## Abstract

Effective fusion of multiple data, including geographical, geological, geophysical, geochemical and dynamic data for hydrocarbon potential mapping, involves both a fusion algorithm and a convenient modelling platform. In this study, fuzzy logic and a geographical information system (GIS) are used to fuse geological and geophysical interpretations in mapping the gas potential of the Kazakhstan Marsel Territory Carboniferous system based on the assumed gas-accumulation model. Non-linear membership functions are used to transform the input data, while the gamma operator is used to combine the multiple datasets. Finally, the Carboniferous system targets, the Visean (C_{1}v) and Serpukhovian (C_{1}sr) units, are mapped. Gas testing *in situ* validated our results.

Petroleum exploration involves the use of multiple data, including geographical, geological, geophysical, geochemical, remote sensing and numerical simulation data, among other types. Most of these data are often highly visual and spatially geo-referenced. The effective fusion of these data can enable the full use of the information collected while also decreasing the geological risk. In the conventional data fusion approach, geologists visually overlay various maps and make determinations based on their professional experience and knowledge. The advantage of this method is that it involves full use of the expert's knowledge through the expert's subjective inferring of even imperfect knowledge from incomplete datasets. Moreover, geologists can conveniently address qualitative variables, which are commonly used for geological applications. The main disadvantage of the conventional method is that the decision-making is subjective: for the same dataset, different geologists may obtain different results – thus, the given result may not be repeatable. Moreover, implementing an accurate spatial overlay, which is crucial to a well site location, is difficult in practice. However, the emergence and rapid development of geographical information systems (GIS) and data fusion technologies provide geologists with a platform and modelling approach for the integration of geological data.

The concept of data fusion was first introduced in the 1970s. Typically, the terms ‘data fusion’ and ‘data integration’ are often synonymous. Other terms, such as ‘multi-sensor data fusion’, ‘multi-source data fusion’, ‘data combination’ and ‘data aggregation’, also appear in the literature (Khaleghi *et al.* 2013), where the term ‘multi-source’ may imply data, staff (teams), disciplines and geoscientific interpretations (Yarus & Coburn 2000). The concept of data fusion is readily comprehensible, and the definition of ‘data fusion’ provided by White (1991) remains the most widely accepted. Nevertheless, its exact meaning varies across disciplines. For petroleum exploration geologists, the ultimate purpose of data fusion is decision-making or obtaining an optimal solution. In this sense, data fusion is somewhat similar to multi-criteria decision-making (MCDM) (Evangelos 2000).

Many methods have been developed for data fusion. These methods can be divided into two categories: data-driven and knowledge-driven. Data-driven methods, such as logistic regression, weight of evidence and neural networks, use training data for modelling and decision-making. On the other hand, knowledge-driven methods use fuzzy logic, the Dempster–Shafer belief theory and other methods to fuse multi-source data. However, these methods must be connected to a suitable platform for convenient use.

As an ideal platform for spatial data management, GIS provides diverse functions for the acquisition, storage, processing and visualization of spatial data. It is, in fact, an ideal platform for integration and visualization of geographical, geological, remote sensing, geophysical and geochemical data (Yang & Liu 1992; Pawlowski 2000; Belt & Paxton 2005; Kumar *et al.* 2015). Furthermore, the data fusion models can be easily coupled with GIS and, therefore, can readily accommodate spatial analysis (Yusupov & Ivakin 2014). For example, GIS may be integrated with Boolean reasoning (Zaidi *et al.* 2015), neural networks (Brown *et al.* 2003) or fuzzy set theory. Among these methods, fuzzy logic is a commonly used fusion model with GIS.

Various applications of fuzzy logic have been developed in resource exploration (An *et al.* 1991; Moon 1998; Brown *et al.* 2003; Porwal *et al.* 2003; Magalhães & Souza Filho 2012; Maroufi Naghadehi *et al.* 2014). The application area is broad because fuzzy set theory is suitable for the description of ambiguous phenomena in the real physical world. Furthermore, fuzzy inference is a human-like reasoning process, similar to the way in which geologists use intuitive inferences for decision-making. Moreover, the fuzzy set is convenient for handling discrete qualitative variables, which are frequently encountered in geological data.

GIS was first employed for petroleum exploration and development in the early 1980s. As Yarus & Coburn (2000, p. 4) stated, the ‘petroleum industry has perhaps provided one of the most natural environments in which GIS could evolve and flourish’. In addition, contemporary applications of GIS are penetrating many workflows involved in petroleum industry processes. For example, Bertagne *et al.* (2000) showed how GIS technology can enable oil companies to work more effectively at different stages of the exploration–production cycle in the Gulf of Mexico; Liu *et al.* (2008) proposed GIS-based modelling algorithms for searching the pathways of secondary hydrocarbon migration; and Arab Amiri *et al.* (2015) discussed the integration of evidential belief functions and GIS for the potential mapping of hydrocarbon resources.

Similar to GIS-based mineral prospectivity modelling (Porwal & Carranza 2015), three procedures are involved in GIS-based petroleum exploration modelling: conceptual modelling, data processing within a GIS framework; and integration of maps using mathematical models. Conceptual modelling depends on the discipline and specific issue being addressed. For petroleum exploration, conceptual modelling generally involves hydrocarbon resource rock, reservoirs, seals, migration and reservation conditions, and so on, while mathematical models employ fusion algorithms for spatial data. Although various algorithms may be used for the integration of petroleum data, the most commonly used algorithms include Boolean reasoning, weights of evidence and fuzzy set theory. Boolean reasoning is the simplest fusion model, which is similar to the visual map overlays of geologists. However, the crisp Boolean reasoning neglects the uncertainty of the physical world. Modelling based on the weight of evidence involves a training set, which is often unavailable in practice. The fuzzy logic-based integration method, on the other hand, accounts for uncertainty and is similar to human-like reasoning. It is therefore widely used for petroleum exploration (Bingham *et al.* 2012).

Based on the assumed conceptual model of gas accumulation, geological and geophysical interpretations of the Marsel territory of Kazakhstan are fused in this paper using fuzzy logic and GIS to map the hydrocarbon potential of Carboniferous strata. The remainder of the paper is organized as follows: a section introducing the basic principles of fuzzy logic; a section illustrating the geological and conceptual model of gas accumulation in the study area; a section presenting the fusion model; followed by a section presenting the results. Our conclusions and discussion are provided in the final section.

## Fuzzy sets and fuzzy logic

### Fuzzy sets and membership functions

The concept of fuzzy sets was first introduced by Zadeh (1965) to distinguish sets with degrees of membership from the classical set, which has clear boundaries; i.e. *x* ∈ *A* or *x* ∉ *A* exclude any other possibility. Fuzzy set *A* is a class with a membership function (MSF) and is defined as a mapping (Zadeh 1965):
where *A*(*x*) is the MSF of *x* to fuzzy set *A*. In fact, a classical set is also a special case of a fuzzy set. Membership is the most important characteristic of a fuzzy set. For a classical set, we have only two memberships: 0 or 1. For a fuzzy set, each element in the set corresponds to a value in [0, 1], which can be identified by a MSF, . Hence, we can describe a classical set by the following MSF:
For example, if we have four core samples, the tested values of porosity are 35, 20, 10 and 5%, respectively: that is, . Then, their corresponding memberships to a high-porosity class may be obtained: for example, . This means that the membership of the sample with 35% porosity equals 1; thus, 35% is deemed as fully belonging to high porosity. In contrast, the value of 5% is considered to rarely belong to high porosity.

The fuzzy sets introduced by Zadeh (1965) are typically called standard fuzzy sets (Klir 2004). With the development of fuzzy set theory, several other ‘non-standard’ fuzzy sets have been proposed and widely used in many applications, such as interval-valued fuzzy sets (Bigand & Colot 2016), type *k* (*k* ≥ 2) fuzzy sets (Karnik *et al.* 1999), level *k* (*k* ≥ 2) fuzzy sets (de Tré & de Caluwe 2003), *L*-fuzzy sets (Goguen 1967), intuitionistic fuzzy sets (Balasubramaniam & Ananthi 2014) and rough fuzzy sets (Sun *et al.* 2014), to name just a few. Any fuzzy set, regardless of whether it is standard or non-standard, is completely and uniquely characterized by one particular MSF (Jang *et al.* 1997). However, in the literature, some confusion remains about the meaning of the MSF and various interpretations are involved. Bilgiç & Türkşen (1999) outlined five different interpretations of MSFs – the respective likelihood, random set, similarity, utility and measurement views. Correspondingly, six fundamental methods used for constructing MSFs are also summarized: that is, polling, direct rating, reverse rating, interval estimation, MSF exemplification and pairwise comparison.

Roughly speaking, MSFs may be grouped into four categories according to their shape – convex (e.g. triangular, Gaussian, bell, trapezoidal), concave, S-shaped and Z-shaped – and each group includes various subtypes that are closely related with a given application (Jang *et al.* 1997). For example, given the linguistic expression ‘around three,’ some possible shapes of MSFs for a specific application may be illustrated in Figure 1 (Klir 2004). Essentially, the construction of MSFs is thus the adjustment of their shapes, and various approaches have been previously proposed. These approaches can be classified into knowledge-, model- and data-based methods.

In knowledge-based methods, the experts define a MSF from descriptive knowledge. For example, Zhu *et al.* (2010) constructed MSFs based on knowledge of typical environmental conditions of each soil type. Demicco *et al.* (2003) defined the triangular-shape MSF to describe water depth. They adjusted the S-shape MSF to describe the linguistic expressions ‘deep’ and ‘fast coral growth rate’, as well as a Z-shape MSF to describe the linguistic expressions ‘shallow’ and ‘slow coral growth rate’.

Nikravesh & Aminzadeh (2001) employed Gaussian MSFs for the description of rock properties (e.g. porosity, grain size, clay content), and they extracted relevant reservoir information. In the work of Tsoukalas *et al.* (1997), a neurofuzzy methodology was used for multiphase flow identification, and triangular MSFs were defined for impedance variables. In model-base methods, the MSFs are modified by specular models. For example, Medaglia *et al.* (2002) introduced a Bezier curve-based mechanism for constructing MSFs of convex normal fuzzy sets. Grauel & Ludwig (1999) proposed smooth MSFs, which are continuously differentiable three times. Pota *et al.* (2013) proposed a hypothesis test approach that transforms the probability distributions into MSFs. In learning-based methods, the MSFs are constructed by training the given dataset, and genetic algorithms (Arslan & Kaya 2001; Palacios *et al.* 2015), neural network algorithms (Wang 1994; Halgamuge *et al.* 1995) and statistics-based methods (Civanlar & Trussell 1986) are commonly used.

Geological variables involve qualitative and quantitative ones. For qualitative variables, we can assign a discrete membership grade according to the respective attribution. On the other hand, for quantitative variables, the corresponding MSFs are often used to build the relationship between the input (crisp value) and output (membership grade). In this paper, non-linear increasing and decreasing functions are adopted, as shown in equations (1) and (2) (Tsoukalas & Uhrig 1997).

For the non-linear increasing MSF, we have:
(1)For the non-linear decreasing MSF, we have:
(2)where *f*_{1} is the spread and *f*_{2} is the midpoint. Parameter *f*_{1} determines the curve gradient, and *f*_{2} is the corresponding value for which the membership is 0.5, as shown in Figure 2.

### Fuzzy logic

Fuzzy logic uses fuzzy rules (e.g. if–then rules) to model the knowledge of experts. In addition, fuzzy rules can model intuitive associations between uncertain input data and uncertain output data. For example, we can build such rules as the following:

IF the source rocks are excellent AND

IF the area is near the hydrocarbon expulsion centre (HEC) AND

IF the area is located in favourable facies AND

IF the overlying strata are mudstone

THEN the area is a favourable reservoir.

In the above rules, expressions such as ‘excellent source rocks’, ‘near’ and ‘favourable facies’ are vague concepts. Indeed, petroleum geologists typically use these vague expressions for decision-making. Fuzzy logic provides a tool similar to such decision-making by combining different fuzzy sets using special operators.

Given two fuzzy sets, *A* and *B*, with respective memberships of *μ _{A}* and

*μ*, we can combine fuzzy sets

_{B}*A*and

*B*by the following operators:

AND operator: , which means taking the minimum value of

*μ*and_{A}*μ*._{B}OR operator: , which means taking the maximum value of

*μ*and_{A}*μ*._{B}Fuzzy algebraic product operator: . Clearly, the result of the algebraic product is smaller than that of the AND operator. This operator is used if the combination of multiple pieces of evidence is less important than any single piece of evidence.

Fuzzy algebra sum operator: . This operator is used if the combined evidence is more important than any single piece of evidence. The result of the algebraic sum is larger than that of the OR operator.

Fuzzy gamma operator: , where exponent

*γ*is called the gamma parameter of [0,1].

The gamma operation is the trade-off of and , when *γ* = 1, ; when *γ* = 0, . For example, given , , we can obtain a continuous curve of v. *γ* , as shown in Figure 3a. Figure 3b shows the result of five operations given and different values of , which range from 0 to 1. It is evident that the gamma operation curve is limited by the sum and product operations.

## Study area

The Marsel territory is located in the middle of the Chu-Sarysu Basin in Kazakhstan. It spans the Kokpansor and Suzak-Baykodau depressions, covering a total area of approximately 1.85 × 10^{4} km^{2} (Fig. 4). Based on the gravity, magnetic and 2D seismic data conducted by the former Soviet Union from 1950 to 1985, 34 structures were discovered and 73 wells were completed on 16 structures. Three small commercial gas fields – West Oppak, Ortalyk and Pridorozhnaya (Fig. 4) – with total gas reserves of 137.9 × 10^{8} m^{3} were discovered. However, most of the exploration data are unavailable, except for some incomplete well-logging data. In 2008, Condor Resources purchased the Marsel territory and conducted new 2D (2661 km) and 3D (426 km^{2}) seismic surveys (Fig. 5). Condor completed four wells: Kendyrlik 5, Tamgalytar 5, Assa 1 and Bug 1. Industrial gas flows were recorded from the Carboniferous and Devonian target strata in wells Tamgalytar 5 and Assa 1, while gas shows were recorded in wells Kendyrlik 5 and Bug 1. The results of the two-stage exploration effort showed that the target strata were generally tight, with a porosity of <12% and an average porosity of 4 – 7%. In addition, the gas saturation was 40 – 75%, with an average of approximately 60%.

Major strata in the Marsel territory include the Palaeozoic and Mesozoic–Cenozoic. The Mississippian is the main target strata, including the Tournaisian, Visean and Serpukhovian. The Lower Taskuduk and Upper Zhezkazghan in the Pennsylvanian and Permian strata are two sets of regional seals.

All Carboniferous strata are comprised of marine sediments with well-developed source–reservoir–cap systems. In the Middle (Visean, C_{1}v) and Upper (Serpukhovian, C_{1}sr) Mississippian, six sedimentary facies zones are recognized: reef-bank complex; shoal; high-energy intra-platform margin; intra-platform high-energy, open platform; and peritidal and outer ramp. Extensive transgression during the later Visean (C_{1}v_{3}) resulted in thick argillaceous sediments, which form the principal source rock in Marsel. The source rock is distributed throughout the entire area; however, it gradually thins from north to south. The major reservoir strata include the Lower Visean (C_{1}v_{1}), Middle Visean (C_{1}v_{2}) and Serpukhovian (C_{1}sr). The transgressive mudstone and gypsum salt rocks at the top of the two largest transgressive system tracts comprise the main cap rocks.

According to existing exploration results, some new features have been noticed. The gas accumulates in both the upper portions of the structural traps and in the lower or slope areas outside the structural traps. The tight and high-porosity reservoirs coexist with adjacent source rocks. Moreover, most of the gas reservoirs in the Marsel territory are characterized by negative or low pressure, while some are characterized by normal or high pressure. All of these features imply that the reservoirs in the Marsel area may involve different petroleum-forming mechanisms. Therefore, they cannot be explained based on only one accumulation mode. Consequently, a superimposed continuous gas field model is assumed: that is, the gas reservoirs were formed by a variety of vertically superimposed tight reservoirs, which related to different fluid dynamic mechanisms of different periods. Moreover, the reservoir spatial distribution is based on the Carboniferous source rocks and is horizontally continuous (Pang *et al.* 2014).

In this paper, the objective is to integrate the geophysical and geological interpretations, and to map the favourable potential (‘sweet spots’) in the Carboniferous strata based on the proposed gas-accumulation model (conceptual model).

## Fuzzy fusion of datasets

### Data collecting and preprocessing

According to the theory of petroleum geology, favourable hydrocarbon potential is closely related to source rock, reservoir and cap-rock conditions, which are characterized by various parameters. For source rock, its thickness, content of total organic carbon (TOC) and hydrocarbon expulsion intensity (HEI) are three important parameters for assessing its favourability. Another related parameter is the distance to the HEC because most discovered oil-gas fields in the world are located close to the HEC. Hence, for the datasets of hydrocarbon source-rock thicknesses with TOC > 1, HEI and HEC are used to define its favourability. For the reservoir, the sedimentary facies plays a crucial role. Its thickness and porosity are also significant parameters for defining its favourability. Thus, these three parameters are selected.

The favourability assessment of the cap rock is the synthesizing of its spatial distribution, rock properties and thickness. According to the proposed gas-accumulation model, the ‘sweet spots’ in the Carboniferous strata are closely related to the fractures; thus, fracture density is used to describe its spatial distribution. As illustrated in Figure 5, most of the study area is covered by 2D seismic surveys, and a small area is covered by 3D seismic surveys. Therefore, the thickness of the gas-bearing strata is derived from the 2D seismic data. Despite its lower reliability, it remains one of the most important parameters for measuring the hydrocarbon potential and in making decisions by petroleum geologists. Therefore, the inputted data for fuzzy rule building include the nine parameters mentioned above. The data are shown in Table 1. It should be noted that the area covered by the 3D seismic survey is small, while the membership grade of the source-rock and cap-rock evidence in the 3D covered areas is nearly uniform. These data are thus not used as input for fuzzy rule building in the 3D covered area.

These data were obtained by different teams; consequently, the data formats likewise differ (CorelDRAW, Double Fox, raster data and text data (*x*, *y*, *z*)). Accordingly, these data are first transformed into the ArcGIS shapefile format. Then, all the data are gridded with a cell size of 200 × 200 m (2D seismic covered area) and 50 × 50 m (3D seismic covered area) using the Kriging method.

### Membership grade output

Each gridded set of data (i.e. a map) may be treated as a fuzzy set, while each cell in the map may be handled as an element of the set. In our work, two types of input are involved: discrete (qualitative) and continuous (quantitative). For discrete input – such as reservoir sedimentary facies and cap-rock attributions – the membership grade is assigned according to the attribution value, as shown in Tables 2 and 3. For continuous input, non-linear increasing and decreasing MSFs are adopted. If the gas-bearing potential decreases with an increase in the original value (crisp value), then the non-linear decreasing MSF is adopted. Otherwise, the non-linear increasing MSF is used. For example, the greater the distance of a cell from the HEC, the lower is the potential of the cell for gas bearing; hence, the non-linear decreasing MSF is used, as shown in Figure 6a. On the other hand, the positivity of the HEI relates to the gas-bearing potential; thus, the non-linear increasing MSF is used, as shown in Figure 6b.

As presented in Figure 6, the MSF curve shape is dependent on parameters *f*_{1} and *f*_{2}. The smaller *f*_{1} is, the more gradual the curve is, whereas the larger *f*_{1} is, the steeper the curve is. Hence, the selection of *f*_{1} is the trade-off of *f*_{1} = 0 (a line with membership = 0.5) and *f*_{1} = ∞ (a step function from 0 to 1). In this work, we give *f*_{1} = 5, which implies that the curve is neither too gradual nor too steep. Moreover, *f*_{2} corresponds to the mean of the maximum and minimum input. The MSF types for different inputs and their corresponding parameters *f*_{1} and *f*_{2} are listed in Table 4.

### Fuzzy combination steps

As shown in Figure 3b, the operations of AND, OR, algebraic product, algebraic sum and gamma give completely different results. The geological (conceptual) model of hydrocarbon accumulation in the Marsel territory implies that the favourable area (‘sweet spots’) of gas-bearing strata is the overlapping area of favourable source rock, favourable facies, favourable cap rock, the fracture developed area and the favourable area of seismic interpretation. Hence, the AND or algebraic product operations may be used. However, these operations may overlook some interesting areas given the uncertainty of the original data. Otherwise, the OR or algebraic sum can be used to magnify the single piece of evidence, thus increasing the geological risk. Based on these considerations, we use the gamma operation to build fuzzy rules. In addition, the 2D and 3D seismic data are individually implemented.

The gamma operation involves three steps. We outline below the procedure with the provided C_{1}v data in the 2D seismic survey covered area.

Assess the single piece of evidence. In practical terms, the assessment of a single piece of evidence (e.g. source rock, reservoir and so on) may involve different variables. In this case, the gamma operation is first used to combine these variables to obtain the membership of the single piece of evidence. We may take the source-rock evidence as an example.

The assessment of source-rock evidence may involve the thickness of the source rocks, TOC, HEI and the distance from the HEC. The map of the distance from the HEC can be built using the GIS buffer function, as shown in Figure 7a. The HEI map of C

_{1}v is shown in Figure 7b. A comparison of the two maps shows their close resemblance; hence, the HEI map plus the thickness are used to assess the source rock favourite. The thickness membership of the source rock of C_{1}v is the combined thickness of C_{1}v_{1–2}, C_{1}v_{3}. A similar operation is employed to obtain the membership of the reservoir evidence.Combine all pieces of evidence – that is, the source rock, reservoir, cap rock, fracture distribution and thickness of the gas-bearing strata interpreted from the 2D seismic data – using the gamma operation. Figure 8 shows the full work flow of combining evidence for the hydrocarbon potential mapping of C

_{1}v. The same operation is employed for C_{1}sr.Combine the potential targets of C

_{1}v and C_{1}sr with AND and OR operators to predict the minimum and maximum favourable areas of the Carboniferous system in the Marsel territory.

A similar procedure may be employed to combine multiple pieces of evidence in the 3D covered area. The visual overlay of 2D and 3D covered areas gives the final result.

## Results and validation

The fused result presented in Figure 9 shows the hydrocarbon potential of the Visean stage (C_{1}v) in the 2D covered area with *γ* = 0.8, 0.85 and 0.9, respectively. The distribution area of potential naturally increases with the increase of *γ*; moreover, the favourable targets occur mainly in the centre and NW area of the territory, while a slight distribution occurs in the east and NE corner of the territory.

Figure 10 shows the fused result in the Serpukhovian stage (C_{1}sr) with *γ* = 0.8, 0.85 and 0.9, respectively. The favourable target area distribution in C_{1}sr closely resembles that in C_{1}v, while the distribution area is smaller than that in C_{1}v.

An effective choice of *γ* depends on the specific issue. The emphasis of the decision-maker on increasing the effects of larger values or decreasing effects of smaller ones may provide an empirical criterion for the selection of *γ*. Generally speaking, the former seems to more clearly reflect the subjective decision-making of petroleum exploration; hence, *γ* may be assigned a larger value. Figure 11 shows various curves of v. with different *γ* values given . As shown in Figure 11, varies from 0 to 1. The large *γ* value reinforces the increasing effects. In this work, we select *γ* = 0.9 as a trade-off of the above two effects. Subsequently, the fused results of C_{1}v and C_{1}sr are combined by AND and OR operators to obtain the maximum and minimum horizontal distributions of potential. Finally, the membership maps are defuzzified into a crisp output, as depicted in Table 5. The final results of C_{1}v AND C_{1}sr, and C_{1}v OR C_{1}sr, are shown in Figures 12 and 13, respectively.

As shown in Figure 12, the locations in which both C_{1}v and C_{1}sr strata are favourable targets occur in the Bulak and Ortalyk regions. The locations in which only C_{1}v or C_{1}sr strata are favourable targets occupy a wider area in Ortalyk, West Bulak, Tamgalytar and South Pridorozhnia, while a small distribution occurs in the NE corner of the territory (Fig. 13).

To date, eight wells in different regions – ASSA-2, TGTR-8 (Ortalyk), KNDK-6 (Kendrylik), TMSK-1 (Tamgalynskaya), TGTR-6 (Tamgalytar), PRDS-18 (South Pridorozhnia), SK-1017 (South Pridorozhnia) and SK-1012 (Tamgalytar) – have been completed. Well-logging and gas testing have been implemented for some of these wells. Results of the well-logging interpretation are outlined in Table 6. It is evident that, in wells ASSA-2 and TGTR-8, gas-bearing strata are interpreted both in C_{1}sr and C_{1}v, whereas in wells PRDS-18 and KNDK-6, gas-bearing strata are interpreted only in C_{1}sr. For wells TMSK-1 and TGTR-6, C_{1}sr and C_{1}v are poor in terms of gas bearing. By comparing the result of the well-logging interpretation with Figures 12 and 13, it is apparent that the distribution of favourable targets shown in the two figures is reasonable.

## Conclusion and discussion

GIS-based fuzzy logic was employed in this study to fuse geological and geophysical interpretations and numerical simulation data based on a superimposed continuous gas-accumulation model. The gamma operator (*γ*) was used to combine multiple pieces of evidence. Finally, the hydrocarbon potential in the Lower Carboniferous (i.e. C_{1}v and C_{1}sr) of the Marsel territory in Kazakhstan was mapped. The results show that the favourable hydrocarbon potential in the Lower Carboniferous is horizontally distributed in Ortalyk, West Bulak, Tamgalytar, South-Pridorozhnia and Kendyrlik. The well-logging interpretation *in situ* was used to validate the prediction.

The integration of GIS and fuzzy logic provides convenient fusion modelling of geological interpretations. However, some issues involved in the process of integration require further investigation. The issues involve the selection of the MSF (linear or non-linear) and parameters (*f*_{1}, *f*_{2}, *γ* and threshold of defuzzification). The non-linear increasing and decreasing MSFs used in this paper may be suitable to build the association between the input and output data, while the choices of *f*_{1} , *f*_{2} , *γ* and the threshold of defuzzification roughly relate to empirical intuition. In principle, the MSF variation (linear or non-linear) and parameters in our work will not completely change the result or potential trend, but the optimization of the parameters may produce a more realistic result.

## Acknowledgements

We extend special thanks to Zhu Xiaoming, Ling Changsong, Yu Fusheng, Huang Handong, Cheng Jianfa and our other colleagues who provided the data used in this paper. The authors would also like to thank the editors from Editage for their language-editing services.

## Funding

This paper was supported by the National Natural Science Foundation of China, grant No. 41472113.

- © 2018 The Author(s)