 may be repeated for different depth intervals in the cased wellbore to determine at least one characteristic related to well integrity for the different depth intervals. In such a case, an acoustic logging tool may be conveyed within the cased wellbore and positioned at axial depth locations corresponding to the different depth intervals. At each axial depth location, the acoustic logging tool may be operated to collect acoustic logging tool (e.g., Figure 1 The at least one characteristic related to well integrity determined in block 415 for different depth intervals in the cased well can be stored in a computer memory and output for display as part of a well log curve to characterize and evaluate the well integrity as a function of azimuth and depth of the cased well.

[0065] TKO method

[0066] As described above, the TKO method may be applied to acoustic waveform data representing acoustic signals received by a receiver array of a tool to derive acoustic data characterizing a dispersion relationship between slowness and frequency in the acoustic waveform data, and such operation may be Figure 4 The following is a detailed description of an embodiment of a TKO method for processing an acoustic waveform received by a receiver array of an acoustic logging tool in response to acoustic excitation by a remote monopole transmitter or a remote dipole transmitter.

[0067] In this embodiment, the acoustic waveform received by the receiver array of the acoustic logging tool is normalized to a normalization factor for each corresponding receiver in the receiver array. For each depth, we denote the normalized monopole or dipole acoustic waveform at the i-th axial receiver after modal decomposition as r i (t), where i = 1,…,N Z , t∈[0,N T ]. Since the dispersion relation is expressed in terms of frequency and slowness, we first use the Fourier transform Transform the received signal into the frequency domain. At a specific frequency f0, R i (f0) can be approximated as The matrix pen method can be used to estimate k i , i = 1, ..., P. In this embodiment, the two matrices R (0) and R (1) is constructed as:

[0068]

[0069]

[0070] R (0) and R (1) The size of (N Z -P)×P. The matrix pen algorithm shows that the poles are actually the matrix pen (R) as described below (0) ,R (1) ) eigenvalues: Y.Hua and TKSarkar, "Matrix pencil method forestimating parameters of exponentially damped / undamped sinusoids in noise," IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.38, no.5, pp.814-824, 1990. This means solving:

[0071] |R (0) -λR (1) |=0, Equation (2)

[0072] or equivalently:

[0073]

[0074] in Represents the pseudoinverse of a matrix.

[0075] After the above eigenvalue calculation, the eigenvalue λ of length P is called the reverse pole estimate.

[0076] Similarly, in calculating the matrix pen (R (1) ,R (0) ), that is, solving |R (1) -λR (0) After |=0, the result λ of P length is called the forward pole estimate. Then, the magnitudes of the forward and backward pole estimates λ can be compared with each other, and those poles with high matching can be selected as good pole estimates based on a given threshold of the magnitude difference. Then, the corresponding slowness can be estimated with respect to the frequency

[0077] STC Method

[0078] As described above, the STC method may be applied to acoustic waveform data representing acoustic signals received by a receiver array of a tool to derive acoustic data representing a slowness-time-coherence (STC) image corresponding to the acoustic waveform data. Such an operation may be Figure 4The following is a detailed description of an embodiment of an STC method for processing an acoustic waveform received by a receiver array of a sonic logging tool in response to an acoustic excitation transmitted by a remote monopole transmitter or a remote dipole transmitter.

[0079] Each received signal r can be transformed using a continuous wavelet transform (e.g., a continuous wavelet transform using Morlet wavelet) i (t) performs bandpass filtering. Morlet wavelet can be expressed as where f c is the center frequency and σ is the constant bandwidth. The continuous wavelet transform is a convolution process in the time domain, equivalently, it is just a multiplication process in the frequency domain. i (t) and The spectrum of can be obtained using the Fourier transform as follows:

[0080]

[0081]

[0082] Therefore, the bandpass filtered signal in the frequency domain is given as:

[0083]

[0084] In order to include slowness information for STC pictures, we introduce N ] The frequency domain shift component S belonging to a set of slowness values ​​of interest s (f) = e j2πfs , to convert the frequency domain signal after bandpass filtering into Shift to the slowness s of interest as The slowly shifted bandpass filtered signal is then converted to the time domain via an inverse Fourier transform:

[0085]

[0086] Finally, regarding slowness and time at the center frequency f c The STC image of the filtered signal bandpass at is obtained by normalizing the axial domain to:

[0087]

[0088] Figures 5A-5C Shown are STC images derived from the acoustic waveform received by a single receiver in response to an acoustic excitation transmitted by a distant dipole transmitter, after modal decomposition and bandpass filtering at three different center frequencies. Figure 5A The STC image is at the modal decomposition and the center frequency f cDerived from the received dipole signal after bandpass filtering at 1.75kHz. Figure 5B The STC image is at the modal decomposition and the center frequency f c Derived from the received dipole signal after bandpass filtering at 4kHz. Figure 5C The STC image is at the modal decomposition and the center frequency f c Derived from the received dipole signal after bandpass filtering at 8.75kHz.

[0089] Figures 6A-6H shows the modal decomposition and the center frequency f c STC images derived from the acoustic waveforms received by eight azimuth receivers in response to acoustic excitations transmitted by a distant monopole transmitter after bandpass filtering at 20 kHz. The rows of each STC image refer to the slowness axis, and the columns of each STC image refer to the time axis.

[0090] As from Figures 5A-5C and Figures 6A-6H It can be seen from the STC images that the STC images after different bandpass filtering reveal different modes of the received waveform, and the STC images in different azimuths indicate azimuth heterogeneity.

[0091] Self-Organizing Map (SOM)

[0092] The main goal of the SOM machine learning system is automatic data clustering and graphical representation of the resulting data clusters. The SOM machine learning system projects high-dimensional input data as vectors into a low-dimensional space of size 2 or 3 and visualizes the two-dimensional or three-dimensional points in a scatter plot. See T. Kohonen, "Self-organized formation of topologically correct feature maps," Biological Cybernetics, no. 43, pp. 59-69, 1982. In addition, such a new set of low-dimensional data can preserve the topological structure of the high-dimensional input data. SOM uses neural networks for dimensionality reduction.

[0093] Figure 7 The neural network structure of the SOM machine learning system with a two-dimensional structure is shown. Assume that each input data x = [x1,…,x m ] are vectors of length m, which establish a neuron input layer, such as Figure 7 In addition, assume that the SOM machine learning system has Figure 7 The box on the right hand side shows the output layer N X ×N Yneurons. Then, a fully connected neural network can be built between the two layers. These connections between the input layer and the output layer have weights, and the set of weights for each output node at position (i, j) that is fully connected to the m input neurons forms the weight vector where i=1,…N X , j=1,…,N Y The weight vector w ij Also called a codebook vector. Before the training of an unsupervised learning or SOM machine learning system begins, all codebook vectors are randomly initialized.

[0094] The SOM machine learning system is trained through one or more training steps. In each training step, suppose there are n input vectors x1,…,x n , and randomly select an input vector x p ∈{x1,…,x n} and pass it to the neural network. p With all codebook vectors w ij The comparison is done and the best matching neuron (BMU) is assigned in the form of the minimum Euclidean distance from it, i.e.,

[0095]

[0096] After computing the BMU for all input vectors, the training process updates the codebook vector w by ij :

[0097]

[0098] where t is the number of iterations (epochs), η(t) is the time-dependent learning rate, and According to x p The topological neighborhood function of the BMU and any neuron at position (i, j):

[0099] In practice, and in is x p The lateral distance between the BMU and any neuron at position (i, j). It has several important characteristics: it is in BMU (x p ) is the largest, it is symmetrical about the neuron, it decreases monotonically to zero when the distance reaches infinity, and has the property of translation invariance, that is, it is the same as BMU(x p )’s position is irrelevant. The point is that not only BMU(x p ) updates its weight, and the weights of its neighbors will also be updated, although not as fast as BMU(xp ) itself. Therefore, the overall effect of each weight update is to move the input x p The BMU and the BMU orientation input x p A vector of weights for adjacent neighbors. Repeatedly computing the BMU and updating the weights preserves the topology of the input data.

[0100] When the SOM machine learning system has been trained, all input vectors are passed to the network again to find a set of BMUs. Now, the input vectors are distributed between the grids of the map. In this way, the trained SOM machine learning system can be used to transform high-dimensional input data according to the discrete structure of the trained SOM machine learning system. In order to visualize the proximity of input vectors in space, a method called a unified distance matrix (U-matrix) can be used, which shows the distance between neighboring neurons, as shown below:

[0101]

[0102] where d ij|i(j+1) , respectively, are the weight vector w ij and w i(j+1) 、w ij and w (i+1)j The Euclidean distance between .

[0103] d ij|i(j+1)|(i+1)j|(i+1)(j+1) =(d ij +d i(j+1) +d (i+1)j +d (i+1)(j+1) ) / 4 and d ij The value of is the average value of the adjacent elements of the U-matrix. The details of the U-matrix are described in: A. Ultsch and H. P. Siemon, "Kohonen's Self Organizing Feature Maps for Exploratory Data Analysis," in Proceedings of the International Neural Network Conference (INNC-90), Paris, France, 1990. If a gray color map is used, the dark color in the U-matrix indicates that the distance between two adjacent neurons is large, while the light color indicates that the distance between two adjacent neurons is close. Therefore, the bright area can be regarded as a cluster, and the dark area can be used as a cluster separator. In addition to gray, different color maps can also be used.

[0104] Figure 8The U matrix of 1800 compressed STC images, each of size 72×240×3, generated by the SOM machine learning system from 1800 input STC images obtained from synthetic acoustic waveforms in a cased well with multi-string casing is shown. The synthetic acoustic waveforms were synthesized for five different predetermined well integrity / cementing conditions, namely (1) annulus A (inner annulus) is hard cement and annulus B (outer annulus) is hard cement; (2) annulus A is light cement and annulus B is light cement; (3) annulus A is water and annulus B is hard cement; (4) annulus A is water and annulus B is light cement; (5) annulus A is water and annulus B is water. In the U matrix, there are some clear boundaries with lighter colors that separate the corresponding clusters with darker colors. The BMUs of the original 1800 input STC images are also marked at the corresponding positions of the U matrix. At the same time, the ground truth class labels of the input STC images and the class labels of the automatic clustering given the U matrix are marked with numbers and dots, respectively. It can be seen that the clustering method of the U matrix based on the SOM machine learning system is able to automatically separate the STC images synthesized from different cementing situations, although in some cases there are some mislabeled results compared to the ground truth.

[0105] SOM with Autoencoder (SOM-AE)

[0106] The SOM machine learning system has only one layer of neural network and does not include a hidden layer. Due to the rapid emergence of deep neural networks, many powerful machine learning algorithms have been developed. In order to integrate the advantages of deep neural networks, an autoencoder (AE) can be used with the SOM machine learning system.

[0107] AE uses a multi-layer neural network structure with an input layer, an output layer with the same number of neurons as the input layer, and one or more hidden layers connecting them. The details of AE are described in: Y.Bengio, "Learning Deep Architectures for AI," Foundations and Trends in Machine Learning, vol.2, no.1, pp.1-127, 2009. Since the training labels themselves are the training data, AE is an unsupervised learning system. AE consists of two components, encoder and decoder, which can be defined as two functions φ and ψ respectively:

[0108]

[0109] in, is the input data from the high-dimensional space, is the compressed data passed through the encoder φ, The data is reconstructed through the output of the decoder ψ. In order to achieve data compression, the encoded data space Input / output data space The dimensionality of is much lower, so AE has a bottleneck topology.

[0110] The purpose of AE is to find the weights of the encoder and decoder so that the decoded output and the original input x -norm loss function is minimized, that is, As with other neural networks, backpropagation can be used to update the network weights of φ, ψ and gradually reduce the reconstruction error via the stochastic gradient descent method and its variants. Fig. 9 A schematic structure of an AE having an encoder 901 , a decoder 902 , and a bottleneck structure at the end of the encoder 901 is shown.

[0111] In the SOM-AE machine learning system, the encoder of AE is expanded in front of the SOM machine learning system, so that the input data of the SOM machine learning system is no longer the original processed sound wave data (such as the TKO and STC results of the received sound wave waveform), but the compressed representation of the processed sound wave data generated by the AE encoder. There are many advantages to doing this. First, the SOM training process is usually slow, especially for high-dimensional input; however, if we replace the high-dimensional input with compressed medium-dimensional data generated by the AE encoder, the SOM training process can be significantly accelerated. The training of AE can also be accelerated using GPU computing. Second, the encoder of AE usually does not encode incoherent random noise, so it can effectively attenuate the noise component of the input data. Therefore, the SOM expanded with the encoder of AE before the AE input is therefore more robust to noisy input data. Third, we can make full use of the power of deep neural networks and let them expand the learning ability of SOM.

[0112] In a non-limiting example, the training steps of SOM-AE include: (1) using a neural network structure and a stochastic gradient descent optimization method, using the input sound wave data as training data to train an autoencoder (AE) model including an encoder and a decoder; (2) applying the encoder module of the AE model to the original input sound wave data to reduce its dimension; (3) training the neural network of the self-organizing map (SOM) by feeding the reduced-dimensional sound wave data (the output of the AE encoder module) as input; and (4) the trained SOM now accepts the output of the AE encoder module, i.e., the reduced-dimensional sound wave data, as input, and outputs a clustering result on a two-dimensional topology.

[0113] Fig.10The structure of the AE for acoustic STC image compression is shown. Each input STC image is a data tensor of size 96×80×1.

[0114] Fig.11 Shows Fig.10 The detailed structure of the AE's encoder, which includes multiple convolutional neural networks and 2D max pooling layers. At the output of the AE's encoder, the compressed acoustic STC image becomes a much smaller data tensor of size 12×10×8. Fig.10 On the right hand side of , we can see that the compressed acoustic STC image is well reconstructed by the decoder of AE, which indicates that the encoder output has learned most of the information of the STC image. Therefore, it is safe to replace the original 7680-dimensional STC image with the 960-dimensional compressed result produced by the encoder of AE as the input of SOM.

[0115] Fig.12 The U matrix of 1800 compressed STC images, each of which is 9×30×8 (2160 dimensions), generated by the SOM-AE machine learning system from STC images of size 72×240×3 (51840 dimensions), derived from synthetic acoustic waveforms in a cased well with multi-string casing, is shown. Figure 8 Similarly, the synthesized acoustic waveforms are synthesized for five different predefined well integrity / cementing situations, namely (1) annulus A (inner annulus) is hard cement and annulus B (outer annulus) is hard cement; (2) annulus A is light cement and annulus B is light cement; (3) annulus A is water and annulus B is hard cement. Given the clustering classes of grayscale points and a given number of ground truth classes, the SOM-AE machine learning system can produce better clustering results in a shorter training time compared to the SOM machine learning system.

[0116] Variational Autoencoder (VAE)

[0117] The AE machine learning system described above can use the encoder part of AE to compress high-dimensional input data into a low-dimensional representation. Such compression information does not contain the distribution of the input data. Therefore, high-dimensional data can be reconstructed from its low-dimensional representation, but new high-dimensional data cannot be generated from any low-dimensional representation randomly sampled in space.

[0118] In contrast, a variational autoencoder (VAE) machine learning system can learn the parameters of a probability distribution representing the input high-dimensional data, and can therefore sample from this distribution to generate new high-dimensional data samples. The details of the VAE machine learning system are described in: D.P.Kingma and M.Welling, "Auto-Encoding Variational Bayes," in The International Conference on Learning Representations (ICLR), Banff, Canada, 2014. As before, assume that the input data belongs to a high-dimensional space. If we can model its probability distribution p(x), then we can generate new data samples But with Because It is a high-dimensional model that is difficult to model directly, so we can set up a latent variable model:

[0119] p(x)=∫p(x|z)p(z)dz, Equation (12)

[0120] in Belongs to can essentially express The unentangled low-dimensional latent variable space.

[0121] Since p(x|z)≈0 for most random z, computing p(x)=∫p(x|z)p(z)dz is computationally intractable. To find those z that produce p(x|z)>>0, it makes sense to investigate p(z|x), since those z drawn from x are more likely to be the latent variables underlying the data x. A method called variational inference can be used to infer the distribution p(z|x) by approximating it with a simpler distribution q(z|x) that is easy to evaluate (e.g., a Gaussian distribution) and minimizing the difference between p(z|x) and q(z|x) using the KL divergence metric, which has the form:

[0122]

[0123] By using Bayes' rule, the above equation (13) can be rearranged as:

[0124] logp(x)-D KL [q(z|x)||p(z|x)]=E q [logp(x|z)]-D KL [q(z|x)||p(z)] Equation (14)

[0125] Note that the right-hand side of Equation (14) is the objective function of the VAE that is maximized. KL [·] ≥ 0, this function tries to find the largest lower bound of logp(x), which is good enough in practice.

[0126] In the above VAE machine learning system, p(x|z) generates high-dimensional data x from its low-dimensional latent representation z, and q(z|x) infers low-dimensional latent representation z from high-dimensional data x. These two processes can be constructed using deep neural networks, and based on the experience of AE, q(z|x) can be regarded as an encoder network whose output is the bottleneck, while p(x|z) can be regarded as a decoder network. The first part of the VAE objective function, E q [logp(x|z)], represents the reconstruction possibility that needs to be maximized. In the second part, D KL [q(z|x)||p(z)] represents the difference between the approximate posterior distribution q(z|x) and the prior distribution p(z) that needs to be minimized. Maximize the likelihood E q [logp(x|z)] is equivalent to minimizing the regression loss function of the network under some optimal network weights. Minimizing D can be achieved by assuming that q(z|x) and p(z) follow a Gaussian distribution. KL [q(z|x)||p(z)], such that Standard Gaussian distribution and in are the mean and variance of q(z|x) for a given input data x. In this case, D KL [q(z|x)||p(z)] can be computed in closed form as:

[0127]

[0128] Note that this term becomes a regularization term added to the regression loss function of the network, where k is the dimension of the latent variable space. Assuming the prior distribution is safe because deep neural networks are able to transform simple Gaussian distributions into any arbitrarily complex distribution.

[0129] For this implementation, instead of providing encoded values ​​directly as in the standard AE encoder, the VAE encoder provides two latent variables It describes the mean and variance of the latent space. The VAE decoder will then extract the To generate a new value, we sample a latent value from . Fig.13AThe simple implementation shown in does not work because the backpropagation for the network weight updates cannot pass through the sampling process. Fortunately, this problem can be solved by using reparameterization, which leaves the sampling process outside the network architecture. It is suggested to randomly sample a variable from a unit Gaussian variable and then pass it through the latent space σ z |x is scaled by its standard deviation and then passed through the latent space μ z |x is shifted by the mean value. The correct implementation with reparameterization is Fig. 13B As shown, there are no obstacles in the back-propagation path.

[0130] High-dimensional processed acoustic wave data (such as TKO data and STC image data) can be used to train VAE and obtain a low-dimensional representation distribution produced by the encoder part of VAE for visualization. In order to visualize the clustering results of low but still greater than 3-dimensional representations, the t-distributed stochastic neighbor embedding (t-SNE) technique can be used. The details of the t-SNE technique are described in: L. van der Maaten and G. Hinton, "Visualizing Data using t-SNE," Journal of Machine Learning Research, vol. Nov, no. 9, p. 2579–2605, 2008.

[0131] Figures 14A-14D Depicted is a t-SNE visualization of a 16-dimensional VAE output derived from high-dimensional TKO data or STC acoustic wave data based on 1800 monopolar and dipole acoustic wave waveforms generated by numerical modeling. Fig.14A yes Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder part of the VAE machine learning system, where the 1480-dimensional processed TKO data derived from 1800 different monopolar sound wave waveforms is used as the input of the VAE machine learning system (1800 different iterations for 1800 different monopolar sound wave waveforms). Fig. 14B yes Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder part of the VAE machine learning system, where the 1480-dimensional processed TKO data derived from 1800 different dipole sound wave waveforms are used as input to the VAE machine learning system (1800 different iterations for 1800 different dipole sound wave waveforms). Fig. 14C yes Fig. 13Bt-SNE visualization of the 16-dimensional output produced by the encoder part of the VAE machine learning system, where the 34,560-dimensional processed STC data derived from 1,800 monopolar acoustic waveforms is used as input to the VAE machine learning system (1,800 different iterations for 1,800 different monopolar acoustic waveforms). Fig.14D yes Fig. 13B t-SNE visualization of the 16-dimensional output produced by the encoder portion of the VAE machine learning system, where the 5180-dimensional processed STC data derived from the 1800 dipole sound waveforms is used as the input to the VAE machine learning system (1800 different iterations for 1800 different dipole sound waveforms). As mentioned before, for Figures 14A-14D For each of the cases, 1800 acoustic waveforms were synthesized for treatment in a cased well using multi-string casing for five different cementing cases, with 360 consecutive waveforms for each case.

[0132] Figures 14A-14D The t-SNE plot results can be formatted using vertical bar charts, such as Figures 15A-15D As shown, each row is delineated by a class label. Fig.15A yes Fig.14A t-SNE visualization and vertical bar chart of clustering results are shown. Fig. 15B yes Fig. 14B t-SNE visualization and vertical bar chart of clustering results are shown. Fig. 15C yes Fig. 14C t-SNE visualization and vertical bar chart of clustering results are shown. Fig.15D yes Fig.14D The t-SNE visualization and vertical bar chart of the clustering results are shown in . The clustering results of the given low-dimensional VAE output are shown in Figures 15A-15D The vertical bars in the figure indicate that the VAE machine learning system has good clustering ability.

[0133] Since the VAE machine learning system has learned The generative model is then used after the distribution of , so the VAE machine learning system can draw samples And pass z to the decoder p(x|z) to generate a new high-dimensional sample x.

[0134] Fig.16 An example of using a VAE machine learning system is shown, which is trained with STC images of size 101×86 (8686-dimensional) to generate new similar STC images by decoding from a 128-dimensional latent variable z. In the example, z1 and z2 are swept from -15 to 15, and z3 is swept to z 128is fixed to 0. The generated STC image decoded from the sampled latent variable z can be plotted on the corresponding grid (z1, z2), as Fig.16 shown.

[0135] Clustering methods

[0136] As described above, one or more clustering methods may be applied to the compressed (low-dimensional) acoustic wave data generated by the unsupervised machine learning system to determine a set of clusters of the compressed (low-dimensional) data, and such a clustering operation may be Figure 4 A portion of box 409 .

[0137] In an embodiment, the clustering method may adopt k-means clustering. In k-means clustering, the compressed set of (low-dimensional) data is divided into k groups or clusters S = {S1, S2, ..., S k}, so as to minimize the within-cluster sum of squares. Formally, the goal is to find:

[0138]

[0139] Among them, μ i is a given cluster S i The average of the midpoints.

[0140] This is equivalent to minimizing the pairwise squared deviations of points in the same cluster.

[0141] Additionally or alternatively, the clustering method may employ agglomerative clustering, in which a compressed set of (low-dimensional) data begins with an initial set of clusters, and pairs of clusters are selectively merged together based on an analysis. The analysis may use a dissimilarity measure between clusters to selectively decide which pairs of clusters should be combined, typically provided by a distance measure between pairs of data elements and a linkage criterion that specifies the dissimilarity of the clusters as a function of the pairwise distances of the data elements in the clusters.

[0142] Additionally or alternatively, the clustering method may adopt other forms of hierarchical clustering (eg, divisive clustering) or other forms of clustering as needed.

[0143] In an embodiment, some or all of the above methods and processes may be performed by a processor, including Figure 4 Some or all of the operations of blocks 401-415 of the workflow of the present invention. The term "processor" should not be interpreted as limiting the embodiments disclosed herein to any particular device type or system. The processor may include a computer system. The computer system may also include a computer processor (e.g., a microprocessor, a microcontroller, a digital signal processor, or a general-purpose computer) for performing any of the above methods and processes.

[0144] The computer system may further include memory such as semiconductor storage devices (e.g., RAM, ROM, PROM, EEPROM, or flash programmable RAM), magnetic storage devices (e.g., floppy disks or fixed disks), optical storage devices (e.g., CD-ROMs), PC cards (e.g., PCMCIA cards), or other storage devices.

[0145] Some of the methods and processes described above may be implemented as computer program logic for use with a processor. In an embodiment, the machine learning system and supporting methods described herein may be implemented by computer program logic. The computer program logic may be implemented as software modules in various forms, including source code form or computer executable form. The source code may include a series of computer program instructions in various programming languages ​​(e.g., object code, assembly language, or high-level languages ​​such as C, C++, or JAVA). The computer program logic may be stored in a non-transitory computer-readable medium (e.g., memory) and executed by a processor. The computer program logic may be distributed in any form as a removable storage medium with accompanying printed or electronic documentation (e.g., shrink-wrapped software), preloaded on a computer system (e.g., on a system ROM or fixed disk), or distributed from a server or via an electronic bulletin board of a communication system (e.g., the Internet or the World Wide Web).

[0146] Additionally or alternatively, the processor may include discrete electronic components coupled to a printed circuit board, an integrated circuit (e.g., a CPU, a domain-specific integrated circuit such as an AI chip, or an application-specific integrated circuit (ASIC), and / or a programmable logic device (e.g., a field programmable gate array (FPGA)). Such a logic device may be used to implement any of the methods and processes described above.

[0147] Fig.17 An example computer system 300 is shown that can be used to implement some or all of the methods and processes described above, including Figure 4 The computer system 300 may be a single computer system 301A or an arrangement of distributed computer systems. The computer system 301A includes one or more analysis modules 303 (a program of computer executable instructions and associated data) that may be configured to perform some or all of the methods and processes described above, including Figure 44. The analysis module 303 is a computer system that is used to analyze and process data from a computer system 301A ...

[0148] Computer processor 305 may include at least a microprocessor, a microcontroller, a processor module or subsystem, a programmable integrated circuit, a programmable gate array, a digital signal processor (DSP), or another control or computing device.

[0149] Storage medium 307 may be implemented as one or more non-transitory computer-readable or machine-readable storage media. Fig.17 In the embodiment of the present invention, storage medium 307 is depicted as being within computer system 301A, but in some embodiments, storage medium 307 may be distributed within and / or on multiple internal and / or external housings of computer system 301A and / or additional computing systems. Storage medium 307 may include one or more different forms of memory, including semiconductor memory devices, such as dynamic or static random access memory (DRAM or SRAM), erasable and programmable read-only memory (EPROM), electrically erasable and programmable read-only memory (EEPROM), and flash memory; magnetic disks, such as fixed disks, floppy disks, and removable disks; other magnetic media, including magnetic tape; optical media, such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that the computer-executable instructions and associated data of analysis module 303 may be provided on one computer-readable or machine-readable storage medium of storage medium 307, or may be provided on multiple computer-readable or machine-readable storage media distributed in a large system that may have multiple nodes. Such one or more computer-readable or machine-readable storage media are considered to be part of the article (or article of manufacture). An article or manufacture may refer to any manufactured single component or multiple components. The one or more storage media may be located in the machine running the machine-readable instructions or in a remote site from which the machine-readable instructions may be downloaded over a network for execution.

[0150] It should be understood that computer system 300 is only one example of a computer system and that computer system 300 may have more or fewer components than shown and may be combined in Fig.17Other components not depicted in the embodiments of the present invention and / or the computer system 300 may have Fig.17 Different configurations or arrangements of the components depicted. Fig.17 The various components shown in the drawings may be implemented in hardware, software, or a combination of hardware and software, including one or more signal processing and / or application specific integrated circuits.

[0151] Although only a few examples have been described in detail above, it will be readily appreciated by those skilled in the art that many modifications may be made to the examples without departing substantially from the subject disclosure. For example, although a particular acoustic logging tool has been disclosed, other acoustic logging tools may be used as part of the methods and systems described herein. Therefore, all such modifications are intended to be included within the scope of the present disclosure as defined by the appended claims. In the claims, the device-plus-function clause is intended to cover the structures described herein that perform the functions described, not only structural equivalents, but also equivalent structures. Thus, although nails and screws may not be structural equivalents because nails use cylindrical surfaces to fasten wooden parts together, while nails use helical surfaces, nails and screws may be equivalent structures in the context of fastening wooden parts. It is the express intention of the applicant not to invoke any limitation of any claim herein under 35 U.S.C. §112, paragraph 6, except for the limitation that the claim expressly uses "devices for..." and related functions.

Claims

1. A method for characterizing the well integrity of a cased well, the method comprising: i) collecting acoustic waveform data of acoustic signals received by a receiver array of an acoustic logging tool for depth intervals of a cased well; ii) determining a high-dimensional representation of the acoustic waveform data collected in i); iii) determining a low-dimensional representation of the acoustic waveform data from the high-dimensional representation of the acoustic waveform data using an unsupervised dimensionality reduction machine learning model, the unsupervised dimensionality reduction machine learning model compressing the unlabeled high-dimensional acoustic waveform data into a low-dimensional latent variable space; iv) clustering the low-dimensional representation of the acoustic waveform data to identify low-dimensional clusters and corresponding low-dimensional cluster labels directly from the low-dimensional representation of the acoustic waveform data; and v) determining cementing properties related to cementing integrity of the annulus of the cased well at the depth interval based on the receiver azimuths of the acoustic waveform data and the geophysical representation of the acoustic waveform data at depth indicated by the low dimensional cluster labels.

2. The method of claim 1, further comprising evaluating cementing properties to determine a well integrity characterization of the cased well.

3. The method of claim 1, wherein the well integrity characterization indicates plugging or abandoning the cased well. 4 . The method of claim 1 , wherein the well integrity characterization indicates an acceptable pressure seal of the cased well at the depth interval.

5. A method according to claim 1, wherein the distribution of the low-dimensional representation of the acoustic waveform data in the low-dimensional latent variable space is different from the distribution of the high-dimensional representation of the acoustic waveform data in the high-dimensional latent variable space, and wherein the different distributions of the low-dimensional representation of the acoustic waveform data produce cluster labels that are different from the cluster labels obtained by clustering the distribution of the high-dimensional representation of the acoustic waveform data after clustering.

6. The method according to claim 1, wherein: The cementing properties determined in v) are related to the well integrity as a function of azimuth and depth of the cased well.

7. The method according to claim 6, wherein: The cementing properties determined in v) characterize the behavior of the cement in the annulus of the cased well as a function of azimuth and depth.

8. The method of claim 1, wherein: ii) The high-dimensional representation characterizes the slowness of the acoustic waveform data.

9. The method according to claim 8, wherein: The high-dimensional representation of ii) characterizes at least one of: slowness of change over time in the acoustic waveform data, slowness of change over frequency in the acoustic waveform data, slowness of change over time and frequency in the acoustic waveform data, and slowness of change over time and space in the acoustic waveform data.

10. The method according to claim 8, further comprising: Dispersion data representing the dispersion relation between slowness and frequency is generated in the acoustic waveform data using a matrix pen method, wherein the dispersion data is part of the high-dimensional representation of ii).

11. The method according to claim 8, further comprising: A slowness-time-coherence method is used to generate slowness-time-coherence image data, which represents a slowness-time-coherence image corresponding to the acoustic waveform data, wherein the slowness-time-coherence image data is part of the high-dimensional representation of ii).

12. The method of claim 1, wherein: The unsupervised dimensionality reduction machine learning model is selected from the group consisting of a self-organizing map machine learning system, a self-organizing map machine learning system with an autoencoder, a variational autoencoder machine learning system, a generative adversarial network machine learning system, and combinations thereof.

13. The method of claim 1, wherein: The unsupervised dimensionality reduction machine learning model is trained with high-dimensional input data derived from simulated acoustic waveforms covering and corresponding to different cased hole situations related to the cementing characteristics determined in v).

14. The method of claim 1, wherein: The unsupervised dimensionality reduction machine learning model is trained with high-dimensional input data derived from measured acoustic waveforms in different known cased hole environments, where the measured acoustic waveforms cover and correspond to the cementing properties determined in v).

15. The method of claim 1, wherein: Clustering includes using k-means clustering.

16. The method of claim 1, wherein: Clustering includes using agglomerative clustering.

17. The method of claim 1, wherein: The cased well has a multi-string casing, the innermost annulus of the multi-string casing being disposed inside at least one outer annulus; and Cementing properties related to well integrity characterize the condition of the cement in the innermost annulus and at least one outer annulus.

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