SYSTEM AND METHOD FOR AUTOMATIC WELL LOG NORMALIZATION IN MULTIPLE WELLS

Information

  • Patent Application
  • 20250067172
  • Publication Number
    20250067172
  • Date Filed
    August 22, 2023
    a year ago
  • Date Published
    February 27, 2025
    23 hours ago
Abstract
Systems and methods for automatic well log normalization are disclosed. The methods include acquiring a target log in a target well and a reference log in a reference well; identifying a stratigraphic interval in the target well and in the reference well; projecting the target log from the target well onto a pseudo target log in a pseudo target well and projecting the reference log from the reference well onto a pseudo reference log in a pseudo reference well; identifying lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log; determining, using the first histogram and the second histogram a regression relationship between the pseudo target log and the pseudo reference log; applying the regression relationship to the pseudo target log to generate a normalized pseudo target log; and determining a reservoir quality of the reservoir that produces hydrocarbons.
Description
BACKGROUND

In the oil & gas and mining industries, wells are drilled for both exploration and production purposes. Wells are commonly logged to acquire data that measures various rock and fluid properties, such as radioactivity, density, electrical, and acoustic properties. Logging is accomplished by lowering physical sensors into a borehole with wireline, or else by using logging while drilling (LWD) technology, where sensor data is collected during the drilling process.


The gamma ray (GR) log is a commonly available log and is one of the few logs available in horizontal wells. GR logs measure the natural emission of gamma rays by a formation. The GR log is important for identifying lithology facies and indicating reservoir quality. However, due to different borehole environments and logging tools, GR logs measured from different wells in the same field need to be normalized before further quantitative analysis, such as shale volume calculation, may be completed. Conventionally, GR log normalization is performed manually by a subject matter expert, such as, e.g., someone highly-trained in petrophysics or geology, using multi-point calibration methods. The GR readings of lithology end-members, such as clean sandstone or pure shale, are recorded from different wells and then used to establish a regression relation between wells. The regression relation is then applied to a target well to normalize its GR log to the reference wells.


The conventional method for well log normalization is performed manually, which is subjective, time-consuming, and may be inconsistent. Furthermore, the conventional method may not be applicable to high-angle or horizontal wells.


SUMMARY

This summary is provided to introduce a selection of 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 as an aid in limiting the scope of the claimed subject matter.


In general, in one aspect, embodiments are disclosed related to methods for automatic well log normalization. The methods include acquiring, using a well logging tool, a target log in a target well and a reference log in a reference well. They further include, using a well log interpretation system: identifying a stratigraphic interval in the target well and in the reference well, the target well and reference well being drilled into a reservoir; projecting the target log covering the stratigraphic interval from the target well onto a pseudo target log in a pseudo target well and projecting the reference log over the stratigraphic interval from the reference well onto a pseudo reference log in a pseudo reference well; identifying lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log; determining, using the first histogram and the second histogram a regression relationship between the pseudo target log and the pseudo reference log; applying the regression relationship to the pseudo target log to generate a normalized pseudo target log; and determining, based on the normalized pseudo target log, a reservoir quality of the reservoir that produces hydrocarbons.


In general, in one aspect, embodiments are disclosed related to a system for automatic well log normalization. The system includes a well logging tool, configured to acquire a target log in a target well and a reference log in a reference well, the target well and reference well being drilled into a reservoir. The system further includes a well log interpretation system, configured to: identify a stratigraphic interval in the target well and in the reference well; project the target log covering the stratigraphic interval from the target well onto a pseudo target log in a pseudo target well and projecting the reference log over the stratigraphic interval from the reference well onto a pseudo reference log in a pseudo reference well; identify lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log; determine, using the first histogram and the second histogram a regression relationship between the pseudo target log and the pseudo reference log; apply the regression relationship to the pseudo target log to generate a normalized pseudo target log; and determine, based on the normalized pseudo target log, a reservoir quality of the reservoir that produces hydrocarbons.


Other aspects and advantages of the claimed subject matter will be apparent from the following description and the appended claims.





BRIEF DESCRIPTION OF DRAWINGS

Specific embodiments of the disclosed technology will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.



FIG. 1 shows a drilled borehole system in accordance with one or more embodiments.



FIG. 2A shows a vertical, deviated, and horizontal well, along with a pseudo well in accordance with one or more embodiments.



FIG. 2B shows a deviated well, a horizontal well, and two pseudo wells in accordance with one or more embodiments.



FIG. 3 shows histograms from gamma ray values and Gaussian models in two wells, along with a linear regression relationship between them, in accordance with one or more embodiments.



FIG. 4 shows a flowchart in accordance with one or more embodiments.



FIG. 5 shows a computer system in accordance with one or more embodiments.





DETAILED DESCRIPTION

In the following detailed description of embodiments of the disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the disclosure. However, it will be apparent to one of ordinary skill in the art that the disclosure may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description.


Throughout the application, ordinal numbers (e.g., first, second, third, etc.) may be used as an adjective for an element (i.e., any noun in the application). The use of ordinal numbers is not to imply or create any particular ordering of the elements nor to limit any element to being only a single element unless expressly disclosed, such as using the terms “before,” “after,” “single,” and other such terminology. Rather, the use of ordinal numbers is to distinguish between the elements. By way of an example, a first element is distinct from a second element, and the first element may encompass more than one element and succeed (or precede) the second element in an ordering of elements.


In the following description of FIGS. 1-5, any component described with regard to a figure, in various embodiments disclosed herein, may be equivalent to one or more like-named components described with regard to any other figure. For brevity, descriptions of these components will not be repeated with regard to each figure. Thus, each and every embodiment of the components of each figure is incorporated by reference and assumed to be optionally present within every other figure having one or more like-named components. Additionally, in accordance with various embodiments disclosed herein, any description of the components of a figure is to be interpreted as an optional embodiment which may be implemented in addition to, in conjunction with, or in place of the embodiments described with regard to a corresponding like-named component in any other figure.


It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a gamma ray log” includes reference to one or more of such gamma ray logs.


Terms such as “approximately,” “substantially,” etc., mean that the recited characteristic, parameter, or value need not be achieved exactly, but that deviations or variations, including for example, tolerances, measurement error, measurement accuracy limitations, and other factors known to those of skill in the art, may occur in amounts that do not preclude the effect the characteristic was intended to provide.


It is to be understood that one or more of the steps shown in the flowcharts may be omitted, repeated, and/or performed in a different order than the order shown. Accordingly, the scope disclosed herein should not be considered limited to the specific arrangement of steps shown in the flowcharts.


Although multiple dependent claims are not introduced, it would be apparent to one of ordinary skill that the subject matter of the dependent claims of one or more embodiments may be combined with other dependent claims.


Presented here, according to one or more embodiments, are systems and methods for automatic well log normalization in multiple wells. Well log data in a target well are normalized to match one or more reference wells so that correct identification of lithology may be performed in the target well.


There are two important features that differentiate embodiments disclosed herein from conventional methods. First, the workflow is fully automated; this includes true stratigraphic projection of wells, histogram analysis of well log data, picking modes on the histograms, and regression of the well log data. Second, the workflow is applicable to a hydrocarbon field that has very complex and diverse well drilling activities, including a mixture of many vertical, deviated, and horizontal wells.


Before further presenting embodiments disclosed herein, the essential elements of a drilling system (100) within a borehole are presented according to one or more embodiments for context. Although the drilling system (100) shown in FIG. 1 is used to drill a borehole on land, the drilling system (100) may also be a marine borehole drilling system. The example of the drilling system (100) shown in FIG. 1 is not meant to limit the present disclosure.


As shown in FIG. 1, a borehole path (103) may be drilled by a drill bit (105) attached by a drillstring (106) to a drill rig located on the surface (107) of the earth. The drill rig may include framework, such as a derrick (108), to hold drilling machinery. The top drive (110) sits at the top of the derrick (108) and provides torque, typically a clockwise torque, via the drive shaft (112) to the drillstring (106) in order to drill the borehole (117). The borehole (117) may traverse a plurality of overburden (114) layers and one or more cap-rock (116) layers to a hydrocarbon reservoir (104) within the subterranean region of interest (102). In accordance with one or more embodiments, the extended bandwidth seismic dataset may be used to plan a borehole (117) including a borehole path (103) and drill a borehole (117) guided by the borehole path (103). The borehole path (103) may be a curved borehole path, or a straight borehole path. All or part of the borehole path (103) may be vertical, and some borehole paths (103) may be deviated or have horizontal sections.


A borehole (117) may be drilled using a drill rig that may be situated on a land drill site, an offshore platform, such as a jack-up rig, a semi-submersible, or a drill ship. The drill rig may be equipped with a hoisting system, such as a derrick (108), which can raise or lower the drillstring (106) and other tools required to drill the well. The drillstring (106) may include one or more drill pipes connected to form a conduit and a bottom hole assembly (BHA) (120) disposed at the distal end of the drillstring (106). The BHA (120) may include a drill bit (105) to cut into subsurface (122) rock. The BHA (120) may further include measurement tools, such as a measurement-while-drilling (MWD) tool and logging-while-drilling (LWD) tool. MWD tools may include sensors and hardware to measure downhole drilling parameters, such as the azimuth and inclination of the drill bit (105), the WOB, and the torque. The LWD measurements may include sensors, such as resistivity, gamma ray, and neutron density sensors, to characterize the rock formation surrounding the borehole (117). Both MWD and LWD measurements acquired in the borehole may be transmitted to the surface (107) using any suitable telemetry system, such as mud-pulse or wired-drill pipe, known in the art.



FIG. 2A shows three wells (200, 202, and 204) penetrating a stratigraphic interval (203) bounded by two interval boundaries (208, 210) in the subsurface. Well (200) is a vertical well, well (202) is a straight but deviated well, while well (204) follows a curved trajectory, beginning vertically, before ultimately becoming a horizontal well. A virtual or pseudo well (206) may be drawn perpendicular to the stratigraphic interval (203) and interval boundaries (208, 210). A pseudo well log in the pseudo well (206) may be formed by performing a true stratigraphic projection of a well log observed in a neighboring well, such as horizontal well (204), onto the pseudo well (206). Herein “true stratigraphic projection” implies projection parallel to the geological layering. It is assumed here that the geological layering is not horizontal, but is inclined at the same angle as the two boundary layers. The pseudo well provides a unique reference frame for evaluating the relevant thicknesses of different layers independent of the well trajectory of actual wells. This reference frame provides thickness of layers independent of the layer dip and is in harmony with the relative thickness of layers at their time of deposition.


The stratigraphic interval of interest may be identified by a subject matter expert trained in geology, petrophysics, geophysics, or a similar art. The stratigraphic interval of interest may be chosen based on the presence of hydrocarbons within it.



FIG. 2B shows a target well (250) and a reference well (252), which could be a mixture of horizontal, vertical, and/or deviated wells. A target log in the target well (250) may be projected onto the pseudo target well (260) to form a pseudo target log and a reference log in the reference well (252) may be projected onto the pseudo reference well (262) to form a pseudo reference log. (If the reference well (252) and/or target well (250) are vertical, and the geological layers are horizontal the pseudo reference log and/or pseudo target log are equivalent to the reference log and/or target log, respectively.) Well log readings from the pseudo reference log in the projected pseudo reference well (262) may be used to normalize well log readings in the pseudo target log of the pseudo target well (260) using the methods detailed below.


In addition to a possible distortion of well log data due to improper stratigraphic projection, there are other potential sources of error in the data. For example, different tools may have been used to collect the same kind of data in different wells (e.g., wireline versus LWD). Characteristics of the different tools may distort and/or bias the readings from one well to another. Further, even if the same tool is used, it may be calibrated differently in each well, again leading to distortions of the data. For these reasons, a method is needed to normalize the well data between wells so that they may be accurately compared.



FIG. 3 shows a first histogram (300) and a second histogram (302) of gamma ray values. Although gamma ray values are used in this example, the method is not limited to the normalization of gamma ray values. Rather, the same method may be applied to any kind of numerical well data, such as resistivity or density logs. The first histogram (300) comes from the pseudo target log in the pseudo target well (260), the second histogram (302) comes from the pseudo reference log in the pseudo reference well (262). Each histogram may be obtained by plotting the number of sample values falling within given sample value ranges irrespective of the spatial location of the sample within the well. If there are several modes (304), i.e., several ranges with higher frequencies constituting local maxima of the histogram, then the histogram may be modeled by a multi-modal function. For example, the modes (304) of the histograms may be used to fit three Gaussian functions corresponding to three different lithologies. However, the functions used to fit the histogram are not limited to Gaussian functions;


any canonical function may be used in place of a Gaussian function. References to Gaussian functions below may then be understood to represent any canonical function, i.e., any well-defined function with a parameterized form.


In the case of fitting Gaussian functions to the multimodal histogram, the modes (304) represent the maxima of the individual Gaussian functions. The number of Gaussian functions depends on the assumed number of lithologies in the wells; this number may vary from field to field. In the example presented here, the Gaussian functions categorize all well log values observed in the wells into the three assumed lithologies. The well log value associated with each mode (304) may be used as an input into a regression (306). The resulting regression function may be linear (alternatively, nonlinear regression functions may be appropriate) and maps well log values from the pseudo target log into normalized well log values such that the histogram of the normalized well log values will more closely resemble that of the pseudo reference well log (whose values and classification are assumed to be more accurate). This normalization procedure then allows for the layers corresponding to the normalized well log values in the pseudo target well (260) to be classified by their lithology.


In the case that the reference (target) well is already perpendicular to the geological layering, the pseudo reference (target) well will be identical to the reference (target) well. The pseudo reference (target) well log will then also be identical to the reference (target) well log.



FIG. 4 presents a flowchart of the method. In Step 410, a target log in a target well and a reference log in a reference well may be both acquired. The logs may be gamma ray logs. The acquired log of the reference well is typically from a better-studied well where there is more confidence in the data. The target well may be less-studied, hence the need to normalize the values of its log to be more in line with those of the reference well.


In Step 415, a stratigraphic interval of interest may be identified. The identification may be performed manually by a subject matter expert in both the target well and in the reference well. The stratigraphic interval may bear hydrocarbons. In one or more embodiments, the same stratigraphic interval may be identified for all wells (target well, reference well). Further, the well survey data from all horizontal wells may be used, and the depth index is converted using true stratigraphic thickness projection (TSTP).


In Step 420, a target log covering a stratigraphic interval from the target well may be projected onto a pseudo target log in a pseudo target well. A reference log over the stratigraphic interval from the reference well may also be projected onto a pseudo reference log in a pseudo reference well. The pseudo logs may be perpendicular to the stratigraphic layering. The values of log data for the target well are interpolated onto a pseudo target log in the pseudo target well, and log values in the reference well are also interpolated onto the pseudo reference log in the pseudo reference well. In some embodiments, the interpolation may be done onto a uniform sampling grid creating a regularly sampled well for each of the pseudo wells, but in other embodiments the interpolated sampling may be irregular.


In Step 430, a histogram is automatically constructed from the log values in the pseudo target well and from the log values from the pseudo reference well. More specifically, in Step 430, within the same stratigraphic interval, the histograms of the gamma ray logs, for example, are plotted in each well. Lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log are both identified. The mode of each Gaussian mode is automatically identified as the log reading of each lithology members. In some embodiments, a multi-Gaussian model or a Gaussian mixture model may be fit to the histograms based on the modes (one Gaussian for each mode). This allows for a categorization of several lithologies based on the peaks of Gaussian functions. In other embodiments, an alternative canonical function may be used in place of the Gaussian model.


In Step 440, the first histogram and the second histogram may be used to determine a regression relationship between the pseudo target log and the pseudo reference log. Modes from a Gaussian model of the log values in the pseudo target well may be matched with modes from a Gaussian model of the log values in the pseudo reference well. This allows for a computer processor to automatically determine a regression relationship (and regression coefficients) for the pseudo target log to generate a normalized pseudo target log.


In Step 445, the regression relationship is applied to the values of log data in the pseudo target well so that the resulting histogram of the modified log values in the pseudo target well appear more similar to those of the pseudo reference log in the pseudo reference well.


In Step 450, a reservoir quality (i.e, the quality of the reservoir for producing hydrocarbons) is determined based on the normalized pseudo target log(s). It is subsequently determined by a subject matter expert and/or a manager whether the stratigraphic interval should be produced.


For datasets of a realistic size, the functional steps of FIG. 4 may not be realistically performed mentally or manually without the support of an appropriately configured computer system. FIG. 5 depicts a block diagram of such a computer system (502) that may be used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures as described in this disclosure, according to one or more embodiments. The illustrated computer (502) is intended to encompass any computing device such as a server, desktop computer, laptop/notebook computer, wireless data port, smart phone, personal data assistant (PDA), tablet computing device, one or more processors within these devices, or any other suitable processing device, including both physical or virtual instances (or both) of the computing device. Additionally, the computer (502) may include an input device, such as a keypad, keyboard, touch screen, or other device that can accept user information, and an output device that conveys information associated with the operation of the computer (502), including digital data, visual, or audio information (or a combination of information), or a GUI.


The computer (502) can serve in a role as a client, network component, a server, a database or other persistency, or any other component (or a combination of roles) of a computer system for performing the subject matter described in the instant disclosure. The illustrated computer (502) is communicably coupled with a network (530). In some implementations, one or more components of the computer (502) may be configured to operate within environments, including cloud-computing-based, local, global, or other environment (or a combination of environments).


At a high level, the computer (502) is an electronic computing device operable to receive, transmit, process, store, or manage data and information associated with the described subject matter. According to some implementations, the computer (502) may also include or be communicably coupled with an application server, e-mail server, web server, caching server, streaming data server, business intelligence (BI) server, or other server (or a combination of servers).


The computer (502) can receive requests over network (530) from a client application (for example, executing on another computer (502)) and responding to the received requests by processing the said requests in an appropriate software application. In addition, requests may also be sent to the computer (502) from internal users (for example, from a command console or by other appropriate access method), external or third-parties, other automated applications, as well as any other appropriate entities, individuals, systems, or computers.


Each of the components of the computer (502) can communicate using a system bus (503). In some implementations, any or all of the components of the computer (502), both hardware or software (or a combination of hardware and software), may interface with each other or the interface (504) (or a combination of both) over the system bus (503) using an application programming interface (API) (512) or a service layer (513) (or a combination of the API (512) and service layer (513)). The API (512) may include specifications for routines, data structures, and object classes. The API (512) may be either computer-language independent or dependent and refer to a complete interface, a single function, or even a set of APIs. The service layer (513) provides software services to the computer (502) or other components (whether or not illustrated) that are communicably coupled to the computer (502). The functionality of the computer (502) may be accessible for all service consumers using this service layer. Software services, such as those provided by the service layer (513), provide reusable, defined business functionalities through a defined interface. For example, the interface may be software written in JAVA, C++, or other suitable language providing data in extensible markup language (XML) format or another suitable format. While illustrated as an integrated component of the computer (502), alternative implementations may illustrate the API (512) or the service layer (513) as stand-alone components in relation to other components of the computer (502) or other components (whether or not illustrated) that are communicably coupled to the computer (502). Moreover, any or all parts of the API (512) or the service layer (513) may be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of this disclosure.


The computer (502) includes an interface (504). Although illustrated as a single interface (504) in FIG. 5, two or more interfaces (504) may be used according to particular needs, desires, or particular implementations of the computer (502). The interface (504) is used by the computer (502) for communicating with other systems in a distributed environment that are connected to the network (530). Generally, the interface (504) includes logic encoded in software or hardware (or a combination of software and hardware) and operable to communicate with the network (530). More specifically, the interface (504) may include software supporting one or more communication protocols associated with communications such that the network (530) or interface's hardware is operable to communicate physical signals within and outside of the illustrated computer (502).


The computer (502) includes at least one computer processor (505). Although illustrated as a single computer processor (505) in FIG. 5, two or more processors may be used according to particular needs, desires, or particular implementations of the computer (502). Generally, the computer processor (505) executes instructions and manipulates data to perform the operations of the computer (502) and any algorithms, methods, functions, processes, flows, and procedures as described in the instant disclosure.


The computer (502) also includes a memory (506) that holds data for the computer (502) or other components (or a combination of both) that can be connected to the network (530). For example, memory (506) can be a database storing data consistent with this disclosure. Although illustrated as a single memory (506) in FIG. 5, two or more memories may be used according to particular needs, desires, or particular implementations of the computer (502) and the described functionality. While memory (506) is illustrated as an integral component of the computer (502), in alternative implementations, memory (506) can be external to the computer (502).


The application (507) is an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer (502), particularly with respect to functionality described in this disclosure. For example, application (507) can serve as one or more components, modules, applications, etc. Further, although illustrated as a single application (507), the application (507) may be implemented as multiple applications (507) on the computer (502). In addition, although illustrated as integral to the computer (502), in alternative implementations, the application (507) can be external to the computer (502).


There may be any number of computers (502) associated with, or external to, a computer system containing computer (502), wherein each computer (502) communicates over network (530). Further, the term “client,” “user,” and other appropriate terminology may be used interchangeably as appropriate without departing from the scope of this disclosure. Moreover, this disclosure contemplates that many users may use one computer (502), or that one user may use multiple computers (502).


Although only a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this invention. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

Claims
  • 1. A method, comprising: acquiring, using a well logging tool, a target log in a target well and a reference log in a reference well; andusing a well log interpretation system: identifying a stratigraphic interval in the target well and in the reference well, the target well and reference well being drilled into a reservoir,projecting the target log covering the stratigraphic interval from the target well onto a pseudo target log in a pseudo target well and projecting the reference log over the stratigraphic interval from the reference well onto a pseudo reference log in a pseudo reference well,identifying lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log,determining, using the first histogram and the second histogram a regression relationship between the pseudo target log and the pseudo reference log,applying the regression relationship to the pseudo target log to generate a normalized pseudo target log, anddetermining, based on the normalized pseudo target log, a reservoir quality of the reservoir that produces hydrocarbons.
  • 2. The method of claim 1, wherein the target log and the reference log each comprise a gamma ray log.
  • 3. The method of claim 1, wherein the target well and the reference well are horizontal or deviated wells.
  • 4. The method of claim 1, wherein the regression relationship is a linear relationship.
  • 5. The method of claim 1, wherein the pseudo target well and the pseudo reference well are perpendicular to the stratigraphic interval.
  • 6. The method of claim 1, wherein identifying lithologies comprises fitting Gaussian mixture models to the first histogram and to the second histogram.
  • 7. The method of claim 6, wherein peak values of the Gaussian mixture models are associated with the lithologies.
  • 8. The method of claim 6, wherein modes of the Gaussian mixture models are used to fit the regression relationship.
  • 9. The method of claim 1, wherein the stratigraphic interval is a hydrocarbon reservoir.
  • 10. The method of claim 1, wherein projecting the target log and projecting the reference log comprise interpolating onto a uniform sampling grid.
  • 11. A system, comprising: a well logging tool, configured to acquire a target log in a target well and a reference log in a reference well, the target well and reference well being drilled into a reservoir; anda well log interpretation system, configured to: identify a stratigraphic interval in the target well and in the reference well,project the target log covering the stratigraphic interval from the target well onto a pseudo target log in a pseudo target well and projecting the reference log over the stratigraphic interval from the reference well onto a pseudo reference log in a pseudo reference well,identify lithologies from a first histogram of the pseudo target log and a second histogram of the pseudo reference log,determine, using the first histogram and the second histogram a regression relationship between the pseudo target log and the pseudo reference log,apply the regression relationship to the pseudo target log to generate a normalized pseudo target log, anddetermine, based on the normalized pseudo target log, a reservoir quality of the reservoir that produces hydrocarbons.
  • 12. The system of claim 11, wherein the target log and the reference log each comprise a gamma ray log.
  • 13. The system of claim 11, wherein the target well and the reference well are horizontal or deviated wells.
  • 14. The system of claim 11, wherein the regression relationship is a linear relationship.
  • 15. The system of claim 11, wherein the pseudo target well and the pseudo reference well are perpendicular to the stratigraphic interval.
  • 16. The system of claim 11, wherein identifying lithologies comprises fitting Gaussian mixture models to the first histogram and to the second histogram.
  • 17. The system of claim 16, wherein peak values of the Gaussian mixture models are associated with the lithologies.
  • 18. The system of claim 16, wherein modes of the Gaussian mixture models are used to fit the regression relationship.
  • 19. The system of claim 11 wherein the stratigraphic interval is a hydrocarbon reservoir.
  • 20. The system of claim 11, wherein projecting the target log and projecting the reference log comprise interpolating onto a uniform sampling grid.