1 Introduction

Carbonates are typically rocks with low primary porosity and permeability (e.g., Agosta et al. 2010). Therefore, secondary porosity and permeability are generated by mineral dissolution (karstification), which is partly controlled by fractures and plays a major role in hydrocarbon and ground water storage (Amthor and Friedman 1991; Lonergan et al. 2007; Questiaux et al. 2010). Dissolution along fractures creates secondary porosity in carbonate rocks, consisting of mega-porosity (centimeter to meter scale), represented by caves, vugs and cavities, and matrix porosity (less than 1 mm) (Lucia 2007). However, an important degree of uncertainty exists in understanding the geometry of fractures and the related secondary porosity in carbonates units. The complex origin and geometry of secondary porosity generated by mineral dissolution makes the modeling of fractured and karstified reservoirs a difficult task (Billi 2005; Agosta et al. 2010). Despite its importance, investigation of porosity in oil reservoirs has been limited to core samples, making it difficult to investigate how preexisting fracture networks influence dissolution and the geometry of the secondary porosity system. In addition, 3D seismic data do not have sufficient resolution to detect closely spaced dissolution along fractures spaced a few meters apart. The GPR method has been used to bridge the gap between natural examples of reservoir stratigraphic geometry at interwell scale (a few to hundreds of meters) and indirectly petrophysical properties (e.g., Gawthorpe et al. 1993; Loucks et al. 2004; Harbi and McMechan, 2011; Reis et al. 2014; Fernandes et al. 2015). Three-dimensional, high-resolution GPR images in outcrop analogs provide detailed information about depositional, structural, and karstic features, whereas GPR attributes contribute for estimating porosity and permeability by means of geostatistical relationships (e.g., Corbeanu et al. 2002; Mount et al. 2014). Recent studies (e.g., Tronicke and Paasche 2017) have also correlated GPR signal parameters (energy, velocity, attenuation) to physical properties (dielectric permittivity, electrical conductivity) allowing detailed prediction of 3D distribution of petrophysical properties, including porosity, permeability, water saturation, and clay content, in outcrop analogs. However, the models derived from investigation of many natural examples are still a matter of debate.

This study investigates the geometry and attributes of porosity associated with karst driven by fractures in the Precambrian Salitre Formation, São Francisco Craton, in Brazil (Fig. 1), which we used as a carbonate reservoir analog. The investigated area hosts the longest cave system in South America and one of the oldest caves in the world (Auler and Smart 2003; Klimchouk et al. 2016; Auler et al. 2017). The karstification is associated with a pervasive dissolution along fractures and sedimentary bedding in the region. In the present study, we focused on the following points using GPR data: (1) the 3D geometry and volumes of fractured and altered zones, and (2) the correlation among GPR attributes, physical (dielectric permittivity and density) and petrophysical (porosity) data to estimate secondary karst porosity in the low-porosity carbonate units in the Precambrian Salitre Formation. Our results indicate that mineral dissolution along the fractures modified physical and petrophysical properties of the carbonate rocks, creating amplitude shadow zones in the GPR data. Mapping this GPR pattern we are able to characterize the 3D spatial distribution of the altered zones and, using GPR attributes, to estimate porosity in the studied carbonate rocks.

Fig. 1
figure 1

Geological maps of the São Francisco Craton (a) and the Irecê Basin (b) in East Brazil, with location of the studied quarry near the Toca da Boa Vista and Toca da Barriguda (TBV-TBR) cave system

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2 Geological Setting

The studied site is located in the São Francisco Craton, a large mass of Paleoproterozoic continental lithosphere surrounded by Neoproterozoic Brasiliano orogenic belts (e.g., Brito Neves and Cordani 1991; Almeida et al. 2000). An extensive carbonate platform overlies the cratonic and surrounding areas during a Paleoproterozoic transgression of an epicontinental sea (Misi and Kyle 1994). The Irecê Basin represents a relatively small and isolated tectonic unit of the ancient carbonate platform, situated in the northern part of the São Francisco Craton (Fig. 1).

An overspread karst system developed in the marine limestones, which are up to 1000-m thick , and dolomites of the Salitre Formation. Carbonate units in this study are composed of grainstones and mudstones intercalated with fine siliciclastic and marl layers. The Salitre Formation rocks were fractured and gently folded by Neoproterozoic tectonic and hydrothermal events, which controlled the mineral dissolution. Karstification mainly occurred along two major sets of fractures, which strike ~ N–S/NNE–SSW and E–W (Ennes-Silva et al. 2016).

The dolomitized mudstones and laminites of the Salitre lithostratigraphic unit are exposed in a small quarry near the giant cave system called Toca da Boa Vista and Toca da Barriguda (TBV-TBR) (Figs. 1, 2a). The TBV-TBR caves comprise over 145 km of passages located in the vicinity of a major NE–SW-oriented thrust fault (Auler et al. 2017). Two sets of fracture increased the fracture permeability and facilitated the rising of ascending fluids (Ennes-Silva et al. 2016). Fluid flow enlarged fractures in a selective manner and created large conduits of dissolution, which range in size from millimeter-scale dissolution features to 10-m-wide cave passages (Fig. 2b). More recent weathering affected the carbonate rocks in the quarry, producing incipient alteration halos of beige color mainly around fractures and bedding planes (Klimchouk et al. 2016). Meteoric water caused dissolution and leaching of organic matter and its substitution by iron hydroxide (limonite).

Fig. 2
figure 2

Karstic features controlled by NNE–SSW and E–W trending fracture system in the studied quarry with location of the GPR survey: a unmanned aerial vehicle image with location of GPR lines; b sub-vertical and orthogonal passage system and karstic cavities along sub-horizontal bedding

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3 GPR Survey

3.1 Data Acquisition and Processing

The GPR data were acquired using SIR-3000 equipment (GSSI Inc.) with 400-MHz antennas and time windows of 150 and 200 ns, which allowed us to map karst features and host rocks as deep as 6.0 m, with an estimated vertical resolution of 0.02 m between successive reflections. The GPR traces were equally spaced at 0.02 m, controlled by an odometer. The survey contains a total of 380 m of GPR 2D lines and 765 m of lines distributed in two regular grids (3D), acquired perpendicular and parallel to the NNE–SSW and E–W trending fracture system (Fig. 2a). The spacings between adjacent GPR 3D lines were of 0.5 m and 0.15 m.

Processing of the GPR data included trace editing, time zero correction, background removal, dewow filtering, energy decay gain, bandpass filtering, and diffraction stack time migration. According to Cassidy (2009), gain functions based on spreading and exponential correction, such as energy decay gain, preserve the relative amplitude information both in time and space, which is very important in the present study. An average velocity of 0.075 m/ns was obtained by matching hyperbolic functions to diffraction hyperbola from 400-MHz GPR profiles (Fig. 3). This velocity was used for diffraction stack migration. No leveling correction was applied since the terrain is fairly flat. In addition, a pseudo-relief attribute that combines the Hilbert trace attribute with the energy attribute (Reis et al. 2014) was applied to enhance lateral variation in GPR facies. The result of the GPR data processing is exemplified in the profile L053 (Fig. 4), in which amplitude shadow zones occur either mainly verticalized, with a few meters wide, or horizontalized and broader (light blue areas in Fig. 4). The reflections are plane-parallel, gently undulating and laterally truncated, exhibiting the thin carbonate bedding, affected by sub-vertical fractures and gentle folds. Fernandes et al. (2015) identified amplitude shadow zones in GPR profiles and associated them with karst structures mapped in a large carbonate outcrop of the Creataceous limestone formation in Potiguar basin (NE Brazil). According to them, empty voids or filled with clay soil are the probable source of the GPR amplitude loss.

Fig. 3
figure 3

GPR profile L053 (location in Fig. 2a) showing hyperbolic diffractions highlighted with associated estimated EM velocities in m/ns

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Fig. 4
figure 4

GPR signature of the fractured and altered carbonate unit (low amplitude zones) in the studied quarry. The location of the Profile L053 is in Fig. 2a. Rectangles highlight areas where karstic features, shown in Fig. 5, are identified in the GPR data

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The amplitude shadow zones have direct correlation with hypogenic karstic structures present in the quarry and dissolution halos around fractures and carbonate bedding caused by weathering (Figs. 4, 5). In hypogenic karsts, the fluids that cause the alteration in the carbonate rocks ascend vertically by fractures until they find low-permeability barriers or baffles, inducing a horizontal flow (Klimchouk et al. 2016). In this way, the karstic zones are preferentially vertical or horizontal. In turn, the downward flow of meteoric water also causes karstification, taking advantage of the same system of fractures and bedding. In the studied quarry, the weathering yielded dissolution halos shown in Fig. 5b, e. Dissolution changes the mineral content (e.g., dolomitization and limonitization), porosity and permeability of the rock, without, however, substantially modifying the original bedding. The electrical properties, including dielectric permittivity, are also altered, creating low-amplitude reflections due to decrease in reflection coefficients and EM impedance contrasts between bed interfaces. We are taking advantage of these distinct GPR pattern to map the karstic zones in three dimensions and using GPR complex trace attributes to estimate their average porosity based on measurements in plug samples.

Fig. 5
figure 5

Karstic features exposed in the studied quarry and identified in the GPR profile (Fig. 4): sub-vertical fracture-controlled cavities (a, c and f); non-altered (blue gray) and altered (beige) carbonate zones (b and e) along fractures and bedding planes; and sub-horizontal cavities along bedding planes (c)

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3.2 GPR Atributtes

Complex trace attributes have been used to estimate the relationships between seismic (e.g., Taner et al. 1979; Robertson and Nogami 1984) or GPR (Corbeanu et al. 2002; Harbi and McMechan, 2011) data and physical properties of the subsurface. Instantaneous amplitude and instantaneous frequency are robust measures of the energy and frequency in the trace at a given time and contain information of petrophysical property as porosity. Thus, we computed these two GPR attributes to identify the dissolved zones (alteration halos of beige color—Figs. 2 and 5) and estimate its porosity indirectly related to changes in the dielectric permittivity of the altered carbonate rocks. The 3D GPR data and its attributes (Fig. 6) provide a detailed view of the karstic zones in the studied quarry. The low amplitude coherent responses in the GPR and instantaneous amplitude correlate quite well with vertical and horizontal altered zones observed in the carbonate rocks exposed in the quarry (Figs. 2, 5, 6a, b). Strong contrast of EM impedance between rock and air generate high-amplitude reflections. However, these karst structures do not occur in the altered zones due to the incipient level karstification. Although the instantaneous frequency shows no obvious GPR pattern of the dissolved areas (Fig. 6c), the frequency content is mainly controlled by contrasts in petrophysical properties and sedimentary features (Corbeanu et al. 2002). In particular we expect no geometric change in the original stratigraphy, but the mineral dissolution should occur preferentially in areas with higher concentrations of fractures, karstic features, stylolites and primary porosity, interfering in the frequency content.

Fig. 6
figure 6

Three-dimensional view of the GPR data set (a) and instantaneous amplitude (b) and frequency (c) attributes, showing the amplitude shadow zones associated to dissolved areas

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Thus, we combined instantaneous GPR amplitude and frequency attributes to improve the estimation of porosity in three dimensions. We noticed that the shadow zones have normalized instantaneous amplitudes smaller than 0.25, but no remarkable response in the instantaneous frequency (Fig. 6). The crossplot between normalized instantaneous amplitude and instantaneous frequency attributes extracted from GPR traces show that low-amplitude (< 0.25) shadow zones generally cluster in narrow ranges of instantaneous GPR amplitude and have a large instantaneous GPR frequency dispersion (rectangle in Fig. 7a). On the other hand, non-altered carbonate rocks show a well-defined distribution in high-amplitude and low-frequency intervals, whose dispersion decreases with the increasing amplitude (rectangle in Fig. 7b). Furthermore, we expect to see low frequency component in the shadow zones due to low amplitude reflections, as a result of attenuation. However, the crossplot shows the opposite. We suggest that the high frequency content in the shadow zones is mainly caused by lateral discontinuities in the reflection interfaces, such as fractures and dissolution structures, which are more common in the alteration halos. In turn, higher amplitudes are concentrate in the low frequency range (< 0.25), suggesting that the dissolution causes more loss of EM impedance than modifications in reflection geometry.

Fig. 7
figure 7

Crossplot of the normalized instantaneous amplitude (NIA) and frequency (NIF) attributes, showing the two clusters of altered (a) and non-altered (b) carbonate populations

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The frequency/amplitude distribution within the clusters “a” and “b” in the crossplot of Fig. 7 allows us to define a stochastic criterion for identifying karstic zones in the 3D volumes. In a conservative estimation, regions with normalized instantaneous amplitude greater than 0.5 can be correlated to non-altered carbonate rocks. A more comprehensive choice can include a larger range of amplitudes (> 0.35) assigned to be non-altered zones. We discuss these hypotheses next chapter, associating GPR attributes with measured relative dielectric permittivities and porosities.

4 Rock Properties and Porosity Prediction

4.1 Plug Samples

Physical (relative dielectric permittivity and density) and petrophysical (porosity and permeability) measurements were performed on 28 plugs extracted from fresh carbonate rocks and alteration halos in the studied quarry face at approximately the same stratigraphic position. The bulk density was calculated as the dry weight of the sample divided by its volume. A displacement method was used to measure effective porosity, submerging the dried samples in a water-filled tank and applying constant vacuum to eliminate bubbles. Effective porosity is proportional to all the water displaced by the sample and measured in a graduated cylinder. Permeability measurements were obtained using an electronic probe permeameter, whose values are in milli-Darcy (mD). However, permeability data show no consistent values and were not considered in the present study. Finally, the samples were cut into ~ 1.5 mm thickness slabs for relative dielectric permittivity measurements using a high-precision impedance analyzer. Measurements of real and imaginary parts of the sample permittivity were made for the 400 MHz frequency to obtain dielectric data for the same GPR antenna frequency used in the field work.

We selected four samples of clearly non-altered carbonate rock and eight samples from the beige altered halos (Table 1) to analyze how weathering dissolution affected the rock properties and to provide parameters for GPR correlation and porosity estimation. Although changes in mineral and textural contents are quite incipient in the plug samples, subtle variations occur in physical and petrophysical properties due to dissolution. In the altered zones, average density and average relative permittivity decrease from 2688 to 2685 kg/m3 and from 7.36 to 6.64, respectively (Table 1). On the contrary, the average porosity increases from 0.95 to 1.01% in the altered rocks. An inverse correlation between density and porosity is consistent since the presence of pores caused by dissolution reduces rock density. In fact, the 12 analyzed plug samples provide a linear correlation coefficient of − 0.478. Considering only the non-altered rocks, the linear correlation coefficient is higher (R = − 0.722), indicating that the weathering affects rock density and porosity differently somehow.

Table 1 Physical and petrophysical properties of carbonate rocks in the Sal quarry
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The porosity and relative dielectric permittivity measured in the plug samples reveal more intrinsic mutual interactions (Table 1 and Fig. 8). The linear correlation coefficient is quite high (R = 0.646), but it reaches 0.999 when considered only non-altered samples. This indicates that the dielectric permittivity of the studied carbonate rocks depends largely on porosity. Other factors (i.e., mineral content, grain size, and water saturation) that also account for variation in bulk dielectric permittivity play a secondary role in our study case due to the incipient dissolution affecting the quarry rocks. Despite the slight rock differences, the crossplot between relative dielectric permittivity and porosity (Fig. 8) shows two different correlation patterns related to non-altered and altered rocks. The altered samples generated a large dispersion of the relative dielectric permittivity and show a relatively higher porosity. The non-altered samples, in turn, show that both properties increase together more intensively. This result gives us confidence to predict the porosity distribution throughout the whole GPR data volumes based on the fact that GPR signal drastically depends on ground dielectric permittivity.

Fig. 8
figure 8

Correlation between porosity (ϕ in  %) and relative dielectric permittivity (εr) of the non-altered (green) and altered (purple) carbonate rock samples

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4.2 Porosity Estimation: CRIM

A classical method to estimate porosity from bulk relative dielectric permittivity (εrb) is the complex refractive index model (CRIM) (e.g., Endres and Knight 1992; Cassidy 2007; Mount et al. 2014). CRIM is a practical volumetric, petrophysical model that incorporates the complex effective permittivities of water (εrw = 79.5), air (εra = 1) and rock (εrs), porosity (ϕ) and water saturation (Sw) (Birchak et al. 1974). A geometrical factor (α) takes into account the electrical field with respect to the internal rock geometry. Time domain reflectometry and GPR studies (e.g., Birchak et al. 1974; Mount et al. 2014) have assumed a value of 0.5 to most geologic materials in the GPR frequency range (100–1000 MHz). Moreover, considering low-loss conditions (i.e., low conductivity materials) the bulk relative dielectric permittivity (εrb) can be obtained by dividing the EM wave velocity in a vacuum (c = 0.3 m/ns) by the EM velocity (v) (Daniels 1996). EM velocities are usually calculated from diffraction hyperbolas in common offset GPR profiles or velocity analysis of common midpoint surveys. In this study, we found several hyperbolic diffractions within the GPR profiles, normally associated with fractures, vugs and other karstic features (Fig. 3). An average diffraction velocity of 0.075 m/ns was estimated by fitting hyperbolic functions to the diffraction geometry in the GPR profiles, resulting in a bulk relative dielectric permittivity of 16 for the carbonate rocks in the studied quarry.

We applied the CRIM method to estimate porosity derived from EM velocities and compare with porosity measured in plug samples. We assumed a completely unsatured carbonate rock (Sw = 0) above the water table (deeper than our GPR investigation depth up to 6.7 m) and used average effective permittivities of non-altered and altered rock (εrs) of 7.36–6.81, respectively (Table 1). The CRIM porosity estimates are 0.74% for non-altered rock and 0.80% for altered rock, which are consistent with measured average porosities of 0.95% and 1.08%, respectively. The estimated porosity using the CRIM model is slightly overestimated by plug porosity measurements, but maintains the characteristic of increased porosity in the altered zones. These differences are expected due to the distinct nature of each particular method, scale of measurements and the heterogeneities within the carbonate rocks, and the presence of fractures and karstic features. However, the consistency of the results enables the use of the GPR data to estimate the porosities of the non-altered and altered zones in the studied quarry.

4.3 Porosity Estimation: GPR Attributes

A disadvantage of the CRIM method is the need for a fairly accurate velocity model to generate an acceptable estimated porosity volume. As in this study the velocities were only obtained in dispersed diffraction in the GPR survey, we chose to estimate porosities based on GPR attributes, as described in the previous Sect. 3.2. The subset image of the Profile L053 (Fig. 5) and its attributes provide a detailed view of the GPR response of the beige altered halos (Fig. 9). The pronounced lateral loss in reflection amplitudes delineates the sub-vertical boundary of the karstic zone. The GPR amplitude contrast is even more evident in the normalized instantaneous amplitude image (Fig. 9c), in which amplitudes < 0.5 are related to karstic zones. The instantaneous frequency image shows no clear pattern to discriminate both carbonate zones (Fig. 9d), although the frequency content of altered rocks varies in a large range as shown in the attribute crossplot (Fig. 7). Drawing two volumes of amplitude > 0.35 and > 0.5 leads to a representative model of the 3D mapping of relatively lower porosity (ϕ = 0.95%) non-altered (blue areas in Fig. 10) and relatively higher porosity (ϕ = 1.01%) altered zones, and indirectly of estimate porosity variability. Although the estimated porosity cubes mimic the same mazelike pattern of sub-vertical dissolved zones, these porosity models are clearly a quite simplified approximation because this petrophysical property was measured in a few locations on the surface. Certainly, new porosity measurements in boreholes may improve the prediction of porosity from GPR data in the studied quarry.

Fig. 9
figure 9

Altered halos along bedding planes associated with fractures in the carbonate rocks, (a) their GPR responses, (b) normalized instantaneous amplitude, (c) and frequency GPR patterns (d)

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Fig. 10
figure 10

Predicted porosity cubes derived from GPR data. Blue areas represent lower-porosity, non-altered zones, where normalized instantaneous amplitude (NIA) is greater than 0.5 (a) or 0.35 (b). The plan view of the porosity cube in shown in c. A NIA profile (a and b) and a NIA time slice (c) show the higher-porosity, altered halos indicated in orange (see the color table in Fig. 9c)

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5 Geometric Characterization of Altered Zones and Karstic Features

The studied quarry is located near the TBV-TBR cave system (Fig. 1). However, no cave is present in this area, only a system of passages spaced 1–3 m in width and 2–4 m in height along NNE–SSW and E–W oriented fractures (Fig. 2). On the other hand, more recent chemical weathering caused mineral dissolution and limonitization along the same conjugate fracture system and carbonate bedding (Fig. 5), which played as preferential pathways for the former karstification. Our GPR survey investigated an area affected by more incipient level of dissolution, comprising centimeter-scale karstic features and altered beige halos (Figs. 4, 5, 6, 9).

The GPR profiles show sequences of sub-horizontal, and sub-parallel reflections, which are slightly undulated and sometimes dipping to the SE (Figs. 4, 11). Undulated and dipping reflections were associated with gentle folding observed in the TBV-TBR cave system by Klimchouk et al. (2016). These authors related folds in the caves to the Brasiliano orogenic cycle that affected the Salitre carbonate units in the Neoproterozoic. Moreover, GPR shadow zones and centimeter-scale karstic features (vugs and small cavities) were able to be mapped in the GPR profiles (Figs. 4, 5).

Sub-vertical amplitude shadow zones intercalated by sequences of high-amplitude reflections is the GPR pattern that unravel the spatial distribution of the altered halos in depth (Figs. 4, 11). The amplitude shadow zones extend for more than 6.7 m depth, which is the maximum depth achieved by the GPR survey in the studied area. The distance between shadow zones and their widths vary from a few meters up to 25 m in the western part of the quarry (Fig. 11). In the NW portion of the Profile 059, the reflections are greatly attenuated, disappearing in depth. The strong amplitude loss of the GPR signal suggests that the intense weathering along sub-vertical fractures has caused depletion of the primary carbonate bedding by mineral dissolution.

Fig. 11
figure 11

GPR Profile L059 showing sub-vertical amplitude shadow zones, related with altered halos and karstic features developed around fractures (light blue areas), and slightly undulated sequences of reflections (red lines)

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The amplitude shadow zones show a mazelike distribution (Figs. 6, 10) parallel to the NNE–SSW and E–W trending conjugate fractures observed in the quarry (Fig. 2). The plan view of the estimated porosity cube (Fig. 10c) depicts a set of sub-vertical zones of higher-porosity altered beige halos surrounded by non-altered carbonate rocks (blue areas in Fig. 10c). The NNE-SSW trending zone crosses the ~ E–W oriented zone, forming a larger area in the intersection. A third narrow zone occurs at the NE edge of the volume with a NE–SW direction. It is noteworthy that the same spatial distribution of these karstic zones is present in the set of passages in the quarry (Fig. 3), suggesting that the conjugate fracture network controlled both the regional karstification events, which affected thick carbonate sequence of the Salitre Formation and generated the cave system, and the more recent weathering, which provoked the mineral dissolution close to the surface.

6 Discussion

6.1 3D Porosity Estimation

Porosity is a key parameter for the estimation of fluid volume in reservoir characterization (Forster et al. 2004; Harbi and McMechan, 2011). In outcrop scale, 3D porosity distribution can be predicted from GPR data calibrated by porosity measured from rock samples. In the studied quarry, we used two approaches to establish the relationships between porosity and relative dielectric permittivity (CRIM petrophysical modeling) and GPR data and porosity (GPR attributes). The CRIM derived porosities for the non-altered (0.74%) and weathered (0.8%) carbonate zones are slightly lower than the overall average porosity measured in plug samples (0.95% and 1.01%, respectively). However, the porosity estimates from each method correspond very well and the overall different between both carbonate zones was preserved. In addition, GPR instantaneous amplitude attribute distinguished satisfactorily both carbonate zones and provided predict porosity volumes (Fig. 10). These positive results demonstrate potential implications for assessment of 3D distribution of petrophysical properties at the interwell scale to populate inputs for reservoir simulation in a Salitre carbonate reservoir analog using high-resolution GPR data. Certainly, 3D porosity estimation requires systematic porosity measurements on surface and boreholes, more accurate velocity models to calculate dielectric permittivity, and more effective calibration the relations between the petrophysical properties and GPR attributes using geostatistical analysis. Further studies should introduce these improvements to allow for better constraint of the CRIM petrophysical model and refining 3D estimates of porosity for the carbonate Salitre Formation.

In addition to the dissolution caused by weathering, centimeter- to meter-scale cavities and vugs are present in the study area (Fig. 5). These karstic features were generated by the karstification and speleogenesis processes that formed the cave systems. They are important heterogeneities in both porosity and permeability in the carbonate formation, but they were not considered in the present GPR survey. Their geometric and petrophysical characterization should be addressed with other imaging approaches. Therefore, they can be useful to guide seismic signature interpretation and reservoir fluid flow simulation for karstified carbonate reservoirs.

6.2 3D Geometric Characterization

The relationships between GPR shadow zones and dissolved carbonate rocks were determined based on plug sample analysis. In the studied quarry, the sample measurements reveal that the dissolution along fractures causes changes in physical and petrophysical properties. Dielectric permittivity decreases, while porosity increases in the altered zones. We also observed a slight decrease in the density of the altered rock samples. As a result, an overall reduction of EM impedance contrasts take place between carbonate bedding and structures, with a notable attenuation of GPR amplitudes (Figs. 4, 6, 9, 11). The reflections are attenuated, but their lateral continuity is preserved (Fig. 9), indicating that the carbonate dissolution affects the mineral content more than the thin bedding of the host rock. The water moisture could be another factor causing attenuation and affecting the reflection amplitude. However, the studied area is situated in a semi-arid region, with long dry seasons and high temperatures. Thus, we consider negligible loss of GPR amplitude due to the water moisture. The sub-vertical amplitude shadow zones form sets of orthogonal bands in depth (Fig. 10), similar to the fracture network that controlled both the karstification of the TBV-TBR cave system and the more recent weathering. Different events of dissolution were nucleated by the NNE–SSW- and E–W-striking conjugate fractures, which acted as pathway for fluid circulation. Laterally extensive amplitude shadow zones (Figs. 4, 11) indicate horizontal redirection of the flow when they reached a hydraulic barrier composed by a less permeable stratigraphic unit.

In general, large karst systems are associated with regional deformation, as in the case of the Ellenburger carbonate reservoir in west Texas (Gale and Gomez 2007; Harbi and McMechan 2011). Steeply dipping conjugate micro- and macrofractures controlled fluid migration and paleocave system in the Ellenburger dolomites, associated with the Pennsylvanian Ouachita orogeny. Similarly, the TBV-TBR cave system is controlled by fractures and folds related to the Neoproterozoic Brasiliano orogeny, which deformed the São Francisco Craton and surrounding fold belts (Klimchouk et al. 2016; Auler et al. 2017). Detailed structural analysis pointed out a close relationship between patterns of karst pathways around conjugate joints and anticlines and regional deformation events in a compressive collisional setting (Ennes-Silva et al. 2016).

Fractured crystalline basement reservoirs exhibit similar characteristics with carbonate reservoirs. Both crystalline and carbonate rocks have typically low primary porosity and permeability and the storage of hydrocarbon and ground water is intrinsically related to fracture properties resulting from combinations of tectonic, hydrothermal and epithermal processes (e.g., Questiaux et al. 2010; Trice 2014). The typical dissolution of calcium carbonate enhances the potential for fluid storage in carbonate reservoirs, whereas this process is much less common in basement reservoirs. Despite this mineralogical difference between carbonate and basement reservoirs, we adapted the conceptual model of the fracture network of the Lancaster basement reservoir (North Sea) and its outcrop analog (Isle of Lewis) developed by Trice (2014) to analyse the potential for enhancement of secondary porosity and fracture connectivity in the studied quarry (Fig. 12).

Fig. 12
figure 12

Schematic representation of the carbonate quarry showing four zones with enhanced porosity by fracturing and dissolution (description in the text)

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Considering the studied quarry, a carbonate reservoir analog, the background consists of very low porosity (< 1.0%) carbonate rocks that support no reasonable background flow. However, we identified four different zones, where primary porosity is enhanced by fracturing and dissolution: (a) the zones with highest porosity in the studied quarry are associated with mazelike 1–4 m height and 1–3 m width passages developed along the conjugate NNE–SSW (0°–20°) and ~ E–W (70°–100°) trending fracture network (Fig. 12). According to (Klimchouk et al. 2016) and Auler et al. (2017), large-scale ascending fluid migration across the São Francisco Craton caused deep-seated karstification in the Neoproterozoic carbonate mega-sequences, creating the large system of caves and passages; (b) the NE-SW (40°–50°) oriented fracture zones controlled a secondary set of passages, providing more high porosity zones and additional connectivity of the fracture network (Fig. 12); (c) the centimeter- to meter-scale karstic features are other important high porosity zones in the carbonate analog reservoir, providing space for fluid flow and accumulation. The intermediate connectivity of these structures is quite complex and anisotropic, depending greatly on their size and intensity of occurrence; and (d) the weathered zones provide local enhanced porosity and connectivity due to mineral dissolution along the sub-vertical fractures and horizontal carbonate bedding. In the studied quarry, at least 6.7 m deep and 25 m wide weathered zones can play an important role in fluid flow and accumulation in a carbonate reservoir.

7 Conclusions

In this study, we used GPR attributes to characterize the distribution of estimated porosity of the uppermost speleostratigraphic level of the large TBV-TBR cave system in the Precambrian Salitre Formation in a small quarry in east Brazil. Sub-vertical or horizontal, low-amplitude GPR zones are associated with beige weathered carbonate rocks, nucleated by steeply inclined fractures. Amplitude and frequency instantaneous attributes enhance the GPR patterns of the non-altered and altered carbonate zones and allow mapping their 3D mazelike geometry. The NNE–SSW and E–W directions of the altered carbonate zones are similar to the regional fracturing trends that control the cave systems and the outcropping passages in the studied quarry.

Measurements in plug samples indicate that the meteoric water flowed through fractures and karstic features, decreasing the relative dielectric permittivity and slightly increasing the porosity in a quite linear fashion. This change in the electrical properties affected the GPR signal, enabling us to estimate the 3D average porosity distribution of the karstic zones. Furthermore, predicted porosity was also calculated from EM velocities derived relative dielectric permittivity using the complex refractive index model (CRIM). CRIM porosities for non-altered and altered rocks are consistent with average porosities from plug samples, showing that the GPR volumes represent a very satisfactory porosity distribution of the slightly karstified Salitre carbonates in the studied quarry. The GPR volumes provide quantitative estimates of the spatial distribution of karstified carbonate reservoir porosity at the outcrop scale that can be used in carbonate reservoir characterization. However, future research should expand to larger scales the plug samples measurements, including boreholes, EM velocity analysis and GPR attributes in order to better calibrate the relationships between electrical and petrophysical properties.