Analysis of Paleokarst Sinkholes in the Arkoma Basin using 3-D Seismic.. Analysis of Paleokarst Sinkholes in the Arkoma Basin using 3-D Seismic... Analysis of Paleokarst Sinkholes in the
Introduction
Paleokarst is karst topography that has been buried by sediment and is no longer part of the active landscape Like modern karst, paleokarst deposits are widespread, and paleokarst sinkholes are increasingly studied and mapped because they are targeted as reservoirs for petroleum When these ancient cavities collapse and are filled or covered by sediment, various breccias can form—including cavern-fill parabreccia, collapse breccia, crackle breccia, and solution-enlarged breccia fractures and vugs, as well as sediment infill and the development of conduits and channels Understanding paleokarst helps geologists reconstruct past environments and regional hydrogeology at the time of karst formation, and these buried features can influence the thickness and distribution of overlying sediments.
In the Tarim Basin of China, paleokarst features are highly sought after by the petroleum industry because breccia within these systems creates secondary porosity that helps rocks retain larger amounts of hydrocarbons than surrounding formations However, if paleokarst features are not properly anticipated or their locations remain unknown, they can pose significant drilling hazards that impact project timelines and well performance Nearby wells may experience drilling mud losses and potential communication with water-bearing formations, compromising reservoir integrity and reducing production efficiency.
This study focuses on paleokarst sinkholes within the Viola Limestone Formation in the Arkoma Basin Paleokarst features lie buried beneath younger sediments, which limits the investigative tools available to researchers As a result, current methods are mainly oriented toward locating these buried features to better understand their distribution and characteristics.
2 in outcrops, penetrating them when drilling and taking core for analysis, and using a geophysical seismic survey to image the subsurface
Dating to the Ordovician period, the Viola Limestone occurs primarily in the subsurface of the North American midcontinent, with surface outcrops in the Arbuckle and Wichita Mountains of Oklahoma It has been mainly exploited by the petroleum industry, and this has improved subsurface understanding through cores and well logs that provide good well control Beds correlating to the Viola Limestone have been identified across a wide region, including South Dakota, Texas, and Colorado The formation was deposited in a shallow ramp environment within an inland Ordovician sea that covered present-day Oklahoma Figure 1 presents the stratigraphic column used in this study, with the Viola Limestone as the primary formation and secondary interests in the Sylvan Shale, Hunton Group, and Woodford Shale.
This study employs a 179.19-square-mile 3-D seismic survey to map and analyze paleokarst features within the Viola Limestone in Coal and Hughes Counties, Oklahoma (as shown in red in Figure 2) The survey data were generously supplied by Devon Energy, EnerVest, Newfield Exploration, and Seismic Exchange Inc By generating professionally calculated attribute volumes—specifically curvature and coherency—we enhance the detection and mapping of paleokarst sinkholes in the Viola Limestone.
3 Figure 1 – Stratigraphic column used for this study Specifically focusing on Ordovician aged
Viola Limestone (Romero and Philp, 2012)
Figure 2 – Study area highlighted in red, in Coal and Hughes County, Oklahoma (modified from
World Atlas, 2015) a Motivation for Study
This study was originally motivated by petroleum wells underperforming in the Fort Worth Basin of Texas, where paleokarst sinkholes in the underlying Ellenburger Formation have been identified as the cause Accidentally hydraulic fracturing too close to these sinkholes allowed large amounts of water to propagate into horizontal wells in the Barnett Shale (Baruch et al., 2012) The original task was to evaluate horizontal Woodford Shale wells within the Arkoma Basin to determine if the same water production issues occurred due to paleokarst sinkhole proximity in the Viola Group However, underperformance due to water encroachment was ruled out for the Viola Limestone paleokarst and the Woodford Shale wells The issue in the Fort Worth Basin is that the underlying Ellenburger Formation is water bearing, so hydraulic fracturing too close to it allows communication into Barnett Shale horizontal wells, and this risk is amplified by the presence of a water-bearing Ellenburger Formation.
Five paleokarst sinkholes in the Ellenburger Formation increase fracture networks and natural porosity, allowing water to migrate into horizontal Barnett Shale wells In contrast, the Viola Limestone hosts numerous paleokarst features—especially where it contacts the Woodford Shale—but the Viola contains less water, so it does not induce the same production issues seen in the Ft Worth Basin.
Although paleokarst poses drilling challenges, it remains a valuable subject for industry analysis Mathews (1994) observed that drilling mud loss and drill bit stalling can occur when natural fractures and secondary porosity formed by paleokarst are intersected by the borehole Early drilling practices responded by pumping large amounts of absorbent material downhole to stem fluid loss Today, operators typically adjust the mud’s viscosity in response to sudden porosity changes associated with paleokarst, aiming to minimize drilling-fluid loss and protect the drill bit and casing from damage and downtime If these adjustments are neglected, mud loss can escalate, causing expensive repairs and nonproductive time Using 3-D seismic mapping to locate paleokarst features can help drillers anticipate porosity changes, optimize mud design, and even avoid troublesome zones altogether.
This study aims to delineate paleokarst sinkholes using seismic mapping techniques By characterizing paleokarst features, it will enrich the geologic history of the area and advance understanding of paleokarst formation processes Consequently, we will analyze paleokarst frequency and diameter within the study area to infer paleo-drainage patterns during the Late Ordovician.
Silurian times This will add to a better understanding of the deposition and diagenetic environments that occurred in the formation of the Arkoma Basin b Data
Devon Energy, EnerVest, Newfield Exploration, and Seismic Exchange Inc have provided a personal academic research license for a 179 square mile 3-D seismic survey named the Greater Northridge Merge 3-D This survey is a merge of five different surveys: Northridge 3-D, King Hollow phases I, II, and III, and Centahoma 3-D The original Northridge 3-D survey was co-financed by Devon Energy and EnerVest King Hollow Phase I, II, & III was co-financed by Devon Energy and Newfield Exploration Centrahoma 3-D was co-financed by Devon Energy and Seismic Exchange Inc These surveys are shown on Figure 3 The Greater Northridge Merge 3-D is located in Oklahoma, on the border of Hughes and Coal Counties The Northridge Merge survey, the merge of all five surveys, has had professionally calculated attribute volumes created by Resolve GeoSciences Inc The two most applicable attribute volumes to this study are coherency and curvature, but other attribute volumes have been provided to see if the paleokarst can be delineated using methods other than the traditional ways
7 Figure 3 – Northridge Merge 3-D area map provided by Devon Energy
Karst is a distinctive landscape formed by a diagenetic process that operates in carbonate and evaporitic rocks, driven by acidic meteoric waters that infiltrate the rocks to create surface and subsurface features (Sykes, 1995) According to White (1988), the most characteristic karst landforms are sinkholes, caves, and underground drainage systems, which lead to sinking streams on the surface that interrupt normal drainage.
Surface karst, the most common type of karst terrain, is also known as epigenetic karst Its formation is driven by chemical imbalances in meteoric water moving through carbonate rocks, with factors such as matrix porosity, mineral composition, degree of fracturing, bed thickness, climate and vegetation, water-table position, and the length of exposure to meteoric water all shaping the process The system evolves toward chemical equilibrium with respect to carbon dioxide and the dissolution of calcium carbonate When water contacts atmospheric CO2, carbonic acid forms, which then reacts with limestone (CaCO3) to dissolve it, producing Ca2+ and HCO3- ions.
As long as CO2 remains in the system, it will continue to dissolve carbonates In karst environments, meteoric water circulating through the system is replenished by surface water that has interacted with atmospheric CO2, renewing the CO2 supply for dissolution This ongoing replenishment drives continued diagenetic alteration of carbonate rocks.
Karst profiles feature two hydrologic zones: the vadose zone above the water table and the phreatic zone below it The distribution of these zones is governed by the position of the water table, which controls groundwater flow and dissolution in karst systems Figure 4 illustrates these zones within a typical karst profile that develops during karstification (Lynch, 1990) Near the surface, meteoric water is drawn into the rocks by infiltration, driving karst processes that shape conduits and caves.
Karst processes gradually enlarge small fractures as slightly acidic water moves through them A typical cross section of the vadose zone is teardrop-shaped, with meteoric water eventually reaching the water table or being stopped by an impermeable formation, marking the transition to the phreatic zone In the phreatic zone, water moves laterally through the formation and forms cave networks, often producing wide tubular passages When the water table changes, the cave system shifts accordingly, creating abandoned caverns or underwater caves, which can collapse to form sinkholes and breccias.
Figure 4- Idealized karst profile (Lynch, 1990 from Esteban and Klappa, 1983)
Geologic History
Figure 2 highlights the study area in central Oklahoma, located within the Arkoma Basin, a Paleozoic, south-dipping sedimentary-structural basin dominated by shallow-water deposits that thicken toward the south The Arkoma Basin extends from central Oklahoma to central Arkansas, a relationship illustrated in Figure 8 It is one of North America’s most prolific petroleum-producing basins (Suneson, 2012) The region experienced three major depositional-tectonic events—the Oklahoma Basin, the Southern Oklahoma Aulacogen, and the Ouachita trough (Johnson et al., 2000; Figure 9) The Oklahoma Basin was a broad shelf-like area with thick and extensive shallow-marine carbonates interbedded with thinner marine shales and sandstones The Southern Oklahoma Aulacogen was a west-northwest–trending trough that persisted until the Pennsylvanian; although the same sediments occurred inside and outside the trough, sediments within the aulacogen are two to three times thicker (Johnson et al., 2000).
The lower Arkoma Basin was part of a Cambrian–Pennsylvanian shelf that lay north of the Ouachita trough, forming the southern boundary of the North American craton as a broad epicontinental sea covered much of the midcontinent This setting favored the development of shallow carbonate shelf deposits interbedded with organic marine shales and sandstones from the Ordovician to the Devonian (Figure 1) Tectonic activity during this time was limited, with the deposition of the Simpson, Viola, Sylvan, and the lower Hunton Group strongly influenced by the rifting event linked to the opening of the Ouachita depositional basin This rifting event shaped subsequent sedimentation patterns in these units.
18 event had specific controls over the thicknesses and geographic extent of the above mentioned formations
Figure 8 – Map showing regional extent of Arkoma Basin, and other basins surrounding it
Figure 9 – Extent of Oklahoma Basin, and Southern Oklahoma Aulacogen (Johnson, et al 2000)
During the deformation of the Ouachita fold belt, the Arkoma Basin evolved into a peripheral foreland basin in the middle Atokan time The Ouachita Fold Belt formed from the collision of the North American plate with the Gondwanan plate in the Early Mississippian, driving widespread deformation and faulting across the shelf to the north The resulting faults are predominantly large normal faults oriented parallel to the Ouachita trend (SW-NE) Figure 10 illustrates the faulting and compression pattern associated with the Ouachita trend, and seismic data from this study also reveal parallel faulting on a smaller scale along the Ouachita trend.
20 data Specifically, there is a large uplifted horst block in the study area that follows the Ouachita trend
The Arkoma Basin in Oklahoma is bounded to the north by the Cherokee Platform and to the south by the Choctaw Fault zone, giving it a width of roughly 20–50 miles and a length of about 250 miles from north to south It extends from the Arbuckle Mountains in central Oklahoma to the Mississippi Embayment in central Arkansas, forming a continuous geological belt across the region.
Figure 10 presents a map of the Arkoma Basin and the Ouachita Mountains, delineating the study area and its coherency to reveal the fault trend that mirrors the regional Ouachita Trend The map shows how faults within the study area align with the Ouachita structural pattern, indicating tectonic coherence between the Arkoma Basin and the Ouachita Mountains, and it is a modification of Suneson, 2012.
Prior to the Simpson Group, the Arbuckle Group formed without stratigraphic discontinuity and is represented as a succession of carbonate mudstones, laminated dolomites, or dolomitic limestones (Ham, 1973) This unit marks a major shift in the depositional environment compared with the older Arbuckle Group The Simpson Group itself is a sandstone-dominated sequence ranging from about 150 to 715 feet in thickness (Amsden & Sweet, 1983), deposited in a shallow marine environment It comprises five formations—Joins, Oil Creek, Mclish, Tulip Creek, and Bromide—deposited over roughly 25 million years (Denison, 1997) The sequence begins with a basal sandstone (Suhm, 1997) and then transitions into thin limestones with varying shale content, ending after sea withdrawal Simpson sandstones are renowned for excellent reservoir qualities, with porosities up to about 30% in some zones, a property attributed to the extensive rounding and sorting of the sediments (Denison, 1997).
1997) Due to the homogeneity of the five formations, one deposition model fits all five Denison
According to a 1997 study, the basal sandstone was likely deposited as eolian dunes; as marine transgression advanced, the platform flooded and eolian sandstone deposition was interrupted; sea level changes produced alternating layers of carbonates and shales; when the carbonate platform was exposed, a new cycle of basal eolian sandstone deposition began b Viola Group
Overlying the Simpson Group, the Viola Group is a carbonate sequence that spans the middle to upper Ordovician (Figure 1) (Amsden & Sweet, 1983) It is defined as the strata between the Bromide and the Sylvan Shale (Denison, 1997) The Viola Group outcrops in the study area, highlighting a key middle-to-late Ordovician carbonate interval in regional stratigraphy.
The Arbuckle Mountains of Oklahoma host the Viola outcrop locations, making this region the primary focus of most Viola-related studies Because these Viola outcrops are concentrated in this area, researchers have largely studied the Viola there, a region that lies close to the study area of this thesis and provides relevant, accessible data for comparison.
Amsden and Sweet (1983) characterize the Viola Group in the Arbuckle Mountains, where the group comprises two formations: the Welling Formation at the top and the underlying Viola Springs Formation The Welling Formation is an organo-detrital limestone, while the Viola Springs Formation, lying below the Welling, is a muddy, irregularly bedded, cherty limestone (Amsden & Sweet, 1983).
Deposition began as the Viola seas transgressed over exposed bromide carbonates during the Ordovician (Denison, 1997) The Viola Group was deposited on a southward-sloping carbonate ramp associated with the Southern Oklahoma aulacogen (Puckette et al., 2000) The basal unit, Viola Springs, is composed of cherty, finely laminated lime mudstones (Denison).
These mudstones are rich in organics and were deposited in stratified waters below the storm wave base (Denison, 1997) The transition from mudstones to grainstones marks the upper half of the Viola Group, the Welling Formation, an interpretation noted by Denison (1997).
The Viola Group is a classic shallowing‑upward sequence, with the lower Viola Springs Formation deposited in deep water and lying above the more shallowly deposited upper formations of the Simpson Group Denison (1997) suggests that the flooding event forming the Viola Springs was exceptionally rapid, after which the marine environment progressively shallowed Ultimately, Viola Group carbonate deposition ended abruptly as the area was flooded by distal clay from distant sources The sequence also records several periods of karstification, including post‑depositional karst features that accompany its evolution.
24 unconformity surface between the Viola Group and the overlying Sylvan Shale, and active karst occurring at areas where the Viola Group outcrops at the surface c Sylvan Shale
The Late Ordovician Sylvan Shale comprises two members: the upper dolomitic shale that grades into dolomite, and the lower dark gray, noncalcareous shale as described by Amsden and Sweet (1983) The apparent shift from the Viola Group limestones to shale is not interpreted as a deepening sea, but rather as an influx of clay that muddies the water, per Denison (1997).
The Sylvan Shale is a fine mudstone that thickens upward into more calcareous and dolomitic layers, with the uppermost sediments including dolomitic shales (Amsden & Sweet, 1983) It is not a major petroleum source but serves primarily as a cap rock sealing hydrocarbons produced and stored in the underlying Viola Group carbonates (Denison, 1997) Relative to the lower-lying Viola Group, the Sylvan Shale is notably weaker, causing it to erode readily in outcrops and making the Viola–Sylvan contact difficult to observe in the field.
Methods
Greater Northridge Merge 3D is a 179.12 square mile seismic survey located in Coal and Hughes Counties, Oklahoma (Figure 12) It was acquired and processed in the late 2000s using dynamite as a seismic source The survey features a bin size of 110 x 110 feet, a CMP fold of 46, and a 1 ms time sample rate Figure 13 displays the frequency spectrum, which ranges from 15 Hz to 105 Hz and has a dominant frequency (fdom) of 60 Hz.
Figure 12 – Greater Northridge merge 3D survey location outlined within Coal and Hughes County Oklahoma
Figure 13 – Histogram of frequency spectrum from OpendTect, taken from Crossline 320 of
Devon Energy provided well logs with formation tops that were used to correlate depths and thicknesses of the local formations, enabling an accurate estimate of the Viola Group’s average velocity By applying a Viola Group top depth of 5,578 feet and a 2-way travel time of 1.224 seconds, the average velocity is derived from the standard depth-to-time relationship, as illustrated by the velocity equations (Equation 1 and Equation 2).
Eq (1) V = 2*(Depth)/Time Eq(2) V = 2(5578 feet)/(1.224 seconds)
The analysis yields a velocity of 9,114.38 ft/s for the Viola Limestone When this calculation is applied over the area with log coverage, the average velocity is approximately 10,000 ft/s Using the equation for wavelength, these velocity estimates can be linked to the corresponding wavelength under the given conditions.
The analysis yields a wavelength of 166 ft, corresponding to a vertical resolution of 41.5 ft Lateral resolution is limited by the greater of the bin size or half the wavelength, as described by Eq 7 and Eq 8 The survey acquisition parameters and the calculated survey data are listed in Table 1.
Eq(5) Vertical Resolution = λ/4 Eq(6) VR = 166/4 Eq(7) Lateral Resolution = max(bin size, λ/2)
Inline Range 1-689 (South - North) Crossline Range 1-798 (West - East) Processing grid azimuth
Vertical Resolution 41.5 ft Lateral Resolution 110 ft Table 1 – Greater Northridge Merge 3D survey parameters, calculated using equations from
A synthetic seismogram was generated from the Rogers Trust 1-24 with formation tops supplied by Devon Energy and is shown in Figure 14 From this synthetic seismogram the top of the Viola Group was picked using OpendTect seismic software and mapped across the survey Figure 15 presents the synthetic seismogram in an inline view across the seismic, while Figure 16 provides a zoomed-in inline view of the Viola Group top alongside Wapanucka Limestone, Cromwell Limestone, Jefferson Sandstone, Caney Shale, Woodford Shale, Hunton Group, Sylvan Shale, and the lower Simpson Group Before the horizon could be auto-tracked across the entire survey, all faults displacing the Viola peak were mapped, using an inline view of co-rendered post-stack migration with coherency attributes to identify regions of low coherence that could indicate faults, as displayed together with the seismic traces (Figure 17).
Figure 18 presents the tracked Viola horizon in time and amplitudes along with the mapped faults, showing paleokarst deposits large enough to be identified from a preliminary time-structure map In Figure 18-b, the horizon is shown with seismic amplitudes across it, where areas of low amplitude correspond to paleokarst sinkhole features caused by breccia from collapse, yielding a reduced seismic response Figure 19 provides a 3D view of the tracked Viola horizon, making fault displacement through the survey readily observable and highlighting a large uplifted horst block in the middle that is easily seen in this perspective Figure 20 offers a zoomed-in view of a single paleokarst sinkhole, while Figure 21 presents the same feature in an inline view with post-stack migration and a co-render of post-stack migration and coherency, illustrating the coherency of the geologic structure of the paleokarst sinkhole.
After mapping the Viola horizon across the survey, the coherency attribute was applied to enhance the horizon and reveal smaller-scale paleokarst features that are not easily visible on the time-structure map Given the abundance of paleokarst, manual counting would be inefficient, so ImageJ—a Java-based image processing software originally developed for medical imaging—was used to automatically count and measure the circular and semi-circular paleokarst features highlighted by the coherency analysis.
Figure 14 – Synthetic seismogram created from Rogers Trust 1-24 well
Figure 15 – Synthetic seismogram well tie in
Figure 16 – Inline view of synthetic seismogram tied into the seismic inline, zoomed in to highlight Viola Group and surrounding formations
Figure 17 provides an inline view of the co-rendered post-stack migration and the coherency analysis used to map faults across the survey, with black lines highlighting areas of low coherency interpreted as faults.
Figure 18 – a) Time structure map of Viola horizon, b) post stack migration amplitudes of Viola
Horizon, c) Time structure of Viola with faults highlighted a) b) c)
Figure 19 – Time structure 3D view of tracked Viola Horizon
41 Figure 20 – Time structure map of Viola Horizon, zoomed in to highlight paleokarst depressions
Figure 21 – a) Post stack migration inline view of paleokarst highlighted in Figure 20, blue line is tracked Viola Horizon, b) coherency attribute of same inline, c) co-rendered image of PTSM and coherency b) a) c)
43 Figure 22 – Coherency attribute applied on the tracked Viola horizon
To highlight paleokarst features, a color bar was selected in OpendTect that best highlighted all the paleokarst features within the coherency attribute (Figure 23) The image was then loaded into ImageJ and calibrated for scale, with every 200th inline and crossline labeled; with a bin spacing of 110 feet, 200 inlines correspond to 22,000 feet, so the entire image is calibrated and measurements are recorded in feet After calibration, the image was changed to an 8-bit grayscale image to enable the software to count the paleokarst sinkholes Next, the image was cleaned by removing linear features interpreted as faults and edge border noise to ensure smooth counting Despeckle was applied to remove single-pixel speckles, and since some paleokarst structures are donut-shaped with internal voids, the Fill Holes tool was used to fill these voids and obtain the total area of each sinkhole The resulting image was then used for the Analyze Particles function to count, measure, and outline all particles (Figure 24).
ImageJ's Analyze Particles tool allows size and circularity to be factored into search parameters, but in this study the image had already been cleaned so no size or circularity limits were applied since only sinkholes remained The final display option selected was outlines, one of several choices including nothing, outlines, bare outlines, ellipses, masks, count masks, overlay outlines, and overlay masks Outlines provided the best output for the study's needs by generating a separate image that displays each counted feature as a bare outline with its count number inside, as shown in Figure 25 Additionally, the software offers multiple visualization options for reporting results.
45 outputs a table that displays the count number, area, perimeter, circularity, Feret’s diameter, Feret’s X & Y, Feret’s Angle, and Minimum Feret’s diameter
Figure 23 – Initial image used for paleokarst counting and measuring in ImageJ
46 Figure 24 – Final image used for analyze particles function in ImageJ This image has had all features not associated with paleokarst removed
47 Figure 25 – ImageJ output overlay, showing the outlines and count numbers of every feature it identified using the analyze particles tool
ImageJ's output table presents pre-selected results from a broad suite of possible measurements Feret’s diameter is defined as the distance between two parallel tangents on opposite sides of a randomly oriented particle (Merkus, 2009) The software computes the particle diameter in the X and Y directions (Feret X and Feret Y), then derives the Feret Angle by showing how far the calculated diameter deviates from the particle center This method provides an effective diameter for non-circular objects In this study, most paleokarst features are circular, though a few outliers are deformed and oblong Table 2 illustrates an example of the ImageJ output data.
An ImageJ particle analysis workflow was used to rapidly count and measure the majority of paleokarst features, but smaller or dimmer features were missed during image processing To quality-control these results, the ImageJ-generated image (Figure 25) was overlaid onto the original paleokarst image (Figure 23) A polygon tool was then used to outline features not detected by the analyze particles tool, and these outlines were saved with the same measurements added to the table Figure 26 shows the overlay technique used to identify features not highlighted by ImageJ's particle analysis, and the resulting table was exported to Microsoft Excel for further analysis.
Count Area Perim Circ Feret Median %Area FeretX FeretY FeretAngle MinFeret AR Round Solidity
Table 2 –Table output example from ImageJ
50 Figure 26 – Figure 25 overlain on Figure 23 to help highlight missed paleokarst features by the software Yellow circles are paleokarst deposits circled by hand using polygon tool in ImageJ
To investigate potential formation factors of paleokarst, we used the curvature attribute Figure 7 shows the application of the most negative curvature attribute on the Viola horizon The most effective approach for analyzing paleokarst is to co-render the most negative curvature with the coherency attribute By doing so, the transparency of the curvature layer can be adjusted so that paleokarst highlighted by coherency is visible together with the curvature signal This co-rendering of coherency and the most negative curvature attribute is shown in Figure 27.
Figure 27 presents a three-panel interpretation: panel (a) co-renders the most negative curvature attribute with the coherency attribute across the tracked Viola horizon; panel (b) provides a zoomed-in view of the paleokarst cluster where coherency and the most negative curvature are co-rendered to enhance feature delineation; and panel (c) shows the same paleokarst cluster with the coherency attribute applied Together, these views demonstrate how combining curvature and coherency attributes improves the subsurface interpretation of the Viola horizon and paleokarst features for more accurate geological analysis.
Results and Interpretations
Using ImageJ, 651 paleokarst sinkholes were identified and measured The average area of these sinkholes is 314,018 square feet, and the average Feret-derived diameter is 777.3 feet Roundness was assessed on a scale where 1 represents a perfect circle, and the mean roundness for these paleokarst sinkholes is 0.707 The total paleokarst area sums to 204,425,670 square feet In the 179.19 square miles surveyed, paleokarst sinkholes occupy 4.09% of the area These results are summarized in Table 3.
Average Feret's Minimum Diameter 518.1 Feet 0.10
Northridge Survey Total Area 4,995,530,496 Feet 2 179.19
Table 3 – Paleokarst Statistics derived from ImageJ analysis
Seismic resolution limits, summarized in Table 1, constrain the detection of paleokarst features in the dataset The lateral resolution is 110 feet, so features smaller than 110 feet cannot be resolved by the seismic data Consequently, the calculations presented in Table 3 and the paleokarst sinkhole counts obtained with ImageJ reflect only seismically resolvable features It is reasonable to infer that many additional paleokarst features exist but remain unimageable due to being below the seismic resolution limit The smallest calculated diameter is 120.83 feet, which comfortably exceeds the 110-foot lateral resolution limit.
Of the seismically resolvable paleokarst deposits, histograms were created to display the range in the diameter, and the distribution of circularity (Figure 28 & 29) Displayed on Figure
Paleokarst sinkhole diameters are tightly grouped in the 500–1,500 ft range with few outliers beyond these limits Seismic resolution limits prevent detection of paleokarst features below 110 ft, as shown by Figure 28 where the data cutoff occurs at around 200 ft The average circularity of the paleokarst sinkholes is 0.77, and Figure 29 shows that most sinkholes fall in the 0.9–1 range, meaning they are nearly perfectly circular.
Figure 28 – Histogram of Feret’s diameter of paleokarst sinkholes
Figure 29 – Histogram of circularity of paleokarst sinkholes a Cumulative Distribution Analysis
White et al (1987) applied sinkhole depth distribution calculations from Troester et al
From the 1984 Tennessee sinkhole study, researchers shifted from depth-based to diameter-based distribution analysis, fitting equations to sinkholes by their diameters rather than their depths Applying this diameter-based technique to the study’s data yielded a trend line that allowed calculation of the number of sinkholes below the seismic resolution and an estimated total paleokarst sinkhole count within the survey White et al (1987) concluded that the distribution could be described by a linear equation fitted to the cumulative distribution on a log-normal plot.
White (1988) notes that most karst terrains exhibit a linear distribution of karst feature sizes In their study, the researchers fitted equation (Eq 9) to the data to show the distribution of sinkholes by diameter In Eq 9, N represents the number of sinkholes and d represents the sinkhole diameter The y-intercept is 560, representing the total number of sinkholes, and the slope is -0.0043.
The histogram derived from counting paleokarst sinkholes in Figure 28 was converted into a cumulative distribution function (CDF) shown in Figure 30 To construct the CDF, the bin-centers were calculated, producing points at the center of each bin that correspond to the count values and the centers of the diameter bins.
Figure 30 – Cumulative distribution of paleokarst sinkholes with calculated center of bins trend line
The points collected from the center of bins line on Figure 30 are plotted on a log-normal plot and a trend line (Eq 10) is calculated and applied
By using the trend line shown in Figure 31, the number of paleokarst sinkholes that are not visible due to seismic resolution limits can be estimated The y-intercept of Eq 10 is 1097, which indicates a total of 1,097 paleokarst sinkholes in the study area based on the distribution of sinkhole diameters Subtracting the 651 sinkholes already detected above the seismic resolution limit leaves a revised total of 446 paleokarst sinkholes.
58 sinkholes fall below the 110-foot seismic resolution limit, while 59.3% of the total calculated paleokarst sinkholes (1097) are above the resolution limit and can be imaged The current sinkhole density is 6.12 sinkholes per square mile Notably, the distribution of paleokarst sinkhole diameters in this study follows a linear distribution, a pattern that reinforces the similarity of these paleokarst sinkholes to a typical karst terrain as described by White (1988).
Figure 31 – Log normal plot of cumulative distribution with (Eq 10) applied to calculate and estimated total number of paleokarst sinkholes in the study area
White (1988) detailed the different types of sinkhole features formed through karst processes Figure 32 shows these sinkhole types aggregated by size This study reports diameters ranging from a minimum of 120 feet (36.5 meters) to a maximum of 3586.3 feet (1093 meters), with an average diameter of 777.4 feet (236.8 meters) Plotting these values on Figure 32 provides a visual depiction of sinkhole size distribution.
Figure 32 demonstrates that the range of sinkhole types comprises three main categories, from the smallest to the largest: compound dolines (sinkholes) at the lower end, caprock-protected dolines in the middle, and tropical cockpits at the largest end of the spectrum.
Figure 32 – Sketch illustrating the size scale and associated types of sinkhole features with this study’s data plotted (modified from White, 1988)
Compound sinkholes form when individual sinkholes grow and merge into a single, larger depression with multiple inlet points (White, 1988) Caprock-protected sinkholes are larger, closed depressions that typically develop along the margins of plateaus (White, 1988).
Caprock protects the tops of plateaus, providing early shielding for the limestone until it is breached, after which deep vertical shafts begin to form in the rock Cockpit sinkholes are large karst features primarily found in tropical environments with thick limestone deposits, and the term derives from Jamaica, the type locality, where these sinkholes resemble the bowl-shaped arenas used for cockfighting.
Figure 32 shows the size ranges of sinkholes identified in this study Seismic mapping identifies three generalized sinkhole types in the area: compound sinkholes, caprock-protected sinkholes, and cockpit sinkholes However, the geologic environment of the time period studied suggests that caprock-protected sinkhole features are unlikely in this setting.
By integrating estimates of sinkhole types by size with calculations of the average size, number, and depression density of paleokarst, and combining these results with the Viola Group’s known environmental and geological context, this study defines a modern-day proxy for the paleokarst identified herein Because paleogeography during and immediately after the Viola Group deposition placed the study area in a tropical marine environment, the Cockpit Karst region of Jamaica aligns with these calculations and environmental descriptions, and thus serves as the modern-day proxy for this study’s paleokarst sinkholes.
Based on methods used by Abad (2013), paleokarst sinkholes where characterized by applying coherency, most negative curvature, and most positive curvature to the Viola horizon
Two paleokarst sinkhole types were identified: curved-bottom and flat-bottom paleokarst sinkholes In almost all cases, applying the most negative and most positive curvature to the Viola horizon in a co-rendered curvature map yields a characteristic image for paleokarst sinkholes The outer edge of the sinkhole typically displays positive curvature along the rim, while the interior shows negative curvature within the depression Figure 33 generalizes this pattern, illustrating the positive-curvature rim surrounding the sinkhole and the negative-curvature interior of the sinkhole depression.
Conclusion
This study initially aimed to determine whether petroleum drilling problems observed in the Fort Worth Basin, associated with paleokarst sinkholes in the Ellenburger Group, also occurred in the Arkoma Basin through paleokarst in the Viola Group that hydrologically communicates with Woodford Shale wells However, the cross-basin link was quickly ruled out for several reasons, and the research shifted to mapping and analyzing paleokarst features within the Viola Group in Coal and Hughes Counties, Oklahoma.
This was done by applying seismic mapping techniques and attribute analysis to better highlight the paleokarst sinkholes In particular, coherency and curvature attributes proved to be
Seismic attribute analysis, combined with ImageJ software, proved most effective in highlighting paleokarst sinkholes and in identifying potential formation causes Although ImageJ was originally developed for medical cell counting and had rarely been used in geological studies prior to this work, it demonstrated rapid, accurate counting and measurement of paleokarst sinkhole features Without ImageJ, the counting and measurement process would have been tedious and unlikely to reach the high level of detail and analysis that this software enables.
Seismic analysis identified and measured 651 paleokarst sinkhole features with an average diameter of 777.3 feet, while a lateral seismic resolution limit of 110 feet restricted imaging to sinkholes larger than this threshold A cumulative distribution function was applied to estimate the total number of paleokarst sinkholes, including those below the resolution limit, based on the diameters of the measured sinks, yielding an estimated total of 1,097 sinkholes and implying about 446 sinkholes were not imaged due to seismic resolution limits Because there is effectively no upper bound to what could be resolved, the methods mapped and analyzed all paleokarst features larger than the resolution limit, with the largest observed diameter reaching 3,586.3 feet.
Using the most negative curvature and the most positive curvature attributes to analyze paleokarst sinkholes reveals a different interpretation than when using the coherency attribute The most positive curvature highlights the outer edges or extents of the sinkhole features, while the most negative curvature highlights the depressions within the paleokarst sinkholes.
Mapping and analysis indicate that paleokarst sinkhole formation is controlled by the Viola/Sylvan unconformity The resulting distribution of paleokarst features forms two distinct linear trends: one parallel to regional faulting and another perpendicular to it.
Regionally, paleokarst features in the Viola Group are linked to the development of the Southern Oklahoma aulacogen These features are most concentrated along the outer, shallower edge of the aulacogen, where increased subaerial exposure during sea-level regressions promoted karst development Paleokarst features in the Ellenburger Group of the Fort Worth Basin are thought to reflect a similar process at the far southwest edge of the Southern Oklahoma aulacogen (Abad, 2013).