Methods and Systems for Borehole Texture Analysis

The present application claims priority to U.S. Provisional Patent Application No. 63/641,135, filed on May 1, 2024, which is incorporated herein by reference in its entirety for all purposes.

The present disclosure relates generally to methods and systems for performing borehole texture analysis of borehole images. More specifically, the present disclosure is related to analyzing borehole image data to identify different types of textures presented therein. Interpretation of borehole images may be utilized for depositional environment analysis and to identify characteristics of a borehole, such as natural or drilling-induced fractures, formation heterogeneity, and sedimentary structure. Different lithology categories may be used to delineate different reservoir types, and each basin may have specific terminologies corresponding to their rock types. However, interpreting borehole images to identify and classify texture features based on certain characteristics of the borehole images may be difficult. Further, the identification and classification process may be inefficient with respect to time and resources (e.g., computing resources, energy).

This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

In certain embodiments, a method including segmenting a borehole image of a first well into a first plurality of zones based on pixel data, segmenting the borehole image of the first well into a second plurality of zones based on covariance data, merging the first plurality of zones and the second plurality of zones to generate an updated borehole image, clustering one or more sets of features of the updated borehole image into one or more clusters based on a classification algorithm, and generating a borehole texture model representative of expected properties of an additional borehole based on the one or more clusters.

In certain embodiments, a system including a controller having a processor, a memory, and instructions stored on the memory and executable by the processor to segment a borehole image of a first well into a first plurality of zones based on pixel data, segment the borehole image of the first well into a second plurality of zones based on covariance data, merge the first plurality of zones and the second plurality of zones to generate an updated borehole image, cluster one or more sets of features of the updated borehole image into one or more clusters based on a classification algorithm, and generate a borehole texture model representative of expected properties of an additional borehole based on the one or more clusters.

In certain embodiments, a tangible and non-transitory machine readable medium including instructions that, when executed by a processor, causes the processor to perform operations including segmenting a borehole image of a first well into a first plurality of zones based on pixel data, segmenting the borehole image of the first well into a second plurality of zones based on covariance data, merging the first plurality of zones and the second plurality of zones to generate an updated borehole image, clustering one or more sets of features of the updated borehole image into one or more clusters based on a classification algorithm, and generating a borehole texture model representative of expected properties of an additional borehole based on the one or more clusters.

Certain embodiments commensurate in scope with the originally claimed invention are summarized below. These embodiments are not intended to limit the scope of the claimed invention, but rather these embodiments are intended only to provide a brief summary of possible forms of the invention. Indeed, the invention may encompass a variety of forms that may be similar to or different from the embodiments set forth below.

One or more specific embodiments of the present disclosure will be described below. In an effort to provide a concise description of these embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Any examples of operating parameters and/or environmental conditions are not exclusive of other parameters/conditions of the disclosed embodiments.

Borehole images may provide information related to texture features that may assist in performing natural fracture identification, drilling-induced feature classification, depositional environment analysis, and the like. Different lithology categories may delineate different reservoir types that may be present within the borehole. With this in mind, the present disclosure details a method in which a data processing system may analyze borehole image data to identify different types of textures that may be present in the respective subsurface region of the earth.

By way of example, the data processing system may receive borehole image data associated with a well or subsurface region and segment the borehole image based on the frequency of pixel data and the difference in pixel value (e.g., image density change). The data processing system may then cluster the resulting image segments based on similarities between different segments. The clustered group of image segments may then be classified with respect to certain categories (e.g., pixel frequency, image density) based on different purposes (e.g., rock texture, crevice depth, geological material, borehole structures). In addition to classifying the image segments, the data processing system may retrieve petrophysical logs that may be associated with the respective borehole, well, subsurface region, or the like. The data processing system may then store the classifications of the segmented borehole images along with the corresponding petrophysical logs within the respective clustered groups. Using the segmented borehole images, clustered groups, and labeled data, the data processing system may train a deep learning model based on patterns, correlations, and associations between the petrophysical logs related to certain clustered groups with respect to different borehole image segments.

After training the model, the data processing system may receive additional borehole image data related to other borehole and identify the image features that may assist the data processing system in determining the different classes and categories of rock properties through the length of the respective borehole. In this way, the data processing system may perform continuous facies analysis of the newly acquired image data based on similar characteristics identified in the depositional environments of the newly received borehole image data and the borehole image data represented in the model. In other words, by performing the techniques described herein, the data processing system may classify sedimentary facies (e.g., bodies of rock) in a continuous spectrum that may highlight gradual changes in the depositional environment that more accurately represents the actual rock properties of the respective borehole. Rock properties may include mechanical strength, hydraulic conductivity, rock texture, crevice depth, geological material, borehole structures, and the like. Additional details with respect to performing borehole image analysis to determine different textures present therein will be discuss below with reference to.

By way of introduction,illustrates a drilling systemthat may employ the systems and methods of this disclosure. The drilling systemmay be used to drill a boreholeinto a geological region. In the drilling system, a drilling rigmay rotate a drill stringwithin the borehole. As the drill stringis rotated, a drilling fluid pumpmay be used to pump drilling fluid, which may be referred to as “mud” or “drilling mud,” downward through the center of the drill string, and back up around the drill string, as shown by reference arrows. At the surface, return drilling fluid may be filtered and conveyed back to a mud pitfor reuse. The drilling fluid may travel down to the bottom of the drill stringknown as the bottom-hole assembly (BHA). The drilling fluid may be used to rotate, cool, and/or lubricate a drill bitthat may be a part of the BHA. The fluid may exit the drill stringthrough the drill bitand carry drill cuttings away from the bottom of the boreholeback to the surface. One or more surface sensorsmay record a variety of different data points associated with the drilling system, including the rotations per minute (RPM) of the drill stringand/or the drill bit. For example, the set of sensorsmay determine the surface RPM of the drilling system. In addition, the sensorsmay be positioned within the drill stringto capture data related to properties of the drill string, the drill bit, and the like while inside the borehole.

The BHAmay include the drill bitalong with various downhole tools, such as one or more logging tools. The BHAmay thus convey the one or more logging toolsthrough the geological regionvia the borehole. As described in greater detail herein, the one or more logging toolsmay be any suitable downhole tool that emits electromagnetic waves within the borehole(e.g., a downhole environment). The downhole tools, which may include the one or more logging tools, may collect a variety of information relating to the geological regionand the state of drilling in the borehole. For instance, the downhole tools may be logging-while drilling (LWD) tools that measure physical properties of the geological region, such as density, porosity, resistivity, lithology, and so forth. Likewise, the downhole tools may be measurement-while-drilling (MWD) tools that measure certain drilling parameters, such as the temperature, pressure, orientation of the drill bit, mapping-while-drilling tools, and so forth.

The one or more logging toolsmay receive energy from an electrical energy device or an electrical energy storage device, such as an auxiliary power sourceor another electrical energy source to power the tool. In some embodiments, the one or more logging toolsmay include a power source within the one or more logging tools, such as a battery system or a capacitor, to store sufficient electrical energy to emit and/or receive electromagnetic waves.

The one or more logging toolsmay also include image acquisition tools that may obtain image data related to the borehole. The image acquisition tools may include an acoustic borehole imager, resistivity imaging tools, and the like. In some embodiments, the acquired image data may present information related to the geological region, such as bedding plans, fractures, sediment structures, breakouts, borehole shape, and the like.

The drilling systemmay include a controllerto control different components of the drilling systemand collect identified data from the one or more logging toolsand/or the one or more sensors. The controllermay be any electronic data processing system that can be used to carry out the systems and methods of this disclosure. That is, the controllermay monitor and regulate various operational parameters of the drilling system. The controllermay receive data from the sensors (e.g., the sensorsand/or logging toolsmeasuring parameters such as drilling depth, rotational speed, torque, pressure, image data, and vibration). Based on these inputs, the controllermay perform various actions adjusting drilling variables, including bit rotation speed, feed rate, and fluid flow.

Communications, such as control signals, may be transmitted from a data processing system(processing system) to the controllerand the communications, such as data signals related to the results/measurements of the sensorsand/or one or more logging tools, may be returned to the data processing systemvia the controller. The data processing systemmay be any electronic data processing system that can be used to carry out the systems and methods of this disclosure. For example, the data processing systemmay include one or more processors, which may execute instructions stored in memoryand/or storage. The memoryand/or the storageof the data processing systemmay be any suitable article of manufacture that can store the instructions. In certain embodiments, the one or more processorsmay include 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. In certain embodiments, the one or more processorsmay include machine learning and/or artificial intelligence (AI) based processors.

In certain embodiments, the memoryand storagemay be implemented as one or more non-transitory computer-readable or machine-readable storage media. In certain embodiments, the memorymay include one or more different forms of memory, including semiconductor memory devices such as dynamic or static random-access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories. The storagemay include solid state drives, magnetic disks such as fixed, floppy and removable disks; other magnetic media including 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 the analysis module(s) may be provided on one computer-readable or machine-readable storage medium of the memoryor the storage, or alternatively, may be provided on multiple computer-readable or machine-readable storage media distributed in a large system having possibly plural nodes. Such computer-readable or machine-readable storage medium or media are considered to be part of an article (or article of manufacture), which may refer to any manufactured single component or multiple components. In certain embodiments, the storagemay be located either in the machine running the machine-readable instructions or may be located at a remote site from which machine-readable instructions may be downloaded over a network for execution.

As illustrated, the data processing systemmay optionally also include a display, which may be any suitable electronic display, and may display images generated by the processor. The data processing systemmay be a local component of the drilling system(i.e., at the surface), within the one or more logging tools(i.e., downhole), a device located proximate to the drilling operation, and/or a remote data processing device located away from the drilling systemto process downhole measurements in real time or sometime after the data has been collected. In some embodiments, the data processing systemmay be a portable computing device (e.g., tablet, smart phone, or laptop) or a server remote from the drilling system. In some embodiments, the one or more logging toolsmay store and process collected data in the BHAor send the data to the surface for processing via communicationsdescribed above, including any suitable telemetry (e.g., electrical signals pulsed through the geological regionor mud pulse telemetry using the drilling fluid).

It should be noted that, although the discussion above relates to a drilling system, other downhole equipment or systems may employ the systems and methods of this disclosure. For example, a downhole tool with an acoustic tool conveyed by slickline, coiled tubing, wireline, or other delivery systems, may utilize the disclosed systems and methods.

Keeping the foregoing in mind, borehole image data may be acquired using some of the equipment described above with respect to. The borehole image data may then be analyzed to determine the texture and facies that may be part of the borehole. For example,illustrates a flow chart of a methodfor generating a borehole texture model based on borehole image data. Although the following description of the methodwill be described as being performed by the data processing system, it should be noted that the methodmay be performed by any suitable computing device in any suitable order. Moreover, at times, the description of the methodbelow may refer to the components described above in; however, it should be understood that these references are merely provided as examples to further clarify the discussion of the method.

Referring now to, at block, the data processing system may receive image data associated with a borehole. The data processing system may receive the image data from the logging tools, sensors disposed inside the borehole, or the like. The image data may include still images of the borehole around the circumference of the borehole. As such, the image data may provide insight as to a mapping and texture of the borehole.

In some embodiments, the logging toolsmay send associated position and accelerometer data along with the image data. The acceleration data and position data may provide information about the location within the borehole from which the image data originates. By way of example,illustrates an example image data of a borehole including raw high resolution dynamic image of the borehole. The example image data ofmay be analyzed to generate histograms and derivatives of the same, such as those illustrated in. These derivatives of the example image data may be used to determine properties and characteristics of the borehole and train a model that may be used to more efficiently determine properties of other boreholes in an efficient manner. In some embodiments, the model may also provide insight into the expected rock properties of the borehole and may be used to control a drilling system based on the expected properties and characteristics of the borehole during the drilling operation. That is, drilling parameters (e.g., speed, revolutions-per-minute, technique, direction) may be adjusted in view of the expected properties of the rock within the borehole. The assorted horizontal lines on the high-resolution image may indicate structures present within the borehole, which an operator may need to address through adjusting drilling operations.

At block, the data processing system may segment the borehole image data received at blockbased on pixel data. That is, the borehole image may be represented as a composition of successive sedimentary zones. The different sedimentary zones of a borehole image may have different statistical properties (e.g., pixel properties). The statistical properties may be used to characterize portions of the borehole image and generate zonation (e.g., segmented zones). In some embodiments, the data processing system may utilize kernel density estimation (KDE), a variogram, and the like to extract certain features of a borehole image. For example, the data processing system may utilize KDE and variogram features to segment the entire borehole image into different sedimentary zones.

With this in mind, in some embodiments, to segment the borehole image data based on pixel data, the data processing system may generate a histogram to describe the distribution of pixel values (e.g., frequency of pixels) in the borehole image in a normalized pixel domain of [0, 1]. For example,illustrates an example that indicates a number of pixels (Y-axis) presented as columns that have a corresponding normalized pixel intensity (e.g., brightness or color value) (X-axis). The histogram composed of columns, however, may have limited precision due to the value domain being discretized.

As such, the data processing system may increase the precision of the histogram using kernel density estimation (KDE). The kernel density may correspond to a Gaussian distribution with the sample value as μ and a variance controlling the bandwidth σ:(μ, σ). As a result, the data processing system may produce a distribution of pixel values of the borehole image, such that the pixel value may be provided at a higher precision than the histogram. That is, contrary to the usual “discrete” histogram where each sample from input data increases a by count of one to the column corresponding to the sample value, the data processing system may form a “continuous” histogram, such that each sample contributes a density distribution with a given bandwidth called kernel density. That is, the KDE generated from the borehole image (e.g., whole image) may provide information about a distribution of pixel values (e.g., frequency of pixels) within the borehole image.

By performing the KDE, the data processing system may generate a smooth curve, which may lend it to analytical methods that may be used to find peaks and troughs. As will be detailed below, the data processing system may focus on each of the expected pixel value ranges to identify the frequency of pixels falling into those ranges. In this way, the frequency of pixels may provide one of the features used by the data processing system to zonate and classify the borehole image.

For instance, the data processing system may calculate a KDE of the whole borehole image with a variance, σ=0.15 (for normalized pixel value domain [0, 1]). By way of example,illustrates an example continuous final distribution determined using the KDE, thereby providing information at multiple precise values. Indeed, the KDE generated from the borehole image provides information about distribution of pixel values within the borehole image.

After calculating the KDE of the borehole image, the data processing system may then calculate a second derivative of the KDE, resulting in a continuous distribution of pixel frequencies. For example,illustrates the second derivative of the KDE represented in

The data processing system may then analyze the borehole image with respect to pixel data to determine statistical properties of the borehole image. For example, the data processing system may apply an analytical method to the continuous histogram ofto determine peaks and troughs. The data processing system may analyze the frequency of pixels within different ranges of pixel values to determine segments of the borehole image. As such, the data processing system may use frequency as one of the features to classify each segment of the borehole image.

Using the second derivative of the KDE illustrated in, the data processing system may determine a number n maxima of the second derivative, as illustrated in. The n maxima may indicate the troughs of the KDE. The data processing system may annotate the positions of the identified troughs in a value domain as {Xi|i=1, . . . , n}. The data processing system may also utilize a smart searching algorithm to annotate the positions in the value domain. The smart searching algorithm may take into account the maxima separated by a negative minima. For instance,illustrates an example in which the retained maxima are {X}={0.13, 0.64, 0.88}. Keeping this in mind, the data processing system may use the retained maxima illustrated inserve to cut off the pixel value domains into 4 intervals,,, and. The frequency of all of the pixel values sum up to 1. As such, the data processing system may utilize some or all intervals as independent features. Specifically, the data processing system may characterize the image utilizing only the low intervals (e.g., below a lower threshold value) and high intervals (e.g., above an upper threshold value).

By way of example,illustrates a process for determining the frequency of the pixels and the KDE. In the illustrated example, the data processing system uses {Xi}={0.13, 0.88}.illustrates a discretized borehole image. In the illustrated example, to discretize the image by pixel values {X}, for each pixel value v the data processing system may utilize formula 1.

Formula 1 may sharpen the features found by the histogram. In the illustrated embodiment, the borehole image has n+1 discrete values as shown in formulas 2-4 below.

As a result of the discretization process, the embodiment illustrated inhas three values {C}={0.065, 0.505, 0.96}.

After the data processing system discretizes the image, the data processing system may determine a frequency curve as illustrated in. To determine the frequency curve, the data processing system may first, for each depth z, count the frequency of each possible pixel values {C, i=1, . . . , n+1}, in a sliding window [z+h, z−h], where the half height h of the window may be chosen to be 20, for example. In the illustrated embodiment, the result is n+1 frequency curves as a function of depth. As discussed above, at a given depth, all frequencies sum up to 1. In embodiments of 3 values, such as the illustrated embodiment, one frequency curve, for example the one computed at middle value C, may be ignored without issue. The two frequency curves generated in the present embodiment are illustrated in. The data processing system may normalize the frequency by number of pixels in horizontal direction. In the present embodiment, the range is [0, 1].

The data processing system may then create a graph of the first derivative of frequencies based on the frequency curve from the previous step.illustrates a first derivative of frequencies curve. Once the data processing system determines a first derivative of the frequencies, it may determine minima and maxima of the frequency curves. The minimaand maximamay indicate the steepest change in frequency, which may suggest possible zone boundaries.illustrates such located boundariessuperposed on the original borehole image from

At block, the data processing system may segment the borehole image based on covariance data. That is, the data processing systems may utilize variograms in place of histograms to zonate the borehole image. A variogram may measure covariance of pairs of data points separated by a given distance. The data processing system may utilize diverse types of variogram to characterize borehole images. An omni-directional variogram, for example, describes the homogeneity of an image. As such, an omni-directional variogram may be sensitive to the texture, while single directional variogram may detect image density change in a direction. In particular, when crossing a zone boundary in the borehole image, difference in pixel value may be larger than some threshold. Thus, the covariance (e.g., square of difference) may be larger than the threshold at certain locations (e.g., expected to reach a maximum at the zone boundary).

illustrates the zonation process using vertical directional variograms. As an example, the vertical variogram of borehole image corresponding tois as follows in. As illustrated in, the covariance illustrated on the Y axis depends on distance separating data points (e.g., range) illustrated on the X axis. At a distance of zero, covariance vanishes as a point value is equal to itself. In some instances in which the range is greater than some threshold, the data points may become uncorrelated. As such, the covariance saturates and reaches the variance of data. To determine a range that may be best suited for describing the covariance change in a borehole image, the data processing system may take the second derivative of the variogram. To take the second derivative of the variogram, the data processing system may calculate the vertical variogram of the whole borehole image as illustrated on the plot in. The data processing system may then calculate the second derivative of the vertical variogram as illustrated on the plot in. Once the data processing system calculates the second derivative, it may then determine the first negative minimum of the second derivative (R), which gives a standard range value in the variogram before reaching the saturated plafond (e.g., maximum emissions). In the illustrated example, R=40 (pixel). For each depth (z), calculate the value at which the covariance equals the variogram value at range R, in a sliding window [z+h, z−h], where the half height h of the window equals to R. The covariance curve as a function of depth is illustrated in. The data processing system may then determine the maximaof the above covariance, suggesting possible zone boundaries.illustrates such found boundariessuperimposed on the original image.

Referring back to the methodof, after performing the borehole image segmentation based on the pixel data (block) and the covariance data (block), at block, the data processing system may merge borehole boundary data determined at blocksand. As illustrated in, the merged borehole boundary data may be determined based on a combination of the boundary locationsidentified based on the pixel data as described in blockand illustrated in borehole imageand the boundary dataidentified based on the covariance data as described in blockand illustrated in borehole image. When the borehole boundary dataof the borehole imageis combined with the boundary dataof the borehole image, the data processing system may generate merged borehole imagewith merged boundary data.

After the borehole boundary data is merged at block, at block, the data processing system may cluster borehole image features of the segmented borehole image based on a classification algorithm. The merged boundary data may provide an indication of different sedimentary zones within the borehole.

For high resolution borehole images, the data processing system may perform the unsupervised classification (e.g., without any prior knowledge) utilizing the sedimentary zones obtained from the segmentation and merging steps described above. For each segmented borehole image, the data processing system may extract a given number N of statistic properties (e.g., features). The data processing system may represent each segment of the borehole image as a point in a space of an N dimension (e.g., feature space). Each axis of the N dimension may correspond to a statistic property (e.g., feature). The classification algorithm (e.g., clustering algorithm) used by the data processing system may group the points into No clusters, which verify that the distance of points inside each cluster is minimal and distance between clusters is maximal.

In the feature space of high dimensionality (e.g., greater than 5, greater than 10), the local optima may be higher than some threshold value making it difficult to analyze. As such, it may be desirable to utilize a clustering method in which the local optimum does not depend on the random initialization and the divergence of determined local minima does not appear arbitrary. To minimize stochastic (e.g., random) results, the data processing system may utilize agglomerative clustering, which may provide a robust result via a dendrogram (e.g., tree-like representation). Agglomerative clustering is a method of hierarchical clustering algorithm based on a similarity known as agglomerative nesting (AGNES), which uses a bottom-up approach. During the AGNES method, an object is initially considered a single-element cluster. All clusters are successively merged based on the similarities between the clusters. Newly formed clusters (e.g., composed of single-element clusters) are linked to other newly formed clusters to create bigger clusters. The clustering process is iterated until all points are a member of a single big cluster (e.g., root).

In addition to the features used for zonation, the data processing system may utilize more statistical properties in its classification process, which may provide more opportunities for the data processing system to characterize the image with thin layers or with a highly hetero-homogeneous texture. For example, the data processing system may utilize a variogram to determine statistical properties that can be used in classifying a borehole. Different image textures may generate variograms with different shapes. The data processing system may extract more parameters from a variogram to use as classification features.illustrates an example variogramthat exemplifies a shoulder height, a sill(e.g., the value that the variogram model attains at the range), and a range(e.g., distance after which the variogram levels off).

The data processing system may also utilize a correlogram to determine statistical properties that can be used in classifying a borehole. The data processing system may utilize an auto-correlogram to characterize the vertical variability of borehole images. The auto-correlogram in a Y direction may provide the data processing system with methods to compute autocorrelation of each trace of zone image and determine a sum of the autocorrelation of all the traces. Once the data processing system has determined the sum of the autocorrelation of all the traces, the data processing system may generate an auto-correlogram(e.g., curve of averaged autocorrelation vs. vertical lag distance) as illustrated in.

Using the auto-correlogram, the data processing system may extract a maximum lag (e.g., furthest time interval at which the autocorrelation function is calculated) and a correlation strengthfrom the second peak in the auto-correlogram. Both the maximum lag and correlation strengthmay be classification features that may be used in embodiments described herein. Furthermore, the data processing system may utilize any extra logging curve with any statistical feature extracted from any borehole image. For instance, the data processing system may compute a mean value of the logging curve within the depth ranges of image zonation and assign the mean value to that image segment as an additional feature.

After the data processing system extracts the desired statistical properties from the variogram and correlogram, the data processing system may complete a similarity computation. In some embodiments, the data processing system may compute a distance metric or a measure of similarity between clusters. For a single point, the data processing system may utilize Euclidean (e.g., straight-line distance between two points in Euclidean space) or Manhattan (e.g., distance between two points by summing the absolute distances of their coordinates) distances. Conversely, for a set of points, the data processing system may utilize a linkage criterion such as Single-linkage (e.g., shortest distance between any two members of two clusters, one from each cluster) or Ward linkage (e.g., analyzes the variance of clusters). In some embodiments, the data processing system may utilize the Euclidean distance and Ward linkage. In other embodiments, the data processing system may utilize the Manhattan distance or the Single-linkage. The data processing system may output the result of the clustering as a binary tree, which may show the sequence in which clusters were merged and the distance at which each merge took place. By way of example,illustrates an embodiment of a hierarchical tree presented as a dendrogram plot. The length of branchesrepresents the distance between clusters before they are merged. As such, longer branches imply more separated clusters, which may stop the merging process at this stage. However, the long branches underneath the root may be excluded to avoid too few clusters.

In the illustrated embodiment, the longest branch with a number of clusters bigger than four is depicted with a red dash. As such, the data processing system may use the longest branch with a number of clusters larger than four to cut the hierarchical tree in the dendrogram plotand enable a first guess at the number of clusters. A user may select the next nlongest branch, which may cause the data processing system to provide the user with more clusters if the user desires. The n is a parameter exposed to the users. The n may default as 0 for the initial cluster number. Further, negative number values for n may result in fewer cluster numbers than the previous nlongest branch may determine. Once the data processing system has determined the initial and adjusted cluster number, the data processing system may improve the zonation results by merging any adjacent zones having the same class.