ThrustFaults-Displacement-Distance-Analysis

This study offers critical automatic workflows to examine the displacement–distance profiles and insert the mechanical stratigraphy.

Abstract

Displacement distribution and profile patterns are controlled by mechanical stratigraphy on a regional scale. Here, we present a detailed analysis of isolated thrust faults in multilayer stratigraphy and their displacement-distance profiles in coal mines, the lower Rhine basin, Ruhr sub-basin, Germany, where claystone, sandstone with siltstones, coarse sandstone and rhyolite tuff act as mechanically controlling elements of stratigraphy to an array of thrust faults. Faults generally show systematic variations in displacement approaching their tips. These variations can be displayed on displacement–distance diagrams - where offsets between multiple pairs of footwall and hanging-wall cut-offs are cross-plotted against a distance measured along the fault surface from a reference point. Coloured displacement-distance profiles according to the stratigraphic lithology and displacement length can help understand the mechanical controls on displacement distribution along thrust faults. Conducting such studies across interpreted subsurface cross-sections can provide more robust constraints in adequately determining displacement-distance profiles, their patterns and displacement-length relationships. Idealised displacement–distance profiles for single isolated faults show diminishing offsets to fault tip-line. However, our results are more complex, with varying profiles that deviate from the idealised pattern. A constant displacement–distance pattern is common in sandstone layers, while variable displacement–distance patterns are more common in the finer-grained units. Thinly interbedded successions display the most complex displacement–distance relationships. Displacement distance profiles, local gradient, thrust length and maximum displacement are considered against the lithological stratigraphy through which each fault cuts. Analysis of fold-thrust displacement profiles shows that the multilayered stratigraphy influences displacement–distance patterns, presumably because additional strain components are heterogeneously developed in the rock wall. A Python script to automatically plot displacement distance profiles with their associated lithology has been developed to aid the analysis of displacement–distance profiles for faults. As our demand for subsurface use increases for a range of activities, including CO2 storage, nuclear waste disposal and energy storage, the importance of understanding fault displacements in multilayered stratigraphy also increases. The work here is designed to aid data collection and analysis in multilayer stratigraphy.

1 Introduction

Understanding the geometry and movement of thrust faults is crucial for a range of structural geology applications in the geoscience discipline. For example, these structures control the traps and prospects of hydrocarbon (e.g. Boyer 1985; Khan et al. 2015), promote hydrocarbon leakage at the compressional zone (e.g. Sun et al. 2021), restrict the seal potential of the caprock that confines the injected CO2 at each potential storage site of carbon capture and storage (CCS) projects (e.g. Kaldi et al. 2013) and control the occurrence and possibility of geothermal resources (e.g. Corbel et al. 2012).

The patterns of the displacement-distance profiles were originally derived from displacement variations vertically along the thrust trace, and the distance from the reference point to the tips of the thrust, wherein any large thrust displacement reduces towards the two ends of the thrust trace (Williams and Chapman 1983). More specifically, the recognition that the displacement-distance profiles were at a maximum near the centre and diminished outwards in all directions to the edge of the thrust where the displacement is zero led to the understanding that the displacement-distance profile permanently had a simple shape of normal distribution in the idealised model (e.g. Williams and Chapman 1983). More recent observations, primarily from regional and outcrop field studies (e.g. Spotila and Sieh 2000; Mazzoli et al. 2005; Watkins et al. 2017) and seismic reflection data (e.g. Bergen and Shaw 2010), have supported an alternative, more complex displacement profile pattern (Shankar Mitra 2002; Kim and Sanderson 2008; Bergen and Shaw 2010). In this, the displacement profiles show variations from the normal distribution by increasing or decreasing the displacement in which the displacement-distance profiles are possibly controlled by mechanical stratigraphy (Couzens and Wiltschko 1996; Farzipour-Saein et al. 2009; Cawood and Bond 2018). However, another explanation could be inaccurate interpretations in which the relation between faults and horizons is misinterpreted, resulting in abnormal fold-thrust geometries and displacement distribution (Shaw et al. 2005; Totake et al. 2018; Cunningham et al. 2021). A third, more kinematic explanation posits that the displacement is transferred either by fault to fault interaction (hard linkage) (Kim and Sanderson 2005; Mouslopoulou et al. 2007; Xu et al. 2014; Totake et al. 2018) or fault to fold interaction (soft linkage) (Kim and Sanderson 2005; Qayyum et al. 2015; Watkins et al. 2017; Totake et al. 2018) which also resulting in a complex displacement profile pattern.

The rheological and mechanical heterogeneity of the stratigraphy surrounding thrust faults can influence the pattern of the displacement profiles and the final geometry of thrusts (Fig. 1) (Muraoka and Kamata 1983; Williams and Chapman 1983). More precisely, the displacement-distance profile of thrust that cuts through competent layers (e.g. rhyolite tuffs) and less competent layers (e.g. claystone or sandstone with siltstones) where they mechanically interact can be with a complex pattern of displacement profile, a situation common in multi-layers sedimentary sequences (Couzens and Wiltschko 1996; Farzipour-Saein et al. 2009; Cawood and Bond 2018). This behaviour can result in anomalous displacement values, inconsistency in the ratio between the maximum displacement and thrust length, as well as variable patterns in the displacement-distance profile (Shankar Mitra 2002; Kim and Sanderson 2008; Bergen and Shaw 2010). For example, a thrust may preferentially propagate laterally along-strike in competent layers, thereby restricting its vertical height limiting its ability to accumulate displacement and thus causing the thrust faults to appear “under-displaced” (Redpath et al. 2022). Mechanical interactions between stratigraphy and thrusts and between thrust and neighbouring folds can also influence thrust geometry and displacement-distance profile (Mazzoli et al. 2005).

In this study, we use a high-resolution coal mines dataset as a series of subsurface cross-sections interpreted by Drozdzewski et al. (1980) from Ruhr coalfield in the Carboniferous, Lower Rhine Basin, Germany (Fig. 2), to investigate the geometry of and displacement patterns on several thrust faults. These data allow us to assess how the mechanical properties of the stratigraphy, inferred from the stratigraphic column and interpreted cross-sections, influence displacement-distance profiles and ultimate thrust geometry, thereby allowing us to test displacement profiles patterns. These thrusts occur in a multipayer stratigraphy dominated by claystone, sandstone with siltstone and coal seams, within which mechanical layering is imposed by regionally developed coarse sandstones and rhyolite tuffs (Fig. 3). The thrusts formed in a broadly similar stress regime, and therefore that any differences in their geometry and kinematics, which result in differences in their displacement profile patterns, likely reflect the stratigraphic heterogeneity and local mechanical interactions. We show that displacement profile patterns and the ratio between the maximum displacement and thrusts length vary on even closely spaced thrusts. We explore why displacement profile patterns of thrusts can significantly vary and how they are distributed on the maximum displacement versus length relationship plot, even when they presently have strong maximum displacement and length relationships that broadly follow other studies (Shankar Mitra 2002; Benedicto et al. 2003; Kim and Sanderson 2008; Bergen and Shaw 2010). Our study shows that displacement-distance profiles alone do not allow us to determine the reasons for variations, complexity and types of displacement profiles patterns. However, coloured the displacement-distance profiles using lithology strata and the analysis of thrusts of varying scales (small, medium and large) within a single population together provide more robust kinematic constraints.

2 Data and Methods

2.1 Data

The study area is explored by high-resolution, closely spaced, coal mines with an aerial extent of 323.29 km2 and a depth of 2 km (Fig. 2). The subsurface data are provided by mine-workings (galleries, adits and shafts) as well as accompanying boreholes and seismic reflection profiles, which are supported by surface exposure enhanced by open-cast pits. These data were interpreted by Drozdzewski et al. (1980), who reported these observations and erected their own geological interpretations on a series of paper maps and cross-sections. They are a set of 12 serial cross-sections with a spacing of 1 to 2 km and tied by two cross-lines (Fig. 2). Further, Drozdzewski et al. (1980) indicate the levels of confidence in their interpretations critically using descriptive criteria. The stratigraphic column present in this study is put together and generated after Drozdzewski et al. (1980), Drozdzewski (1993), Suess et al. (2007), Cleal et al. (2009) and Uhl and Cleal (2010) (Fig. 3). The lithology, formations names, coal seams and stratigraphic units in this stratigraphic column are constrained by correlating the stratigraphic units from Drozdzewski et al. (1980) to other recent studies (e.g. Cleal et al. 2009; Uhl and Cleal 2010).

Dataset can be found in the following links:

Interpreted Images https://drive.google.com/drive/folders/1j4PBXQyVx89rkVTvMS7Yjl7e7y5OTDrC?usp=sharing
Digitised Cross Sections https://drive.google.com/drive/folders/1EabQCWqC1JExdLTRCJRx8MDAGHAhHy5N?usp=sharing
All the maps and cross-section of the Ruhr subbasin, lower Rhine basin is available in the North Rhine-Westphalia Geological Survey – State Office – (GD NRW) for a fee https://www.gd.nrw.de/pr_kd.htm
All the CSV files used in this study https://drive.google.com/drive/folders/14f8_Hzbos23ww6Do96CO2KGeDIIE870h?usp=sharing

2.2 Displacement-distance calculations and plots

We study 14 subsurface cross-sections (12 in-lines and 2 cross-lines) that are located in the Ruhr coalfield and documented for coalmines exploration, the latter of which is only 2D structurally interpreted and studied along the western side of the coalfield (Fig. 2a). Within these 14 cross-sections, we investigate 346 thrust faults traces and plot the displacement-distance profiles for 98 of them, where we have 848 measurement points. 323 of these data points were measured in the rhyolite tuff layer, 289 within sandstone with siltstones, 149 in the coarse sandstone and 87 within the claystone. We focus on 98 exceptionally well-identified thrust faults that form part of a larger array of fold-thrust structures (Fig. 4). These thrust faults are also selected because we can comprehensively calculate the displacement of coal seams horizons and the distance from a reference point to the tips of the fault trace, therefore, generating displacement-distance profiles that allow us to constrain displacement distributions across their surfaces (e.g. Williams and Chapman 1983; Chapman and Williams 1984; Totake et al. 2018) and analyse the displacement distribution related to lithological changes in this multi-layered system. We accurately calculated the offset between multiple pairs of footwall and hanging-wall cut-offs for the coal seams horizons vertically along faults traces using Petroleum Experts’ Move Suite structural modelling software (Fig. 4). We, therefore, investigate their offset distribution (displacement, throw and heave), including geometry measurements (i.e. fault length, dip angle and azimuths), with reasonable precision (Appendix - Tables 1 and 2). Further, we used the stratigraphic column (Fig. 3) to colour the displacement-distance profiles (Fig. 5) and infer at which stratigraphic levels the maximum displacement of the thrust occurs, which may relate to the depth at which the thrusts nucleated (e.g. Bigi et al. 2010; Ferrill et al. 2016).

In most cases, thrust faults in the study area have a complicated trajectory, and some faults consist of multiple fault traces or contain fault-related folding (Fig. 2). This makes it difficult to confidently analyse the variation of displacement due to lithologic control (Fig. 4). One reason for that is some measured points of displacement are missing within a single fault segment as a consequence of repeated movements or the effects of this ductile or continuous deformation due to related foldings (e.g. Walsh and Watterson 1991; Hongxing and Anderson 2007; Forster and Lister 2008; Jackson et al. 2017; Lăpădat et al. 2017; Pan et al. 2022). Since many of the thrust faults in the study area have complicated geometry, where extensive thrusting and folding occur at the top of the coal seams formations (Fig. 2 c and d), it may be the case that displacement variations become significantly higher than the idealised original fault model (e.g. Williams and Chapman 1983) (Fig. 1).

We follow the method of Williams and Chapman (1983) to construct displacement-distance plots that show how displacement varies vertically on a given thrust trace for multiple horizons, as well as the patterns of displacement profiles (e.g. Fig. 5). We also calculated displacement gradients (i.e. change in displacement/distance on fault trace over which the change occurs) across the thrust surface, noting that relatively high variation gradients may reflect mechanical interactions with adjacent thrust faults or host stratigraphy layers (e.g. Couzens and Wiltschko 1996; Farzipour-Saein et al. 2009; Cawood and Bond 2018). To investigate the patterns of displacement profiles, we coloured the displacement-distance profiles for the lithology of the strata. The displacement-distance profiles were coloured by giving each coal seam horizon a colour code and then applying this colour code between the points of displacement measures to reflect the information of the mechanical stratigraphy (Fig. 5). Then we measured thrust length (L) as the vertical distance from the thrust trace upper to lower tip, thrust angle, thrust average plunge dip and azimuth, and hanging-wall and foot-wall bedding plane dip and azimuth (Appendix - Tables 1 and 2). Further, we identified the uncertainty in each measured point by three classes (Proven, Assumed and Secured) after Drozdzewski et al. (1980). Using these geometric data, we examined displacement variations along thrust traces and lithology, which again can be used to infer whether the displacement profile patterns related to displacement transfer to adjacent faults by hard-linkage, fold by soft-linkage or mechanical interactions and changes in mechanical properties of the stratigraphy (Couzens and Wiltschko 1996; Farzipour-Saein et al. 2009; Cawood and Bond 2018).

3 Geological Setting

3.1 Western Ruhr coalfield in the lower Rhine basin

The crystalline basement rocks located in the Northwest of Germany can be divided by approximately NW-SE to SW-NE running graben and horst systems from the Hercynian and Rhenish geological mountain-building events (Brink 2021). The sea flooded these systems, and primarily marine carbonates were deposited on the horsts and Stillwater shales in the grabens during the Late Devonian and Early Carboniferous times (Brink 2021). The terrain became a coal-rich foreland basin throughout the Late Carboniferous Variscan Orogeny, where the grabens responded through thrusting and folding with different anticlinal patterns (Wrede 2005). These grabens were the location of the Late Carboniferous sub-basins, including the Ruhr coal-rich sub-basin in the western sector (Fig. 2 and 3) (Brink 2021). Therefore it probably acted as a perfect example to study thrust complex structures.

During the Devonian, a strong influx from the northern source areas resulted in the deposition of multi-layered clastics in the Ruhr sub-basin (e.g. Drozdzewski et al. 1980; Franke et al. 1990; Drozdzewski 1993; Wrede 2005). These clastic sediments were deposited in entirely marine conditions, with the exception of the areas in the northeastern corner deposited in continental conditions. They formed a broad shelf region that, during the Lower Devonian period, included the whole present-day Rhenish Massif (Franke et al. 1990). The shallow coastal clastic facies retreated to the northwest during the Devonian, giving way to hemipelagic sequences formed of silt-sized grains, sandstone turbidites and condensed shales or carbonates. During the Mid Devonian period, the production of platform and reef carbonates on the clastic shelf was caused by a decrease in clastic inflow, where several reefs developed on volcanic mounds in the hemipelagic domain. At least from the Mid Devonian, a southern source region (the Mid-German Crystalline Rise) has deposited clastics into the northwest basins. Subsidence in the foreland basin was balanced by clastic influx by the Carboniferous age. Sedimentation proceeded in the environment of the Ruhr sub-basin coal-bearing to the Upper Carboniferous (Franke et al. 1990).

Volcanic rocks are also observed within the sub-basin sedimentary sequence (Franke et al. 1990) (Fig. 3) as throughout the Devonian to the Early Carboniferous, the area was affected by extensive volcanic activities. The rhyolites represent the initial volcanic activity that occurred in the Lower Devonian. However, most volcanic rocks are basaltic, ranging in age from the Mid Devonian to the Variscan, with peaks in the Late Devonian. Moreover, Lower Carboniferous lavas were reported in the area by Franke et al. (1990). This volcanic lineament, lavas and tufts partly occurred at trending NNW-SSE following the orientation of the faults (Franke et al. 1990; Wrede 2005). These volcanic rocks possibly represent a narrow basin oceanic floor (see Franke et al. 1990). In the Ruhr sub-basin, the whole palaeozoic sequence was folded at the end of the Carboniferous. Folding in the Ruhr basin is strongly disharmonic, defined by large synclines and anticlines with intense minor folding (e.g. Fig. 2c and d). These folding display a wide range of amplitudes and wavelengths. Thrust faults are generally restricted to the limbs of the anticlines with dimensions ranging from several metres to a few kilometres. Isolated thrusts occur at different stratigraphic levels and are not linked to detachment thrusts. Thrusts are involved in fold Geometry and are deformed more or less concurringly to folding (Fig. 2c and d). The thrusts we study were probably formed in response to the contractional phase of the Variscan Orogeny.

4. Faults Data Method

The 98 thrust faults studied here cut through 25 coalbed seams in six formations (Horst, Essen, Bochum, Witten, Sprockhovel & Kasberg formation) alternating sandstones, siltstones and clay-rich with Rhyolite volcanic tuffs in Ruhr coalfield as interpreted by Drozdzewski et al. (1980) in the Carboniferous, Lower Rhine Basin, Germany (Fig. 1 and Appendix - Table 1). The lithologies between coalbed seams range in thickness from 45 m to 230 m. Most fault thrusts that are interpreted in these lithologies appear on the upper part of the cross-sections in Essen formation “Hu” coal seam (Fig. 1b), where the thrust tips cut the upper and lower lithological interfaces between the coal units (Drozdzewski et al. 1980). Other fault thrusts interpreted more or less deeply into the lower formation on the cross-sections with coal units, and their tips cross-cut several layers (Fig. 1b). However, all the faults are interpreted as isolated thrusts where there is no fault interpreted as bed-parallel thrust or detachment thrust within the cross-sections (Drozdzewski et al. 1980). Just above 54% of the thrusts’ upper tips initiate in the coarse sandstone, rhyolite tuff or sandstone lithologies between coal seams “La”, “Hu”, “F-2” and “Hu-1” (Fig. 9c) while about 63% of the lower tips die in the same lithologies between coal seams “Gs”, “Ka”, “Pr” and “Er” (Fig. 9d). The lengths of the interpreted thrusts range from 5.2 km to 324 m (Table 1). These thrusts exhibit refractions as branching of synthetic and antithetic thrusts. Conjugate thrusts with opposing vergences were also observed by Drozdzewski et al. (1980) and Wrede (2005), which has been described as “Fish-tail-structures” (Fig. 2). The dips angle of faults ranges from min. of 1° to max. of 87° in the Ruhr coalfield with mean dips angle of 27° (Table 1). Additionally, it is observed that 25% of the thrusts have dip angles of 16° or less, 50% have dip angles of 26°or less, and 75% have dip angles of 36° or less (Table 1). Looking at the thrust dips in different lithologies, we found that the dip angles of faults range from min. of 1° to max. of 87° in the sandstone with siltstones (Table 2b) and in the rhyolite tuff range from min. of 1° to max. of 77°, with mean dips angles of 28° and 25°, respectively (Table 2d). However, in coarse sandstone, the max. dip reaches 45° with a mean of 23° (Table 2c). Although, in claystone, the max. does not exceed 68° with a mean of 37° (Table 2a). The bedding plane of the coalbed layers dips range from 0° to 84° in both the hanging wall and footwall (Table 1). The mean of the bedding plane dips of the coalbed layers is 20° on the hanging wall, while on the footwall it is 16° (Table 1). Moreover, it was detected that 25% of the bedding planes have an angle of 6° or less, 50% an angle of 14° or less, and 75% an angle of 28° or less (Table 1).

5. Displacement – Distance Method

We analyse relationships between displacement and distance along thrust faults that cut multi-layered sandstones, siltstones, rhyolite tuff, claystone and coals using a mine dataset in the Ruhr coalfields. These coalmines dataset provides a detailed interpretation of thrusts faults recorded in subsurface cross-sections that allow investigating relationships between displacement and distance along thrust faults that cut multi-layered stratigraphies. The fault displacement of the interpreted coalbed horizons and of the thrusts faults on the cross-sections is measured in the vicinity of each fault plane vertically with an uncertainty close to 10 m, and we assume that displacement to be zero at fault tips (Fig. 3). Distance data include the vertical distance along the faults planes between coalbed horizons and the upper fault tips as reference points within the surrounding lithologies units (Fig. 3). In the cross-sections, the coalbeds horizons are the lithological interfaces between sedimentary formations as well as internal coalbed seams within these sedimentary units where the faults are reversed thrust faults. We established 98 displacement profiles by cross-plotting the displacement data against the distance data (Fig. 7 and Appendix - Table 2). We also calculated the vertical throw and heave between horizons cut-offs and reference points on the faults planes, as well as the dips and azimuths of the faults and their adjacent bedding planes (Appendix - Table 1). All faults show reverse displacement and are often associated with folding, with a maximum value of 1.15 km to 2.1 m and a throw of 387 m to 0.3 m, while the mean of displacement is 209 m and the throw 65 m (Table 1). The heave of the interpreted thrusts ranges from 0.5 m to 978 m, with a mean heave of 186 m (Table 1). Additionally, we use the uncertainty nomenclature after Drozdzewski et al. (1980) to reflect the uncertainty classes as an envelope on the displacement distance profiles. Drozdzewski et al. (1980) define the uncertainty nomenclature as, first, “proven” that is, the direct observation on cross-sections. Second, “secure” is the interpretation within 100 m on cross-sections. Third, “assumed” is the interpretation beyond 100 m on cross-sections following.

6. Automatic Displacement Method

Based on the manual displacement–distance profiles workflow summarised here (Fig. 3 and 4), a Python script to calculate the displacement and distance along the faults from 2D cross-sections was written where the workflow summarised in Fig. 6. The script plots the displacement–distance profiles automatically and colours the background of the profiles with the rock formations (Fig. 6). Moreover, we created an error envelope reference to the uncertainty nomenclature of the horizons and faults inherited in the interpreted cross-sections from Drozdzewski et al. (1980) (see Fig. 6f). Additionally, the algorithm will suggest a smooth displacement–distance curve as a semi-circular line between faults tips where it acts as a baseline to quantify the displacement–distance variations. Our Python script, cross-section examples, and displacement–distance profiles data are open source and freely available on GitHub. They can allow researchers to produce displacement–distance profiles quickly, incorporate the mechanical stratigraphy information, and increase the interpretation accuracy by a realistic distribution of the displacement across the length of the faults. The final product is particularly useful for understanding thrust growth on multilayer stratigraphy and investigating the displacement–distance profiles variations with lithology. From the data exploratory and analysis viewpoint, this also enables investigation, for example, of a higher number of faults in a shorter time to produce the displacement profiles.

7. Displacement Profiles - Results

At Ruhr coalfield, where displacement data was measured from the interpreted subsurface cross-sections at coalbeds horizons, while the maximum and minimum displacement were recorded for each fault, then they add up to calculate the cumulative displacement. The cumulative maximum displacement reaches 3.48 km and invariably lies within the coarse sandstone of coalbeds “Fi” and “Di” followed by Rhyolite tuffs units of “Zo8” coalbed (Fig. 8a). The cumulative minimum displacement reaches 1.25 km and lies within the claystone of coalbeds “Sb”, “Er” and “Mg”. Furthermore, the upper and lower thrust tips initiate or die within the coarse sandstone, sandstone, or rhyolite tuff units (Fig. 8b). These observations indicate that the thrusts nucleated within the competent units then propagated towards the overlying and underlying clays units and finally cross-cut several layers. However, by looking at the count of where the maximum displacement occurs in the coalbed horizons for all faults, we found that coalbed “Hu” with sandstone lithology has the most frequent occurrence of maximum displacement followed by “Ka” then “Zo8” (Fig. 8c) also coarse sandstone and sandstones of “Gu” and “Hu” coalbeds have the most frequent occurrence of minimum displacement (Fig. 8d).

The displacement profiles for the 98 thrusts studied at the Ruhr coalfield exhibit a complex profile shape with a wide range of profile patterns (Fig. 5 and 7). These profiles show a steep increase in the upper tips with little variation in the central part of the thrust, whereas the displacement drops abruptly at the lower tips, producing a complicated wide range of profile shapes (Fig. 7). Ideally, Displacement–distance profiles for single isolated faults show diminishing offsets to fault tip-line (Fig. 3). Our findings seem to be more complicated, with fault slip gradients that differ from the ideal bell shape profile (Chapman and Williams 1984). These include Trapezoid, Right Triangle, Positively Skewed, Negatively Skewed, Semi-circle and Overlap shapes. Sandstone strata are associated with a continuous displacement–distance pattern. A variable displacement–distance pattern, on the other hand, is correlated with finer-grained units. The most intricate displacement–distance connections are seen in thinly interbedded successions.

The upper tips displacement gradients range from a min. value of -0.66 (a negative value indicates a negative slope) to a max. value of 14.88, with a mean value of 0.57 for thrusts touching the upper horizons of coalbeds seams (Table 3a). However, the lower tip displacement gradients range from a min. of -16.28 to a max. of 0.74, with a mean of -0.33 (Table 3c). In the central part of the thrust (away from the thrust tips), the displacement gradient is much smaller, ranging from -2.64 to 1.12 with a mean of -0.18, with 50% of the values above -0.15 and 75% of the values above -0.015 (Table 3b). Such low values indicate that the change in displacement is minimum in this area. The sum of the gradient values within the sandstone with siltstone units exhibit a higher range of values between 48 to -38, followed by the Rhyolite tuff with a range of 21 to -29, and the coarse sandstones with a range of 21 to -8 (Fig. 9a). The clay units show the lowest range of 7 to -9 (Fig. 9a). These results indicate that the displacement difference in the silty sandstone is significant while the difference in the clay units is minimal.

These variations of displacement profiles and their associated steep gradients may suggest that lithological units between coalbeds interfaces and their mechanical stratigraphic behaviour both controlled thrusts propagation (Teixell and Koyi 2003; Cawood and Bond 2018, 2020; Parker and Pearson 2021; Wigginton et al. 2021). A constant displacement–distance pattern is related to sandstone layers, while a variable displacement–distance pattern correlates with the finer-grained units. Thinly interbedded successions display the most complex displacement–distance relationships. This shows that the mechanical stratigraphy can influence fault slip patterns, presumably because there are additional strain components that are heterogeneously developed, depending on rock type. The thrusts may be controlled by stratigraphy of the units at one or both tips, so each part of the fault may be considered an independent half fault. Although the near-tip gradients of these controlled thrusts by mechanical stratigraphy vary from one thrust to another, they display a linear relation when cross-plot the fault length with the max. displacement (Fig. 10). The slope of this line seems to divide the displacement profiles of the thrusts according to their nature and control of the rock type.

Although those thrust faults were restricted to the upper part of the sections, we observed that thrusts are not confined by stratigraphy; instead, they propagate upward and downward into different lithology units with the increase of displacement. This suggests that thrusts cut through and propagate across the restrictor units, such as clay-rich units, by displacement accumulation. At each profile, the displacement variation increases with the heterogeneity of the stratigraphy unit (Fig. 9a). Therefore, a constant displacement gradient occurs within the constant homogeneous lithology units. However, thinly interbedded successions display the most complex displacement–distance relationships. The maximum displacement and fault length show linear relation when cross-plotted against each other, where the displacement increase with the thrust length along the best fit line on the linear relation (Fig. 10).

In this study, the relationship between displacement profile patterns, maximum displacement, and fault length in log-log plot was analysed to determine that the patterns of the profiles form clusters around the best fit line on the linear relation (Fig. 10). Moreover, the maximum displacement of specific profiles (Triangle and Trapezoid) is approximately ten times higher than other profile patterns (Bell and Semi-circle). In our displacement profiles, we display the interpretation uncertainty as an error envelope around the displacement–distance plot. However, in the measured data, 45% of the displacement points are “Assumed” uncertainty class, 40% of the points are “Secured”, and 15% of the points are “Proven”. The data collected from the interpreted cross-sections in coalfield multilayer stratigraphy concur in showing that displacement profiles vary with the lithology or mechanical stratigraphy surrounding thrust faults (Fig. 9b). We now explore potential reasons for these displacement profile variations.

8. Discussion

Investigations of displacement–distance profiles, measurements of reverse offsets along thrusts planes, calculating maximum displacement values, displacement gradients and thrust lengths reveal how the displacement profile evolves in cross-section during thrust propagation in a multilayer stratigraphy. Fig. 4 summarises the main steps, and Fig. 5 highlights how lithological variations and mechanical stratigraphy can influence the shape of the displacement profile. Our analysis is based on data collected from coalmine interpreted subsurface cross-sections with isolated thrusts cut multi-layered sandstones, siltstones, rhyolite tuff and coal sequences and can apply to other alternating stacks of more or less competent units. We observed that thrust faults have various displacement profile patterns (Fig. 10 length vs displacement) as they grow in these multi-layered successions, where the propagation of the thrust across the multi-layered boundaries and then across several coalbed layers (Fig. 5 and 7) results in further development of the displacement profile. These various displacement profiles contain Trapezoid, Right Triangle, Positively Skewed, Negatively Skewed, Semi-circle and Overlap shapes (Fig. 10). According to this analysis, displacement profiles and gradients are highly variable throughout thrust planes. Despite these variations, all displacement profiles show that the gradient increases progressively near the upper tip as slip accumulates along the thrust plane and decreases gradually near the lower tip while a shallow gradient zone develops near the initiation point in the central part. Thrusts propagation in the clay units is characterised by a low range of displacement gradients controlled by the lithology of the unit, whereas the displacement gradient in the sandstone and rhyolite tuffs layer displays an increase (Fig. 10). Thrust faults in claystone lithologies are also constantly characterised by lower fault angles than the thrusts in the coarse sandstones or the rhyolite tuffs, which suggests that mechanical stratigraphy controls thrust angle (Table 2). Furthermore, a comparison between maximum displacement and lithologies between coalbeds suggests that thrusts are initiated either in the coarse sandstone or in the Rhyolite tuffs units (Fig. 8a), as observed by the maximum displacement on coalbed horizons “Fi”, “Di” and “Zo8”. These show that mechanical stratigraphy control of thrust propagation, corresponding to the sedimentary interfaces between the coarse sandstone or Rhyolite tuff units and thinly interbedded successions in the sandstone layers, results in modifications of displacement profiles. Moreover, 75% of thrust faults are interpreted as low-angles dips, between about 1° to 36°. However, the maximum dip angle is 87°, which suggests that their orientations may vary considerably because thrust faults cut through stratigraphic sections as ramps or flats. Additionally, repeated slip on other thrust and associated folding can cause low-angle faults initially to rotate to steep angles. Both the manual and the automated displacement distance profile approaches allow investigation of thrust propagation in multilayer stratigraphy besides reflecting the uncertainty envelop on the displacement profiles. For the automated approach, the benefits of generating displacement distance diagrams and visualising uncertainty envelop quickly and automatically could be beneficial in examining thrust interpretations and in recognising and identifying any potential interpretation pitfalls. The displacement distance profiles presented here are plotted from the interpreted cross-section inherited from the previous studies of Drozdzewski et al. (1980). Although this study used 98 thrust faults to plot the displacement distance profiles, the uncertainty in the profiles is high. This might be because most data points used to plot the displacement distance profiles are either “secured” or “assumed” (Fig. 9b). However, our automatic displacement distance profile analysis could be performed before completing the subsurface cross-sections interpretations. In this way, a geologist could generate the displacement profiles with their uncertainty envelope, equivalent to that illustrated in Fig. 6, showing the thrust growth on multilayer stratigraphy and investigating the displacement-distance profiles variations with lithology. We see this as one of the key benefits of our displacement distance analysis approach.

9. Conclusion

Our data strongly suggest that displacement profiles patterns are controlled by mechanical stratigraphy, where thrust propagation within each lithological unit is characterised by specific displacement gradients for each such unit. This conclusion is consistent with a number of studies based on observations of the nature of thrusts (Chapman and Williams 1984; Couzens and Wiltschko 1996; Teixell and Koyi 2003; Cawood and Bond 2018, 2020; Parker and Pearson 2021; Wigginton et al. 2021). Collectively, data from the coalfield mines as isolated thrusts within multi-layered system suggest that:

• Displacement profiles have complex profile shapes with a wide range of profile patterns controlled by the mechanical stratigraphy of the units.

• Displacement gradients increase steeply on the upper parts of the thrusts and drop sharply on the lower parts of the thrusts while the gradient remains almost constant or has local variations on the middle parts of the profile.

• Correlation between the maximum displacement and length of thrusts exhibits a linear relationship controlled by mechanical stratigraphy where the displacement profiles patterns spread around this regression line.

Accordingly, our gradient values are much lower within the clay units than within the coarse sandstone or the Rhyolite tuff layers. However, the variation in the displacement gradients in the silty sandstone layers investigated here displays a wide range of variations with respect to the other lithologies, which is expected given the heterogeneity of the lithology content of these units. Indeed, the complexity of displacement-distance relationships is generally likely to rise with the increase in the heterogeneity of the lithology units. Nevertheless, the gradients obtained in this study increase with increasing the interaction of thinly interbedded successions. This indicates that the effect of the mechanical stratigraphy is combined by other parameters such as rock strength or by a heterogeneous stress distribution in relation to the layering. In light of these results, the displacement distance analysis and its gradient variations of thrusts faults in multilayer systems and with the support of its mechanical stratigraphy is the key to gaining further insights into thrust faults evolution.

Future work

To develop a workflow and web-based front end for the script, which will allow to interpret complete geological data.

Acknowledgements

The work contained in this repositories contains work conducted during a PhD study undertaken as part of the Natural Environment Research Council (NERC) Centre for Doctoral Training (CDT) in Oil & Gas funded 50% through its National Productivity Investment Fund grant number NE/R01051X/1 and 50% by the University of Aberdeen through its PhD Scholarship Scheme. The support of both organisations is gratefully acknowledged. The work is reliant on Open-Source Python Libraries, particularly numpy, OpenCV, cv2 matplotlib, bruges and pandas and contributors to these are thanked, along with Jovian and GitHub for open access hosting of the Python scripts for the study.