WO2023023717A1

WO2023023717A1 - Estimating underground organic content

Info

Publication number: WO2023023717A1
Application number: PCT/AU2022/050944
Authority: WO
Inventors: Vincent Crombez; Guillaume RONGIER
Original assignee: Commonwealth Scientific And Industrial Research Organisation
Priority date: 2021-08-25
Filing date: 2022-08-22
Publication date: 2023-03-02

Abstract

This disclosure relates to estimating underground organic content. A processor creates a trained hierarchical model by training first and second levels of a stochastic model, both levels being stochastic processes using rock properties as input and organic content as output. The organic content of the first level comprises measurements of cuttings samples, which represent a spatially averaged measurement of the underground organic content. The organic content of the second level comprises measurements of drill core samples, which represent a point measurement of the underground organic content. The second level models the core samples, having a mean value that is represented by the first level, modelling the cuttings samples. The processor then uses an application sample, comprising rock properties, as an input to the trained model to estimate the underground organic content for the application sample by sampling the stochastic process of the second level.

Description

"Estimating underground organic content" Cross-Reference to Related Applications [0001] The present application claims priority from Australian Provisional Patent Application No 2021902732 filed on 25 August 2021, the contents of which are incorporated herein by reference in their entirety. Technical Field [0002] This disclosure relates to estimating underground organic content. Background [0003] Estimating organic content in underground rocks is an important step in the exploration of oil and gas. Typically, after a well is drilled, geophysical logs are acquired along the well while rock samples are gathered to measure their organic content. However, only a limited number of samples can be selected and analysed, limiting the understanding of the distribution of organic content in the subsurface. [0004] Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general knowledge in the field relevant to the present disclosure as it existed before the priority date of each claim of this application. [0005] Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps. Summary [0006] A method for estimating underground organic content, the method comprises: creating a trained hierarchical model by: training a first level being a first stochastic process using one or more rock properties of first training samples as input and the underground organic content of the first training samples as an output, the underground organic content of the first training samples comprising measurements of cuttings samples, which represent a spatially averaged measurement of the underground organic content, and training a second level being a second stochastic process using one or more rock properties of second training samples as input and the underground organic content of the second training samples as an output, the underground organic content of the second training samples comprising measurements of drill core samples, which represent a point measurement of the underground organic content, the second stochastic process, modelling the core samples, having a mean value that is represented by the first stochastic process, modelling the cuttings samples; and using an application sample, comprising at least a measurement of rock properties, as an input to the trained hierarchical model to estimate the underground organic content for the application sample by sampling the second stochastic process. [0007] In some embodiments, the first training samples or the second training samples are from a first borehole and the underground organic content is estimated for samples from a second borehole different to the first borehole. [0008] In some embodiments, the first stochastic process or the second stochastic process is trained on geological data indicative of rock properties in multiple depth intervals. [0009] In some embodiments, the rock properties comprise initial rock properties and variation of the rock properties over time. [0010] In some embodiments, the rock properties are related to formation of rocks and their evolution over time. [0011] In some embodiments, the method further comprises training a third level being a third stochastic process using one or more rock properties of third training samples as input and the underground organic content of the third training samples as an output, the underground organic content of the third training samples comprising measurements of well logging samples, which represent a point measurement of the underground organic content, the third stochastic process, modelling the well logging samples, having a mean value that is represented by the second stochastic process, modelling the drill core samples. [0012] In some embodiments, the well logging data comprises multiple types of geophysical measurements, each of the multiple geophysical measurements being taken at a respective depth of the well corresponding to one of the samples. [0013] In some embodiments, the method further comprises training a further level on stratigraphic data. [0014] In some embodiments, the method further comprises determining parameters of a mean function defining the mean value depending on the rock properties. [0015] In some embodiments, the method further comprises determining parameters of a covariance function defining a correlation between rock properties. [0016] In some embodiments, the trained hierarchical model is implemented by a hierarchical covariance function. [0017] In some embodiments, determining the parameters comprises optimising an objective function. [0018] In some embodiments, the objective function is based on a marginal likelihood. [0019] In some embodiments, the stochastic processes are respective Gaussian processes. [0020] In some embodiments, estimating the underground organic content comprises applying a non-linear transformation to the stochastic processes. [0021] In some embodiments, the stochastic processes are warped Gaussian processes. [0022] In some embodiments, the underground organic content comprises hydrocarbon content. [0023] Software that, when executed by a computer, causes the computer to perform the above method. [0024] A computer system for estimating underground organic content comprises a processor configured to: create a trained hierarchical model by: training a first level being a first stochastic process using one or more rock properties of first training samples as input and the underground organic content of the first training samples as an output, the underground organic content of the first training samples comprising measurements of cuttings samples, which represent a spatially averaged measurement of the underground organic content, and training a second level being a second stochastic process using one or more rock properties of second training samples as input and the underground organic content of the second training samples as an output, the underground organic content of the second training samples comprising measurements of drill core samples, which represent a point measurement of the underground organic content, the second stochastic process, modelling the core samples, having a mean value that is represented by the first stochastic process, modelling the cuttings samples; and using an application sample, comprising at least a measurement of rock properties, as an input to the trained hierarchical model to estimate the underground organic content for the application sample by sampling the second stochastic process. [0025] Disclosed herein is a method for estimating underground organic content based on samples of rock properties, the samples comprising a first set of samples which comprise an organic content value and a second set of samples which do not comprise an organic content value, the method comprising: using the samples of the first set to train a hierarchy of two or more levels, the hierarchy comprising a first level being a stochastic process that models variations common to the samples ; and one or more subsequent levels being stochastic processes, the stochastic process of level l being a parameter of the stochastic process of level l+1, the one or more subsequent levels modelling variations between samples within one borehole or between samples from different boreholes; and using one of the samples from the first set or the second set as an input to the hierarchy to estimate the underground organic content for that one of the samples by sampling the last stochastic process of the hierarchy. [0026] Disclosed herein is a computer system for estimating underground organic content based on samples of rock properties, the samples comprising a first set of samples which comprise an organic content value and a second set of samples which do not comprise an organic content value, the computer system comprising a processor configured to: use the samples of the first set to train a hierarchy of two or more levels, the hierarchy comprising a first level being a stochastic process that models variations common to the samples ; and one or more subsequent levels being stochastic processes, the stochastic process of level l being a parameter of the stochastic process of level l+1, the one or more subsequent levels modelling variations between samples within one borehole or between samples from different boreholes; and use one of the samples from the first set or the second set as an input to the hierarchy to estimate the underground organic content for that one of the samples by sampling the last stochastic process of the hierarchy. [0027] Optional features described of any aspect of method, computer readable medium or computer system, where appropriate, similarly apply to the other aspects also described here. Brief Description of Drawings [0028] An example will be described with reference to [0029] Fig.1 illustrates an example site. [0030] Fig.2 illustrates the organic content and stratigraphic units along the first well in Fig.1. [0031] Fig.3a illustrates measurements of organic content along with the geophysical logs. [0032] Fig.3b illustrates the continuous space made by the input variables. [0033] Fig.4 illustrates a computer system for estimating underground organic content. [0034] Fig.5 illustrates a stratigraphic correlation scheme that indicates which units penetrated at different locations belong to the same stratigraphic unit. [0035] Fig.6 illustrates a method for estimating underground organic content. [0036] Fig.7 illustrates a user interface to graphically display determined estimates of organic content. Description of Embodiments [0037] The present disclosure provides a method, as performed by a computer processor, for estimating underground organic content. The method is based on samples of rock properties taken from the underground. Those samples comprise measurements of various rock properties, which may be acquired as geophysical logs, and stratigraphic data. For some of the samples, but not for all of them, the rock properties also comprise organic content that has been measured for those samples. Organic content can be measured by analysing drill cores or drill cuttings, for example. However, these measurements of organic content are expensive and time consuming. Therefore, there are many samples for which rock properties are available but no organic content measurement is. In fact, rock properties, excluding organic content measurements, are acquired for most boreholes in practical applications. A borehole as used herein is any hole that results from any type of drilling operation including drilling for exploration/surveying or for extraction. Well are also boreholes but used for extraction of oil or gas, for example. When reference is made herein to ‘wells’ it is understood that the disclosed methods are equally applicable to other boreholes that are not for the primary purpose of extraction. [0038] The processor uses the samples with available organic content to train a prediction model using rock properties other than organic content measurements as described below. The processor can use the model to predict organic content. While the processor may perform this prediction on samples where organic content is not available, it is equally possible to compute a prediction where organic content is already available in order to obtain an indication of noise and measurement errors. [0039] Fig.1 illustrates an example site 100 having a surface 101. Everything under the surface is considered underground. There is a first well 102 and a second well 103. Further wells are indicated by circles across surface 101. In each of the first well 102 and the second well 103, measurements of organic content have been performed, such as by analysing a drill core or cuttings in a laboratory. The results are illustrated as shaded areas where the position along the well downwards indicates the depth at which the corresponding measurement was made. For example, for second well 103, top (near surface) measurements in an interval 104 indicates relatively low organic content as indicated by light shading. In contrast, for the subsequent measurements in interval 105 below the top interval 104, the organic content is relatively high as indicated by a dark shading. In addition to organic content measurements, geophysical logs have been acquired in wells 102, 103, 107, and all subsequent wells in the site. Geophysical logs and organic content are referred to as “rock properties” herein, which means the samples from second well 103 form a set of samples, some of which comprise an organic content value. [0040] Similarly, first well 102 has measurements of rock properties along the depth of the well 102 and the respective carbon content is also indicated by shading. So some of the samples from first well 102 are also in the set of samples which comprise an organic content value, together with the samples with organic content from second well 103. The relatively thin layers of high organic content in both wells 102 and 103 may be due to a layer 106 of high organic content extending under surface 101. There is also a third well 107 for which no carbon content measurements are available but only geophysical measurements and stratigraphic units have been gathered. So the samples from the third well 107 are said to be part of a second set of samples which do not comprise an organic content value. It is an aim to estimate the organic content of any sample, such as samples along the third well 107. [0041] Stratigraphic information may be provided to the disclosed method by user input and is also included in the term “rock properties” herein. Stratigraphy is the science of understanding the variations in successive bodies of rocks and their composition. These rocks may be sedimentary, volcanic, metamorphic or igneous. Lithology means "the composition or type of rock such as sandstone, limestone, or granite." Accordingly, lithostratigraphy means the variations in compositions or type of rock in successive units. Sequence stratigraphy, a branch of stratigraphy, focusses on the dynamic of sedimentary bodies by grouping depositionally related strata in sequences. Sequence stratigraphy therefore includes the study of sea level variations, sediment supply and source variation through time. This approach differs from chronostratigraphy, that tracks the depositional ages of the rock strata through geologic time. All of these types of information, and potentially others, can be provided by a user (such as by a drawing) and can be converted to numerical values associated with respective (x,y,z) locations to be compatible with the calculations disclosed herein. [0042] Fig.2 illustrates the organic content from first well 102 in more detail. In particular, the bar chart 201 indicates the total organic carbon (TOC) at each depth value. For example, the sampling rate of the TOC data may be 1 m, but could have other values. One method of measuring organic content as shown in bar chart 201 is to extract drill cores and measure organic content at multiple locations along the drill core. The data obtained from drill core analysis is one of the main training inputs of the methods disclosed herein. Another way of measuring organic content is by analysing drill cuttings, which typically provides an average over several metres. While core analysis can provide a higher spatial resolution (i.e. sampling rate) than cuttings analysis, it is difficult and expensive to extract drill cores. It is further noted that for other methods of estimating organic content, it is typically difficult to use the core analysis data together with the cuttings analysis data in a single prediction. As a result, those methods provide a less accurate estimate. In contrast, the methods disclosed herein can effectively fuse the core analysis data with the cuttings analysis data to provide a more accurate estimate because more data is now available to train the prediction model. [0043] Fig.2 also illustrates the shading from Fig.1 indicating low, medium or high organic content, which resembles data typically obtain from cuttings analysis. More particularly, first interval 202 and second interval 203 indicate low organic content, which is represented by relatively short bars in the bar chart 201. Third interval 204 indicates medium organic content, which is represented by medium length bars in chart 201. Finally, fourth interval 205 indicates high organic content, which is represented by long bars in chart 201. Fifth interval 206 and sixth interval 207 again indicate low organic content indicated by short bars in chart 201.Fig.2 illustrates different sampling rates and type of sampling. More particularly, in this case, samples 202-207 are average samples, such as those determined from cuttings. More particularly, as the well is drilled, the cuttings are caught and once the drill has advanced a predetermined depth, such as 5 m, the cuttings are analysed as a single sample. That is, the cuttings from those 5 m of drilling are mixed into a single physical sample. As a result, the analysis of that sample will be an average over those 5 m of drilling as shown by intervals 202- 207 in Fig.2. In Fig.2, the “darkness” of the intervals 202-207 indicates the organic content, such that a relatively dark interval (e.g., 205) indicates high organic content and a relatively light interval (e.g., 202) indicates low organic content. [0044] Fig.2 also shows different stratigraphic units including a first stratigraphic unit 208, such as sand, a second stratigraphic unit 209, such as silt, a third stratigraphic unit 210, such as shale, finally, a fourth stratigraphic unit 211, such as sand again. Unlike the intervals 202-207 that indicate quantitatively the organic content by their darkness, the units 208-211 are hatched to indicate different types without reference to organic content or other quantitative measure. Both indications 202-207 and 208-211 are referred to as rock properties. It is noted that the averaging of drill cuttings is typically not aligned with the transitions between the stratigraphic units and as a result, the transitions between stratigraphic units 209 and 210, for example, are not accurately measured by the measurements 204 and 205. [0045] It is further noted that the direct measurement of organic content, such as pyrolysis, is a complex process. It is not desirable to perform this process many times along a well due to the required effort and cost. [0046] On the other hand, there are geophysical sensors that can sample rock properties at a much higher sampling rate, such as every 1 m or less, which is referred to as “geophysical logs” or simply “logs”. Typically, logs are available for all samples from all boreholes considered herein and including the samples where organic content is measured. However, there are a significant number of samples for which no organic content values is available. It is therefore an aim to accurately estimate the organic content for samples where direct measurements of organic content are sparse or not available. In other words, the proposed methods infer the organic content from a set of training data comprising geophysical measurements and few lab measurements of organic content. [0047] High resolution organic content is useful to reliably estimate the potential of a rock for hydrocarbon generation and plan for extraction of natural resources by open cut or underground mining for solid materials, such as coal, or by drilling wells to extracts liquids or gas, such as for oil or gas. The problem, however, is that it is not always practical or possible to measure the organic content at high resolution. Therefore, the organic content is estimated or predicted. These two terms are used interchangeably herein. [0048] More particularly, the disclosed methods use, as input data, geophysical measurements and stratigraphic information in combination with some organic content measurements. These geophysical measurements are typically obtainable or available at a relatively high sampling rate. The disclosed methods process the geophysical measurements to estimate the organic content. Geophysical measurements may include any one or more of: · Resistivity measurements, · Sonic measurements, · Density measurements, · Gamma ray measurements, · Neutron measurements, · Spontaneous potential measurements, · Calliper measurements. [0049] Fig.3 illustrates measurements of organic content 301 as indicated by the length of bars in a bar chart. It can be observed that the measurements are identical to those in Fig.2 but some values are missing. However, it is still important to predict the organic content between the measurements. For example, there is a medium content measurement 302 and a high content measurement 303 but there are no measurements in between. Therefore, the organic content between measurement 302 and measurement 303 needs to be predicted. [0050] Fig.3 also illustrates first geophysical measurement 304, second geophysical measurement 305 and third geophysical measurement 306 along the well. For completeness, Fig.3 also shows the stratigraphic units 307 as shown in Fig.2. The disclosed method effectively “learns” the relationship between the geophysical measurements 304, 305, 306, the stratigraphy 307 and the organic content 301 where measurements of the organic content are available. Elsewhere, the disclosed methods estimate the missing organic content measurements from the geophysical measurements and the stratigraphy. More particularly, in practice it is often the case that there are no organic content measurements at all for some wells. Therefore, the methods disclosed herein can use relationships over other wells to predict organic content along a well without organic content measurements. [0051] One way of predicting organic content where it is not measured is by using a Gaussian process (GP). A stochastic process is a collection of random variables, and a Gaussian process is a type of stochastic process in which any finite set of those random variables has joint Gaussian distribution. The random variables of a stochastic process are indexed over a continuous domain, often time or space, but in the case herein that domain is the geophysical space. So instead of Euclidean coordinates (x,y,z) or time (t) like in other applications, the disclosed method uses geophysical data, such as resistivity, sonic, density, gamma ray, stratigraphy, etc. as inputs to the Gaussian process. [0052] Fig.3a illustrates a continuous domain 350 of geophysical features. The continuous domain 350 has dimensions 351, 352, 353 for features 304, 305, 306, respectively. For each point in that space, the organic content can be modelled as a random variable in a stochastic process. A further dimension (i.e., input) may be the stratigraphic information 307. [0053] The input data can be transformed before being used for training and prediction. Transformations can be specific to each input or applied to all the inputs. Specific transformations aim at turning the inputs into the format best suited for regression – for instance attributing a number to a lithostratigraphic unit – or to improve the accuracy of the predictions – for instance by using the logarithm of the resistivity instead of the resistivity. Transformations applied to all the inputs aim at limiting bias when the inputs have different ranges by performing feature scaling. In one example, standardization can be applied to each input independently:

Where x₀ is the original input,

is the mean of the original input, σ₀ is the standard deviation of the original input, and x is the standardized input. [0054] For a vector of transformed input data x , a Gaussian process is fully specified by a mean function m(x) and a covariance function k(x,x') , and is denoted as:

As such, the random variables of the Gaussian process represent the values of the function ƒ. In general, ƒ is considered a latent variable, and the observed variable y (e.g. organic content) is a combination of ƒ and some Gaussian noise ε:

In examples herein, x is a set of values from geophysical data, y is the measured organic content corresponding to that set, ε is noise due to measurement or interpretation errors, and ƒ(x) is the noise-free value of organic content. In some examples, the noise is assumed to be zero, i.e. ε = 0 which means ƒ denotes the organic content. [0055] The covariance function, also called kernel, can be stationary, which means the covariance only depends on the distance between two points and not on the location of those two points, or may be non-stationary. Most kernels depend on two parameters: the length scale ℓ and the variance σ². The former measures how close in continuum 350 two points x and x' have to be to influence each other significantly, while the latter measures the magnitude of the effect of the covariance function. In one example, the covariance function is the exponential kernel:

[0056] The mean function may be set to a constant function equal to zero for simplicity. In most examples herein, a constant mean function is used, which is more flexible and gives better results on experimental case studies. It is also possible to define a mean function that varies over each random variable. [0057] A Gaussian process can be fitted (i.e. trained) to some training data following a Bayesian approach, in which a prior directly over functions is updated in light of observed data, moving to a posterior distribution. For a training set of inputs X and corresponding outputs y, and a set of inputs X_∗ for prediction, the posterior is denoted as:

Where:

and K(X_∗, X) is the covariance matrix between all pairs of n training points and n_∗ prediction points, and similarly for K (X, X), K (X_∗ ,X_∗), and K (X, X_∗). [0058] In addition, training a Gaussian process involves finding all its hyperparameters θ, i.e., the variance of the noise , the parameters of the covariance function, and the parameters of the mean function if any. This may be done automatically following an optimization procedure that searches for the best set of hyperparameters as defined by an objective function. In general, the objective function is the log marginal likelihood:

Although other objective functions can be used. [0059] Any of the hyperparameters can also be defined by a user. For example, if there is a high confidence in the quality of the data, can be set to 0 or a small value

rather than being optimized to introduce that prior knowledge into the Gaussian process. [0060] More information on Gaussian processes can be found in Rasmussen and Williams (2006) “Gaussian Processes for Machine Learning”, MIT Press, which is incorporated herein by reference. [0061] While a Gaussian process can be a useful tool for prediction (also referred to as regression), it cannot efficiently take into account the variability of well data, which can be, for instance, different geophysical logs from different wells or different sample types of organic content, like samples from cuttings or cores. Therefore, this disclosure provides an improved method, as performed by a processor of a computer system, where multiple data sources can be used simultaneously by a Gaussian process to provide a more insightful and accurate prediction. [0062] To do so, the processor follows a Bayesian hierarchical approach by creating a hierarchical model of multiple stochastic processes, such as Gaussian processes. In general, a hierarchical model is an arrangement of items that are represented as being "above", "below", or "at the same level as" one another. In the example of a computer implementation, a hierarchy is a data structure of data objects that are arranged in different levels. These data objects depend on and/or communicate with each other in the same sense as employees in an organisation report up or down from their respective layers of the organisational hierarchy. This approach relies on the idea that samples from a well data of a specific type – e.g., resistivity or organic content from a core – share some common trend because they arise from the same physical principles and the same geological context, but differences between samples arise from differences in the local geology, or in the sample acquisition or analysis. Thus, one can define a hierarchy in which a first level captures the common trend using a first stochastic process, and a second level (or more) captures the differences between groups of samples using a second stochastic process (or more). [0063] It is possible to define different levels in the hierarchy depending on the available data and their variability. For example, if only samples from cores are available, a first level models variations common to all core samples, and a second level models variations between wells. In another example, if samples from cuttings and cores are available, a first level models variations common to all the samples from cuttings, a second level models the variations between samples from cuttings and samples from cores, and a last level models variations between wells. More levels can be defined to ingest further information, such as changes of rock over time or rock formation. [0064] To implement the hierarchy, there is disclosed a hierarchical Gaussian process, in which the Gaussian process of level l is used as mean function in the level l + 1, and which, for L levels, is denoted as:

Where represents a group of data at level l.

[0065] Note that the covariance functions k₁, k₂, … , k_L have independent parameters. So, with every new layer in the hierarchy, there is a new set of hyperparameters corresponding to the covariance function for that layer. Note that the hierarchy can be arbitrarily extended to represent the structure of the data. Each covariance function may be an exponential function, but they can be different. [0066] The linearity of the hierarchy means that any samples from the stochastic process ƒ_L(s) are jointly Gaussian distributed with a mean defined by m(s) and a covariance

defined by:

Thus, a hierarchical covariance function in a single Gaussian process can implement the hierarchy, denoted as:

[0067] As mentioned above, the process may involve three layers for cuttings, core and wells, respectively:

While the first layer of a hierarchical Gaussian process may represent a latent variable that is not observed, it was found that predictions are more accurate when considering underground organic content as measured in cuttings as the first layer instead of an unobservable latent. In that case, the second layer has a single group, the organic content as measured in core samples, and captures the difference between organic content as measured in cuttings and organic content as measured in cores. The third layer captures the variations in the measures of underground organic content due to differences between wells, e.g., variations in local geology or in measurement tools. In that case, there are as many groups as wells. [0068] In yet a further example, the hierarchical model includes two layers, including a first layer stochastic process for modelling the cuttings and a second layer stochastic process for modelling the cores. In that case, the mean value of the second layer is represented by the first layer, so:

[0069] A hierarchical Gaussian process can predict groups unseen during training, such as a new well. In such case, the predicted uncertainty is higher than with the wells seen during training, as should be expected. Thus, it still provides a useful estimate. [0070] More information on this process can be found in Hensman et al. (2013) “Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters”, BMC Bioinformatics, 14:252, which is incorporated herein by reference. [0071] To better manage inputs of different types, the method may include performing automatic relevance determination (ARD). ARD lets the Gaussian process have a different length scale for each input dimension 351, 352, 353, which makes the Gaussian process more flexible and improves predictions since the inputs can have different characteristics. In a hierarchical Gaussian process, each level can use a covariance function with automatic relevance determination. [0072] For example, the exponential kernel with automatic relevance determination becomes for D input dimensions:

[0073] Automatic relevance determination also provides an insight into how the Gaussian process considers each input: a long length scale implies little variation of the output along that dimension, so little relevance of that input according to the Gaussian process. [0074] More information on this process can be found in Williams and Rasmussen (1996) “Gaussian processes for regression”, in Touretzky et al. (eds), Advances in Neural Information Processing Systems 8, MIT, which is incorporated herein by reference. [0075] While the hierarchical Gaussian process described above enables the fusion of different sources of information on rock properties, including logs, stratigraphy and organic content, it is restricted to a Gaussian distribution. But the distribution of organic content tends to be right-skewed and shows more variability with higher values of organic content, which means that a Gaussian process may not properly capture the uncertainty around the predictions. In addition, the organic content is bounded between 0 and 100 %. But the predictions of a Gaussian process are boundless, which can lead to inaccuracies locally. [0076] All this can be corrected by using a warped Gaussian process, in which a non- linear transformation is applied to the predictions to generate a non-Gaussian process with non-Gaussian noise. As such, the full, improved method is a warped hierarchical Gaussian process with automatic relevance determination, which can be denoted as:

Where g is the warping function and g^-1 is the inverse warping function. A normal Gaussian process corresponds to a special case of this method: a hierarchy with a single level and the identity function as warping function. [0077] Similarly to the mean function and the covariance function, the warping function can have parameters to better adapt it to the data at hand. Those parameters join the hyperparameters θ that are optimized during training. The log marginal likelihood is modified to take the transformation into account:

[0078] In one example, the warping function is based on the logit function:

And the inverse warping function is based on the sigmoid function:

Where a = 100 when predicting organic content. Thus, a transforms the values of organic content from the range (0, 100 %) to the range (0, 1), and g transforms that output to the range (-∞, +∞), which is better suited to Gaussian processes. [0079] More information on this process can be found in Snelson et al. (2003) “Warped Gaussian Processes”, Advances in Neural Information Processing Systems (NIPS) 16, which is incorporated herein by reference. [0080] Fig.4 illustrates a computer system 400 for estimating underground organic content. The computer system 400 comprises a processor 401 connected to program memory 402, data memory 403, a communication port 404 and a user port 406. The program memory 402 is a non-transitory computer readable medium, such as a hard drive, a solid state disk or CD-ROM. Software, that is, an executable program stored on program memory 402 causes the processor 401 to perform the method in Fig.6, that is, processor 401 uses samples with organic content values to train a hierarchy of stochastic processes including a variable from a first process that is used as a parameter in the second process. Processor 401 then uses samples as an input to the hierarchy to estimate the underground organic content. The term “determining an estimate” refers to calculating a value that is indicative of the estimate. This also applies to related terms. [0081] The processor 401 may then store the estimate on data store 403, such as on RAM or a processor register. Processor 401 may also send the determined estimate via communication port 406 to a server, such as a server hosting a geomodel, which comprises any geoscientific uses, or to a user device 407 that generates a user interface 408 showing the estimate to a user (not shown). [0082] The processor 401 may receive data, such as core essay measurements and cuttings measurements, from data memory 403 as well as from the communications port 404 and the user port 406. In a further example, the user interface 407 enables the user to enter geological data. Such geological data is indicative of rock properties in multiple intervals of the underground. For example, the user may enter the depth and/or thickness of units and rock types into a user interface, such as “granite, start 20 m, end 40 m”. [0083] Fig.5 illustrates a stratigraphic correlation scheme that indicates which units penetrated at different locations belong to the same body. The presentation in Fig.5 has been created by an expert user, such as a geologist by analysing the drill hole 102,103 and 107 from Fig.1 or geophysical well logs. As set out above, the exact boundaries between different rock bodies are not known. However, there are sophisticated tools that can generate estimates. Further, an important source of information is the knowledge of specialists who have many years of experience in stratigraphy. In the case of Fig.5, such an expert devised likely boundaries. For example, the expert estimates that there is a linear boundary 501 at the bottom end of the first unit. [0084] From other sources, such as knowledge about the history of the rock formations in this area, the expert knows that there is a fault line in the second unit. Therefore, the expert has entered a fault line 502 into the representation in Fig.5. The bottom unit has a linear boundary as indicated by the expert. The structure of the boundaries may also be based on seismic measurements, for example, or other measurements that do not directly provide boundaries but generate useful data for the expert to derive a reasonable estimate. [0085] Processor 401 can now train (i.e., fit) the warped hierarchical Gaussian process with automatic relevance determination to the data represented in Fig.5. This way, the method is able to predict organic content as measured on cores or organic content as measured on cuttings for any well. The method also provides estimates of the uncertainty around the predictions. That uncertainty comprises a constant noise estimated during training that corresponds to acquisition or interpretation errors. [0086] In one example, the processor 401 receives measurement data from a drill rig 405 via communications port 404, such as by using a Wi-Fi network according to IEEE 802.11. The Wi-Fi network may be a decentralised ad-hoc network, such that no dedicated management infrastructure, such as a router, is required or a centralised network with a router or access point managing the network. [0087] Although communications port 404 and user port 406 are shown as distinct entities, it is to be understood that any kind of data port may be used to receive data, such as a network connection, a memory interface, a pin of the chip package of processor 401, or logical ports, such as IP sockets or parameters of functions stored on program memory 402 and executed by processor 401. These parameters may be stored on data memory 403 and may be handled by-value or by-reference, that is, as a pointer, in the source code. [0088] The processor 401 may receive data through all these interfaces, which includes memory access of volatile memory, such as cache or RAM, or non-volatile memory, such as an optical disk drive, hard disk drive, storage server or cloud storage. The computer system 400 may further be implemented within a cloud computing environment, such as a managed group of interconnected servers hosting a dynamic number of virtual machines. [0089] It is to be understood that any receiving step may be preceded by the processor 401 determining or computing the data that is later received. For example, the processor 401 determines measurement data, such as by filtering or de-noising, and stores the measurement data in data memory 403, such as RAM or a processor register. The processor 401 then requests the data from the data memory 403, such as by providing a read signal together with a memory address. The data memory 403 provides the data as a voltage signal on a physical bit line and the processor 401 receives the measurement data via a memory interface. [0090] It is further noted that computer system 400 may be in communication with a underground modelling system, such as a block model server, or other geological modelling system. In that case, processor 401 may receive the geological data from that modelling system, such as by calling an application programming interface (API) or reading a database. [0091] It is further noted that the particular solution of the hierarchy of stochastic processes provides an especially efficient and accurate way of estimating organic content. In particular, the stochastic processes can provide meaningful results even after only a small number of measurements of organic content, especially thanks to their quantification of uncertainties grounded in Bayesian theory. This is in opposition to other approaches such as neural networks, which can require large amounts of data to provide any meaningful estimate and have difficulties in quantifying uncertainties. [0092] Fig.6 illustrates a method 600 as performed by processor 401 for estimating underground organic content. Fig.6 is to be understood as a blueprint for the software program and may be implemented step-by-step, such that each step in Fig.6 is represented by a function in a programming language, such as C++, Java, or Python. When applicable, the resulting source code is then compiled and stored as computer executable instructions on program memory 402. [0093] Processor 401 receives multiple samples of rock properties. Processor 401 then creates 601 a trained hierarchical model. This involves training a first level and a second level. The first level is a first stochastic process and the training uses rock properties of first training samples as input and the underground organic content of the first training samples as an output. The first training samples are cuttings samples as shown at 307 in Fig.3a. As such, they represent an average of the rock properties and are used as the input of the first stochastic process. The average of the underground organic content is the output of the process.; [0094] Processor also trains the second level that is a second stochastic process using one or more rock properties of second training samples as input and the underground organic content of the second training samples as an output. The second training samples are drill core samples. As such, they represent a point measurement of the underground organic content as the output of the stochastic process. The input of the stochastic process for the drill core samples is the same input as for the first level modelling cuttings samples, that is the rock properties. Importantly, the second stochastic process, modelling the core samples, has a mean value that is represented by the first stochastic process, modelling the cuttings samples as shown in the equations above where the second process has a mean

of ƒ_cuttings(x) , which is the first process. Finally, processor 401 receives an application sample, that is, a sample from a location that needs to be estimated for organic content. The application sample comprises at least a measurement of rock properties. Processor 401 uses that sample as an input to the trained hierarchical model to estimate the underground organic content for the application sample by sampling the second stochastic process. [0095] In another example, the samples comprise a first set of samples that comprise an organic content value and a second set of samples that do not comprise an organic content value. In other words, for the second set, the organic content value is removed, missing or has not been measured. Processor 401 uses the samples of rock properties of the first set to train a hierarchy of two or more levels of stochastic processes. As set out above, this hierarchy is fitted to or trained on rock properties, which may include geophysical measurement data, or user-provided stratigraphic data as shown in Fig.5, and organic content data. The hierarchy comprises a first level that is a stochastic process, which models variations common to the samples. In other words, the stochastic process of the first level considers all samples together in one process and treats them equally. In that sense, for any sample that has identical rock properties, the modelled variation is also identical, regardless of where the sample is located. The hierarchy further comprises one or more subsequent levels that are also stochastic processes. The stochastic process of level i is a parameter of the stochastic process of level i + 1. The one or more subsequent levels model variations between samples within one well or between samples from different wells. In other words, there is at least a first stochastic process modelling variations common to all samples and a second stochastic process modelling variations between groups of samples, which may be groups of samples within the one well or groups of samples from respective different wells. The first stochastic process is a parameter of the second stochastic process. [0096] Finally, processor 401 estimates the underground organic content within a first of the one or multiple wells. More particularly, processor 401 obtains one of the samples, which includes rock properties. Processor 401 then predicts organic content for that sample. The rock properties will often include geophysical logs but may also include stratigraphic data. Further, that sample may comprise an organic content value. Processor 401 uses the rock properties excluding the organic content value, that is, processor 401 uses the geophysical logs data and stratigraphic data of the sample as an input to the trained hierarchy to estimate the organic content by sampling the last stochastic process of the hierarchy. If the sample already includes an organic content value, the processor 401 can still obtain an estimate or prediction in addition to that available organic content value. [0097] Fig.7 illustrates a user interface 700 generated by processor 401 to graphically display the determined estimates of organic content. Processor 401 generates this display by determining an estimate for each of multiple depths along the well and represents the organic content at each sample by the length of a bar in a bar chart, for example. Further, and as illustrated in Fig.7, the processor 401 not only determines a single estimate, but also calculates the uncertainty around that estimate. Therefore, user interface 700 shows the prediction 702, a 50% confidence interval 703 and a 95% confidence interval 704.. [0098] In further examples, processor 401 estimates the probability that the samples have an organic content above a predetermined threshold 705. As shown in Fig.7, the processor 401 highlights the region of high organic content by a box 701. This way, the user can easily see where are the regions of high organic content and how certain the processor is that those regions have indeed high organic content, and, accordingly, plan an operation, such as extraction of hydrocarbon or other resources. It is further possible to automatically provide the identified region to an automated or autonomous mining machine to direct a drill to the identified region and extract from there without additional or only minimal user input. [0099] It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the above-described embodiments, without departing from the broad general scope of the present disclosure. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

Claims

CLAIMS: 1. A method for estimating underground organic content, the method comprising: creating a trained hierarchical model by: training a first level being a first stochastic process using one or more rock properties of first training samples as input and the underground organic content of the first training samples as an output, the underground organic content of the first training samples comprising measurements of cuttings samples, which represent a spatially averaged measurement of the underground organic content, and training a second level being a second stochastic process using one or more rock properties of second training samples as input and the underground organic content of the second training samples as an output, the underground organic content of the second training samples comprising measurements of drill core samples, which represent a point measurement of the underground organic content, the second stochastic process, modelling the core samples, having a mean value that is represented by the first stochastic process, modelling the cuttings samples; and using an application sample, comprising at least a measurement of rock properties, as an input to the trained hierarchical model to estimate the underground organic content for the application sample by sampling the second stochastic process.

2. The method of claim 1, wherein the first training samples or the second training samples are from a first borehole and the underground organic content is estimated for samples from a second borehole different to the first borehole.

3. The method of claim 1 or 2, wherein the first stochastic process or the second stochastic process is trained on geological data indicative of rock properties in multiple depth intervals.

4. The method of claim 3, wherein the rock properties comprise initial rock properties and variation of the rock properties over time.

5. The method of claim 3 or 4, wherein the rock properties are related to formation of rocks and their evolution over time.

6. The method of any one of the preceding claims, wherein the method further comprises training a third level being a third stochastic process using one or more rock properties of third training samples as input and the underground organic content of the third training samples as an output, the underground organic content of the third training samples comprising measurements of well logging samples, which represent a point measurement of the underground organic content, the third stochastic process, modelling the well logging samples, having a mean value that is represented by the second stochastic process, modelling the drill core samples.

7. The method of claim 6, wherein the well logging data comprises multiple types of geophysical measurements, each of the multiple geophysical measurements being taken at a respective depth of the well corresponding to one of the samples.

8. The method of any one of the preceding claims, wherein the method further comprises training a further level on stratigraphic data.

9. The method of any one of the preceding claims, further comprising determining parameters of a mean function defining the mean value depending on the rock properties.

10. The method of any one of the preceding claims, further comprising determining parameters of a covariance function defining a correlation between rock properties.

11. The method of claim 10, wherein the trained hierarchical model is implemented by a hierarchical covariance function.

12. The method of claim 10 or 11, wherein determining the parameters comprises optimising an objective function.

13. The method of claim 12, wherein the objective function is based on a marginal likelihood.

14. The method of any one of the preceding claims, where the stochastic processes are respective Gaussian processes.

15. The method of any one of the preceding claims, wherein: estimating the underground organic content comprises applying a non-linear transformation to the stochastic processes.

16. The method of any one of the preceding claims, wherein the stochastic processes are warped Gaussian processes.

17. The method of any one of the preceding claims, wherein the underground organic content comprises hydrocarbon content.

18. Software that, when executed by a computer, causes the computer to perform the method of any one of the preceding claims.

19. A computer system for estimating underground organic content comprising a processor configured to: create a trained hierarchical model by: training a first level being a first stochastic process using one or more rock properties of first training samples as input and the underground organic content of the first training samples as an output, the underground organic content of the first training samples comprising measurements of cuttings samples, which represent a spatially averaged measurement of the underground organic content, and training a second level being a second stochastic process using one or more rock properties of second training samples as input and the underground organic content of the second training samples as an output, the underground organic content of the second training samples comprising measurements of drill core samples, which represent a point measurement of the underground organic content, the second stochastic process, modelling the core samples, having a mean value that is represented by the first stochastic process, modelling the cuttings samples; and using an application sample, comprising at least a measurement of rock properties, as an input to the trained hierarchical model to estimate the underground organic content for the application sample by sampling the second stochastic process.