Abstract

Erosion of the leading hanging-wall cutoffs of thrust sheets commonly obscures the magnitude of thrusting. The Jones Valley thrust fault in the southern Appalachian thrust belt in Alabama, USA, is exposed along a northwest-directed, large-scale frontal ramp, and the leading part of the thrust sheet has been eroded. Previously published and newly collected vitrinite reflectance data from Pennsylvanian coal beds document a distinct, northeast-trending, elongate, oval-shaped thermal anomaly northwest of the trace of the Jones Valley fault. The northwest edge of the thermal anomaly is ~18 km northwest of the fault trace, suggesting the original extent of the eroded thrust sheet. The anomaly ends both northeastward and southwestward along strike at lateral ramps. The southeast edge of the anomaly corresponds to the location of a footwall frontal ramp.

A three-dimensional heat conduction model for simultaneous horizontal (two-dimensional) and vertical heat flow in a rectangular thrust sheet is designed to test whether the documented thermal anomaly (%Ro = 1.0–1.6) may reflect the former extent of thrust-sheet cover. The model uses a 3-km-thick thrust sheet with horizontal dimensions of 10 × 30 km, as well as a three-dimensional analytical solution to the heat conduction equation, whereby the thrust sheet cools both laterally and vertically. The model reproduces the magnitude and oval shape of the vitrinite reflectance anomaly at 100–500 k.y. after thrust emplacement. The geothermal gradient reaches a steady state at ~2 m.y., and is never fully reestablished even for long times because of lateral cooling in the hanging wall.

Thickness and extent of the thrust sheet from the thermal model are consistent with balanced and restored cross sections of the Jones Valley thrust sheet based on geologic data; a thrust sheet ~3 km thick was emplaced ~18 km onto the foreland over the site of the thermal anomaly. The three-dimensional thermal evolution of both the hanging wall and the footwall is distinct from that predicted from one-dimensional models; a three-dimensional model predicts less heating of the footwall because of horizontal heat loss across bounding ramps.

INTRODUCTION

In exposed thrust belts, the leading hanging-wall cutoffs of the thrust sheets commonly have been removed by erosion, and as a result, the magnitude of thrusting is difficult to quantify. Tectonic thickening by thrust imbrication and stacking increases the thickness of the effective cover, which acts as a thermal blanket; therefore, the thermal history of an exhumed footwall may record the original (post-emplacement) extent of a subsequently eroded thrust sheet (e.g., O'Hara et al., 1990). The areal extent of a thermal anomaly induced by excess cover constrains the magnitude of thrusting by showing the original (pre-erosion) extent and thickness of the thrust sheet over the footwall. As an example, the Jones Valley fault in the southern Appalachian thrust belt in Alabama, USA, is exposed along a northwest-directed, large-scale frontal ramp (Fig. 1); the leading part of the Jones Valley thrust sheet, including the leading hanging-wall cutoffs, has been eroded. Previously published (Winston, 1990a) vitrinite reflectance data document a distinct thermal anomaly northwest of the trace of the Jones Valley fault; a map of coal rank, using volatile matter and vitrinite reflectance, confirms the extent of the anomaly (Fig. 2)1 (Pashin et al., 2004, 2008). The location of the thermal anomaly corresponds to that of the possible original leading part of the Jones Valley thrust sheet, which has been eroded. The purpose of this research is to quantify the possible original extent and geometry of the thrust sheet in the context of the location and magnitude of the thermal anomaly in the eroded footwall.

GEOLOGIC SETTING OF THE THERMAL ANOMALY

The previously documented thermal anomaly has an elongate, oval shape parallel to regional structural strike along the southeastern edge of the Black Warrior foreland basin at the leading edge of the Appalachian thrust belt (Figs. 1 and 2). The southeast boundary of the anomaly is along the Blue Creek anticline-syncline pair, relatively low-amplitude structures northwest of the trace of the Jones Valley thrust fault (Fig. 2). The anomaly ends northeastward along strike at the Bessemer transverse zone, an alignment of cross-strike links (lateral ramps and displacement-transfer zones) across the Appalachian thrust belt (Figs. 1 and 2). At the Bessemer transverse zone, the Opossum Valley thrust sheet ends southwestward along strike in the footwall of the Jones Valley fault, and displacement is transferred via a dextral lateral ramp to the Jones Valley fault. The southwest end of the anomaly is across strike northwest of a sinistral curve in the Jones Valley fault, indicating a sinistral lateral ramp (Fig. 2).

The Pennsylvanian Pottsville Formation forms all of the present outcrop area in the footwall and more distal foreland of the Jones Valley fault, including the area of the vitrinite reflectance anomaly. The Pottsville Formation includes two distinct parts (Fig. 3). The lower Pottsville is characterized by relatively quart-zose massive sandstones and includes thin shale intervals and some coal beds. The upper Pottsville has a classic “coal measures” stratigraphy, dominated by mudstones and including numerous coal beds and some sandstone (Fig. 3) (Pashin, 2004, 2005). These are the commercial mineable coals of the Warrior coal field and are also the resource for coalbed methane production. Exposed and subsurface coal beds provide for an array of samples for vitrinite reflectance analyses to document the extent and magnitude of the thermal anomaly.

DOCUMENTATION OF THE THERMAL ANOMALY

Data

This study combines previously published vitrinite reflectance data (Table 1) (Winston, 1990a) with new data (Table 2). The previously published data (Table 1) are measurements of mean maximum vitrinite reflectance (%Rmax), whereas the newly collected data (Table 2) are measurements of mean random vitrinite reflectance (%Ro). A standard conversion of %Rmax = 1.06 %Ro (Hower, 1978) was applied (Table 1) for preparation of the contour map of reflectance values in Figure 2.

Coal samples have been collected from outcrops, underground mines, surface mines, core holes, coalbed methane wells, and petroleum exploration wells. The samples span the stratigraphic range of coal beds from the Brook-wood coal group down into the lower Pottsville (Fig. 3). Localities for collection of new samples for this research were spaced around the location of the previously recognized thermal anomaly, as well as more distant from the anomaly to confirm background values.

Geothermal Gradient

Assuming a steady state, where the upward heat flow is constant, the geothermal gradient is given by λ = q/k, where q is heat flow and k is the thermal conductivity of the rock. The geothermal gradient varies from one lithology to another, especially in coal-bearing shale-rich successions (e.g., Fig. 3), because the thermal conductivities of shale and coal are much less than those of limestone and sandstone (Blackwell and Steele, 1989). As a result, a succession of shale and coal acts as a thermal blanket and, locally at least, increases the geothermal gradient (Cercone et al., 1996).

In several core holes and wells, coal samples from multiple horizons were analyzed. From these vertical successions of data, a geothermal gradient was calculated by converting %R to temperature (T), using the time-independent equation, T(°C) = [ln(%R) + 1.26]/0.00811, from Barker and Goldstein (1990). Calculations from different boreholes indicate geothermal gradients between ~65 °C/km and ~35 °C/km (Fig. 4).

Vitrinite reflectance data for the Mary Lee coal (Fig. 3) show a consistent regional background with %R values of <1.0 (Winston, 1990a), indicating a maximum temperature of ~155 °C. Density logs show that shale in the coal-bearing succession is fully compacted, indicating a minimum thickness of sedimentary cover of ~3 km (Hines, 1988). A thickness of 3 km of sedimentary cover is consistent with %R = 1.0 for Mary Lee coal (Carroll et al., 1993) and an average geothermal gradient of 45 °C/km. The computed local geothermal gradient through the coal-bearing interval in two boreholes is 64 °C/km (Fig. 4). The gradient cannot be that great through the entire stratigraphic section within the thermal anomaly, however, because an average geothermal gradient of 64 °C/km through a 3-km-thick cover would yield background temperatures of >200 °C at the Mary Lee stratigraphic level, higher than documented thermal indicators. The geothermal gradient is steepened by low thermal conductivity in successions with relatively high proportions of shale and coal, and the measured 64 °C/km gradient apparently is a stratigraphically localized anomaly. A regional gradient of 45 °C/km is more appropriate here and is similar to measured gradients of 38–47 °C/km in the coal-bearing shale-dominated successions of the Appalachian basin in Pennsylvania (Cercone et al., 1996).

The applicability of an average geothermal gradient of 45 °C/km for this area can be tested for the stratigraphic section shown in Figure 3, by weighting the thermal conductivities of different lithologies with respect to thicknesses. Figure 3 indicates ~45% sandstone, >53% shale, and <2% coal over a total thickness of 2 km. Assuming thermal conductivities of 2.5, 1.0, and 0.2 W/mK for sandstone, shale, and bituminous coal, respectively (Singer and Tye, 1979; Blackwell and Steele, 1989), the mean thermal conductivity is 1.66 W/mK. This value is the same as that estimated by Cercone et al. (1996) for the stratigraphic column in the northern Appalachian basin. A geothermal gradient of 45 °C/km indicates a heat flow of 75 mW/m2, which is a reasonable value for a continental orogenic site (Bott, 1982).

Normalizing the Data to the Depth of the Mary Lee Coal

To remove the thermal effects of different amounts of sedimentary burial at different stratigraphic levels, vitrinite data from stratigraphically higher and lower coals were normalized to the stratigraphic level of the Mary Lee coal by using the geothermal gradient in a particular bore hole or by using a gradient of 64 °C/km for the coal-bearing interval (Tables 1 and 2). The Mary Lee coal was selected for the norm because more data are from that level than any other, and because it is near the middle of the stratigraphic interval of data sources.

MAP DISTRIBUTION OF THE THERMAL ANOMALY

The data normalized to the Mary Lee level closely constrain a local thermal anomaly northwest of the eroded leading edge of the Jones Valley thrust sheet (Fig. 2). The oval anomaly is elongate parallel to northeasterly Appalachian structural strike, and it ends in both directions along strike. Steep gradients define both the northwest and southeast edges of the anomaly. The area of anomalously high coal rank is ~300 km2 and has vitrinite reflectance values of 1.2–1.6 %Ro, a maximum of >0.6 %Ro above the regional background (Fig. 2) (Culbertson, 1964; Telle et al., 1987; Winston, 1990a, 1990b; Pashin and Hinkle, 1997).

DISCUSSION OF POSSIBLE CAUSES OF THE THERMAL ANOMALY

Various causes have been or can be suggested for the thermal anomaly. The oval-shaped geometry and areal extent of the anomaly impose significant constraints on the cause. The anomaly has a relatively small area and relatively steep gradients, especially at the southeast and northwest margins, giving a short-wavelength–high-amplitude (steep gradient) profile. Therefore, possible causes that yield a long-wavelength–low-amplitude (gentle gradient) profile are rendered unlikely. The thermal anomaly must be a result of locally higher temperature than the regional temperature (Winston, 1990b).

Possible causes of increased heat flow include plutonism at depth (e.g., Telle et al., 1987) and/ or excess radioactivity in the underlying crust. Lack of a gravity or magnetic anomaly associated with the area of high-rank coal (Winston, 1990b), as well as a lack of other independent verification and a lack of known late Paleozoic plutons in the southern Appalachian thrust belt, casts doubt on the former interpretation. Excess radiogenic heat from the crust would produce a broad, long-wavelength–low-amplitude thermal anomaly, unlike the configuration of the documented anomaly. Although frictional heating along active faults may be important on a centimeter scale, it is not thought to be important on a kilometer scale during thrust emplacement (e.g., Bustin, 1983; O'Hara, 2004).

Advective heat transport associated with local uplift and rapid erosion provides another alternative heating mechanism. Rapid removal of ~3 km of overburden could produce substantial heating in ~500 k.y. (Turcotte and Schubert, 2002); however, the wavelength and amplitude of the documented anomaly require a local steep-sided uplift that is precluded by the outcrop and subsurface geology. A regional isostatic uplift would have a long wavelength relative to amplitude. The estimated heat flow (~75 mW/m2) is not anomalous for this region, suggesting that local anomalous heat flow is not the cause of the anomaly.

Hydrothermal fluid flow also has been suggested as a cause of the anomaly (e.g., Winston, 1990a), involving either orogenic fluids derived from the Appalachian orogen on the southeast (e.g., Goldhaber et al., 2003) or circulation of hot meteoric water. Calcite-filled fractures (joints and cleats) in the Pottsville Formation indicate that fractures did serve as conduits for fluid flow in the basin (Pitman et al., 2003). Oxygen isotope analyses of the calcite, however, indicate that this fluid flow is consistent with influx of low-temperature (30–50 °C) meteoric water late in the history of the basin. This water would have been too cool to cause the observed anomaly in the coals of ~50 °C above background (~155 °C) at the depth of the Mary Lee coal. The lack of higher temperature hydrothermal mineralization in the coal cleats that formed during maturation (Pitman et al., 2003) argues against a hydrothermal origin for coal maturation. Orogenic fluids derived from the southeast would be unlikely to produce the observed oval-shaped anomaly, which is separated from the frontal large-scale thrust fault and isolated in the foreland; instead, such an anomaly would be expected to extend into the foreland directly from the structural front, contrary to the observed pattern. In the absence of shallow-level igneous plutons beneath the anomaly, convective circulation of hot groundwater is also an unlikely source of the anomaly.

Localized excess thickness of sedimentary cover is a possible cause of a thermal anomaly. The observed area of anomalous coal rank, however, cannot be explained by a locally greater depositional thickness of sedimentary cover because the contours of %R are not affected by the Blue Creek anticline (Fig. 2), indicating late syntectonic to posttectonic coalification (Winston, 1990a; Pashin et al., 1999). Furthermore, the local magnitude and abrupt boundaries of the anomaly are not compatible with reasonable gradients of depositional thickness in a foreland basin, such as the setting of Pottsville deposition (Thomas, 1988; Pashin, 2004).

We propose, instead, that the thermal anomaly is primarily the result of local excess tectonic cover caused by emplacement of a thrust sheet (O'Hara et al., 2006). The anomaly is inferred to be in the footwall of the now-eroded thrust sheet, the eroded leading trace of which is the Jones Valley fault southeast of the anomaly (Fig. 2). Both along-strike ends of the anomaly are aligned with lateral ramps, a dextral lateral ramp on the northeast and a sinistral lateral ramp on the southwest. A three-dimensional thermal model is needed to test whether a thrust sheet of the possible dimensions of the Jones Valley thrust sheet will account for the documented thermal environment.

DESIGN OF A THREE-DIMENSIONAL COOLING MODEL

That thin-skinned thrust sheets are commonly bounded by both frontal and trailing ramps has been long recognized (e.g., Rich, 1934; Boyer and Elliott, 1982). Similarly, along-strike terminations of thrust sheets at lateral ramps, transverse faults, displacement-transfer zones, and displacement gradients are widely recognized (Boyer and Elliott, 1982; Laubscher, 1985; Price, 1988; Thomas, 1990; Thomas and Bayona, 2002). In a model thrust sheet (Fig. 5), after thrust emplacement, cooling is inferred to occur laterally across a leading hanging-wall frontal ramp, two hanging-wall lateral ramps, and a trailing hanging-wall fault-bend fold over a footwall frontal ramp, as well as downward by heating of the footwall. This requires three-dimensional modeling to better understand the thermal history of both the hanging wall and footwall.

Three-dimensional cooling of an instantaneously emplaced thrust sheet with horizontal dimensions of 10 × 30 km and a thickness of 3 km is used to model the coal-rank anomaly mapped in Figure 2. These dimensions were selected to represent the mapped extent of the thermal anomaly and the maximum excess temperature (~50 °C, Fig. 2) above the background level in the footwall within a reasonable time frame. A thrust sheet 3 km thick produces temperatures in the model that correspond to those indicated by vitrinite reflectance data (Fig. 2), and the 3 km thickness is consistent with stratigraphic thickness in thrust sheets regionally (Thomas and Bayona, 2005). In contrast, models using thrust sheets 5 km and 1 km thick produce temperatures that are greater and lesser, respectively, than those indicated by the vitrinite reflectance data. The oval heating pattern in the footwall (Fig. 2) is interpreted to represent the thermal imprint of the now-eroded thrust sheet. The sides of the thrust sheet are kept at constant ambient temperature (T = To), and the temperature with depth in the footwall is given by T = Tb + λ(zc), where Tb is temperature at the top of the footwall, λ is geothermal gradient, z is total depth, and c is thrust-sheet thickness. The 3D thermal diffusion equation to compute the temperature distribution, T(x,y,z,t), is:  
formula
where T is temperature, x and y are orthogonal horizontal coordinates, z is depth (vertical direction and positive downward), κ is thermal diffusivity, t is time, a and b are the orthogonal horizontal dimensions of the thrust sheet, c is the thickness of the thrust sheet, and (1+f) is the ratio of thickness in the footwall underlying the thrust sheet to that of the thrust sheet. The boundary conditions are given by equations 1b and 1c, and the initial condition is given by equation 1d (Appendix). The solution to this equation under these conditions is presented in the Appendix.

RESULTS OF THE THERMAL MODEL

The thermal model can be represented graphically for three-dimensional cooling at the center of a thrust sheet with dimensions of 3 × 10 × 30 km. Dimensionless depth is plotted against dimensionless temperature for different dimensionless times (Fig. 6). For both very rapid (e.g., Oxburgh and Turcotte, 1974) and geologically reasonable thrust velocities (1–10 cm/yr; Karabinos and Ketcham, 1988), the footwall undergoes heating (i.e., prograde metamorphism) because of downward heat flux across the thrust fault as the geotherm is reestablished. In the three-dimensional model (Fig. 6), the temperature reaches a steady state at ~2 m.y., and the geotherm never is fully reestablished, because of lateral cooling of the thrust sheet. For earlier times, however, the results of one-dimensional and three-dimensional models are very similar (Fig. 6) (e.g., Furlong and Edman, 1984).

At the base of the thrust sheet in the model (Fig. 6), the dimensionless depth is 3 km/3 km = 1.0, and at the depth of the Mary Lee coal (3 km beneath the thrust fault) it is = 2.0. The dimensionless time τ ( = κt/c2) at 1 m.y. is 3.5, where κ = 10−6 m2/s, t = 3.15 × 1013 s, and c = 3000 m. From Figure 6, these values (z/c = 2.0 and τ = 3.5) give a dimensionless temperature (scaling factor) of 1.3. The temperature at a depth of 3 km below the thrust fault at 1 m.y. is then [20 °C + (45 °C/km × 3 km)] × 1.3 = 202 °C. This temperature is close to the maximum attainable as the temperature reaches a steady state ~2 m.y. after thrusting.

Figure 7 shows the temperature contours at a depth of 3 km in the footwall for various times after emplacement of the thrust sheet. An elongated oval pattern develops after 100 k.y. (Fig. 7D) and intensifies up to 1 m.y. (Fig. 7F). Vertical cooling of the hanging wall and heating of the footwall, in combination with lateral cooling across the bounding ramps of the hanging wall, imprint an oval pattern of heating in the footwall. The maximum temperature obtained is ~200 °C (Fig. 7). Using the time-independent conversion of Barker and Goldstein (1990), this temperature is in good agreement with a %Ro value of 1.6, which corresponds to 213 °C. Using the kinetics-based software (EasyR%; Sweeney and Burnham, 1990) and a mean heating rate corresponding to ~200 °C over 500 k.y., a similar value for %Ro is calculated to be 1.55. Therefore, both a time-independent conversion and a time-dependent conversion of the observed %Ro values yield a similar temperature of ~200 °C. This temperature is close to the maximum obtainable using a three-dimensional cooling model at this depth (Fig. 6). The similarity between the observed vitrinite reflectance pattern (Fig. 2) and predicted isotherms (Fig. 7), in both shape and magnitude, suggests that the anomaly was caused by heating of the footwall by a now-eroded thrust sheet, which in addition to heating the underlying rocks, also cooled laterally. In this respect, the thermal anomaly is analogous to the burn pattern produced on a silk shirt by an overly hot clothes iron. For reasonable erosion rates (e.g., 1 mm/yr), a 3-km-thick thrust sheet would not be removed by erosion before heating of the footwall occurs (500 k.y.; Fig. 7E). Imbrication of the thrust sheet may have contributed to the thermal anomaly, and the thermal diffusivity may have been anisotropic, but for simplicity, these possibilities were not considered here.

A challenge to the applicability of the model is that the southeast margin of the thermal anomaly is along the Blue Creek anticline ~8 km northwest of the present trace of the Jones Valley fault at a frontal ramp (Fig. 2). The footwall immediately northwest of the present map trace of the Jones Valley fault shows background-level vitrinite reflectance. The geometry of the frontal ramp must accommodate that temperature distribution.

RELATIONSHIP OF THERMAL MODEL TO STRUCTURAL GEOLOGY

Northwest Edge of the Thermal Anomaly; Leading Edge of the Jones Valley Thrust Sheet

A balanced and restored structural cross section (Fig. 8) is consistent with the emplacement of a 3-km-thick thrust sheet 18 km northwest-ward onto the foreland, corresponding to the location and magnitude of the thermal anomaly. The now-eroded leading part of the thrust sheet is reconstructed to cover the area of the thermal anomaly (Fig. 8B). The palinspastic reconstruction (Fig. 8C) uses line-length balancing of the regional stiff layer (massive carbonates of the Upper Cambrian–Lower Ordovician Knox Group) and area balancing of the regional weak layer that hosts the Appalachian décollement (shale-dominated succession of Middle Cambrian–lower Upper Cambrian Conasauga Formation). The restored cross section is consistent with similarly restored cross sections along strike (Thomas and Bayona, 2005). The stratigraphic composition and thickness of the eroded thrust sheet are modeled from regional stratigraphy. The magnitude of the thermal anomaly indicates a total cover thickness above the Mary Lee coal group of ~6 km. This is modeled in the cross section as ~3 km of sedimentary cover in the footwall, indicated by the background coal rank outside the anomaly of <1.0%Ro (Fig. 2) and a 3-km-thick tectonic cover corresponding to the Jones Valley thrust sheet (Fig. 8). The structural cross section (Fig. 8B) shows an interpretation of the thickness and extent of the eroded part of the Jones Valley thrust sheet; the projection of an inferred synthrusting erosion surface limits the thrust-sheet thickness to 3 km, conforming to a total 6-km-thick cover necessary to account for the magnitude of the thermal anomaly. The palinspastically restored cross section (Fig. 8C) shows the relation of the stratigraphy in the now-eroded thrust sheet to that in the presently preserved footwall.

The northwest edge of the thermal anomaly is interpreted to mark the location of the hanging-wall frontal-ramp cutoff along the leading limb of a fault-bend (ramp) anticline at the leading edge of the Jones Valley thrust sheet. The northwestern gradient of the thermal anomaly corresponds to the northwestward thinning of the thrust sheet at the hanging-wall frontal ramp (Fig. 8). The highest temperature values in the thermal anomaly correspond to the crest of the ramp anticline.

The interpreted magnitude of translation of the Jones Valley thrust sheet is tested in a palinspastic restoration (Fig. 8C) by balancing two independent stratigraphic criteria. Seismic reflection profiles show a large mass, lacking in internally coherent reflectors, beneath the preserved frontal ramp of the Jones Valley thrust fault (Thomas and Bayona, 2005; Thomas, 2007). A well along strike to the northeast and additional seismic reflection profiles indicate that the subsurface mass is a ductile duplex (mushwad) of the shale-dominated Middle to lower Upper Cambrian Conasauga Formation (Thomas, 2001). Area balance of the mushwad palinspastically restores the thick Cambrian shale into the Birmingham basement graben, the geometry of which is documented in seismic reflection profiles (Fig. 8) (Thomas, 2001, 2007; Thomas and Bayona, 2005). The regionally persistent Upper Cambrian–Lower Ordovician Knox Group of massive carbonate rocks, the regionally dominant stiff layer in Appalachian structures, is anomalously thin, where most of the upper units are locally truncated at a regional unconformity beneath Middle–Upper Ordovician strata (Bayona and Thomas, 2003; Thomas and Bayona, 2005; Thomas, 2007). Systematic reconstruction along strike shows that the area of anomalously great truncation of the upper Knox Group restores palin-spastically within the Birmingham graben, and mechanical modeling indicates that the excess erosion is a result of basement fault inversion during Taconic (Ordovician) tectonic loading (Bayona and Thomas, 2003). Successful area balancing of the thick Cambrian shale in the Birmingham graben and the comparable restoration of the truncated Knox Group within the graben are consistent with an 18 km displacement required to place the leading edge of the Jones Valley thrust sheet over the area of the thermal anomaly. The internally consistent geometry of the restoration is a strong test of the validity of the cross section.

Along-Strike Limits of the Thermal Anomaly; Jones Valley Lateral Ramps

Northwest of the Jones Valley fault, the Sequatchie anticline is a detachment anticline along the foreland limit of the regional décollement, marking the front of the Appalachian thrust belt along the southeast side of the Black Warrior foreland basin (Fig. 1). The trailing limb of the Sequatchie anticline defines the Coalburg syncline, the southeast limb of which is steeply upturned to overturned.

The thrust-belt structures show abrupt along-strike changes in structural profile across the Bessemer transverse zone, which is a cross-strike alignment of cross-strike links (lateral ramps, transverse faults, displacement transfers, and displacement gradients) in thrust-belt structures (Thomas, 1990; Thomas and Bayona, 2005). Northeast of the Bessemer transverse zone, the Opossum Valley fault is a leading splay of the Jones Valley fault (Figs. 1 and 2), and the steep upturn of the southeast limb of the Coalburg syncline is in the footwall of the Opossum Valley thrust sheet, which forms the footwall of the Jones Valley fault. South-westward along strike across the Bessemer transverse zone, the Sequatchie anticline ends through a displacement gradient, and beyond the southwest end of the anticline, the Coalburg syncline merges with the Black Warrior foreland basin. The Opossum Valley thrust sheet ends southwestward in the Bessemer transverse zone at a lateral ramp in the Jones Valley footwall (Fig. 2). The Blue Creek fault extends along strike southwestward from the lateral ramp at the southwest end of the Opossum Valley thrust sheet; however, the Blue Creek fault passes southwestward into a blind fault beneath the low-amplitude Blue Creek anticline and a trailing syncline. The structural geometry of the Blue Creek anticline-syncline pair reflects an upper-level flat-and-ramp geometry of the Blue Creek fault (Fig. 8). The steep upturn of the trailing limb of the Coalburg syncline in the footwall of the Opossum Valley fault is transferred sinistrally via a lateral ramp to the trailing limb of the Blue Creek syncline in the Blue Creek hanging wall, which is in the footwall of the Jones Valley fault. The steep to overturned southeast limb of the Blue Creek syncline includes a folded southeast-verging backthrust. The Jones Valley fault cuts southwestward across the Opossum Valley lateral ramp onto the steep upturned trailing limb of the Blue Creek syncline in the Blue Creek thrust sheet (Fig. 2). The steeply upturned southeast limb of the Blue Creek syncline and the structurally comparable southeast limb of the Coalburg syncline represent the folded footwalls of the Jones Valley fault and Opossum Valley fault, respectively. Because the trailing cutoff of the Opossum Valley thrust sheet is the leading cutoff of the Jones Valley fault, the lateral ramp at the southwest end of the Opossum Valley fault must have had a counterpart dextral lateral ramp in the now-eroded leading part of the Jones Valley thrust sheet. The dextral lateral ramp corresponds to the northeast end of the thermal anomaly (cf. Fig. 2 and Fig. 5).

Along strike southwestward, near where the Appalachian structures pass southwest-ward beneath postorogenic cover of the Gulf Coastal Plain, the trace of the Jones Valley fault describes an abrupt sinistral curve (Fig. 2), marking a sinistral lateral ramp. Across strike to the northwest, plunging folds indicate a similar lateral ramp in the Blue Creek fault, conforming to an Appalachian transverse zone approximately along the present eroded edge of the Gulf Coastal Plain (Surles and Thomas, 2006; Surles, 2007), here termed the Coastal Plain transverse zone (Figs. 1 and 2). The sinistral lateral ramp in the Jones Valley fault corresponds to the southwest end of the thermal anomaly.

Southeast Edge of the Thermal Anomaly; Jones Valley Footwall Frontal Ramp

The southeast (trailing) edge of the thermal anomaly corresponds to the present location of the Blue Creek anticline-syncline pair in the footwall of the Jones Valley fault and is ~8 km northwest of the presently exposed trace of the Jones Valley fault. Southeast of the anomaly, vitrinite reflectance values are at the background level (Fig. 2), consistent with a 3-km-thick cover. The Jones Valley fault ramps through the steeply upturned beds along the southeastern trailing limb of the Blue Creek syncline. The thermal values are consistent with a footwall flat approximately at the level of the Mary Lee coal across a flat structural shoulder between the steep upturn on the southeast and the shallow depression of the Blue Creek syncline on the northwest (Fig. 8). Emplacement of the Jones Valley thrust sheet over a flat approximately at the level of the Mary Lee coal results in negligible footwall stratigraphic cover and a 3-km-thick tectonic (thrust-sheet) cover. The northwest edge of the footwall flat is approximately at the Blue Creek anticline, which may have deflected the Jones Valley fault upward into a northwest-vergent foot-wall frontal ramp, accounting for the base of the southeastward gradient of the thrust-related thermal anomaly. The southeastern base of the southeastward gradient, ~8 km northwest of the present eroded trace of the Jones Valley fault, is interpreted to mark the base of a footwall frontal ramp where the fault cuts upsection in the footwall northwestward in the direction of transport from a stratigraphic level near the Mary Lee coal group (over the area of background thermal values) to a stratigraphic level ~3 km higher over the area of the thermal anomaly (Fig. 8). In that configuration, the southeastward gradient of the thermal anomaly corresponds in area to that of the southeast-dipping footwall frontal ramp.

Regional Distribution of Displacement on the Jones Valley Thrust Fault

Regionally, the Jones Valley fault ends northeastward along strike in the Harpersville transverse zone through a displacement gradient (Fig. 1) (Thomas and Bayona, 2005). From zero displacement at the northeast end, displacement increases southwestward along strike of the Jones Valley fault; however, because the leading hanging-wall cutoffs have been eroded, the amount of thrust translation has not been quantified. Lateral ramps at the Bessemer and Coastal Plain transverse zones bound a leading salient of the Jones Valley thrust sheet; however, the leading part has been eroded. The thermal anomaly, which is documented by vitrinite reflectance (Fig. 2), shows the original extent of the Jones Valley thrust sheet, thereby quantifying the magnitude of thrust translation. The Jones Valley fault may have a classic bow-and-arrow trace and thrust displacement, decreasing to zero in both directions along strike from a maximum of ~18 km at the thermal anomaly.

DISCUSSION AND CONCLUSIONS

Crustal thickening as a result of thrusting in orogenic belts is recognized as an important cause of regional metamorphism, and thermal models of thrust belts have provided valuable insight into the interplay between tectonics and metamorphism (e.g., Oxburgh and Turcotte, 1974; Chamberlain and England, 1985; Karabinos and Ketcham, 1988; Spear et al., 1990). To date, most thermal models have been based on heat conduction in one or two dimensions for a thrust sheet of infinite horizontal extent. Two-dimensional modeling of thrust sheets in the horizontal and vertical directions shows that the time-temperature history varies considerably with the lateral position within the thrust sheet (Karabinos and Ketcham, 1988; Shi and Wang, 1987; Huerta and Rodgers, 2006). In this study, we use a three-dimensional heat conduction model to evaluate simultaneous vertical and two-dimensional horizontal heat transport in a rectangular thrust sheet. The three-dimensional model reproduces both the magnitude and the oval shape of anomalously high coal rank parallel to the thrust front in the southern Appalachians. Thickness and extent of the Jones Valley thrust sheet from the thermal model are consistent with balanced and restored cross sections based on geologic data. A thrust sheet ~3 km thick was emplaced ~18 km onto the foreland over the thermal anomaly. With these initial and boundary conditions, a solution to the three-dimensional heat conduction equation reproduces the magnitude and shape of the thermal anomaly in a time interval of 100–500 k.y. An important result of the three-dimensional model is that the geotherm in the hanging wall or foot-wall is never fully reestablished even after long times, because of lateral heat loss.

Lateral ramps are recognized as important features of thrust sheets. The three-dimensional thermal evolution of both the hanging wall and the footwall in thrust systems is distinct from that predicted by one-dimensional models; a three-dimensional model predicts less heating of the footwall because of horizontal heat loss across bounding lateral ramps. Horizontal cooling across ramps bounding thrust sheets may be an important orogenic cooling process, and may partly explain the paucity of thrust-related heat anomalies in the geologic record.

APPENDIX: SOLUTION PROCEDURE

We solve the 3D thermal diffusion equation to compute the temperature distribution, T(x,y,z,t):  
formula
where T is temperature, x and y are orthogonal horizontal coordinates, z is depth (vertical direction and positive downward), κ is thermal diffusivity, t is time, a and b are the orthogonal horizontal dimensions of the thrust sheet, c is the thickness of the thrust sheet, and (1+f) is the ratio of thickness in the footwall underlying the thrust sheet to that of the thrust sheet.
The boundary conditions are:  
formula
and  
formula
where λ is the geothermal gradient.
The initial condition is:  
formula
where H(z), the Heaviside or step function, is given by:  
formula
where we assume that the z-coordinate is positive downward. In order to solve the partial differential equation defined by equation 1 analytically, we need homogeneous boundary conditions. This can be easily accomplished by the transformation:  
formula
which leads to  
formula
The last term of equation 3b is the geothermal gradient multiplied by the Dirac-Delta function, δ(z – c). Therefore, equation 3b can be rewritten as:  
formula
Substituting equations 3a and 3c into equation 1, the diffusion equation is transformed into:  
formula
with homogeneous boundary conditions:  
formula
 
formula
and a transformed initial condition:  
formula
A pseudo-source term, Q(z), now appears in the diffusion equation (equation 4a), given by:  
formula
Although the last term of equation 4e is not defined (because it is the derivative of the Dirac-Delta function), the Fourier coefficients of the series solution of equation 4a are all defined, and can be exactly computed. This is because the differential operator is cancelled by the integral operator during Fourier coefficient determination, giving back the Dirac-Delta function (see below). Equation 4 can be solved using the method of eigen-function expansions. Assume that the solution is the summation of an infinite series of eigen-function products, having the form:  
formula
Equation 5a satisfies all the boundary conditions of equation 4. We further assume that both the initial condition Φ(z) and the source term Q(z) can be similarly expressed, i.e.,  
formula
and  
formula
The Fourier coefficients for Φ are given by:  
formula
Substituting equation 4d into equation 6a, the Fourier coefficients for the eigenfunction expansion of Φ are:  
formula
Similarly, substituting equation 4e into equation 6a (with Φ replaced by Q), the Fourier coefficients for the eigen-function expansion of Q are:  
formula
Both ϕmnq and qmnq are non-zero only if both m and n are odd. Substituting equations 5a and 5b into equation 4a, we obtain a first-order ordinary differential equation for the Fourier coefficients for u: Amnq(t), in terms of the Fourier coefficients for Q and Φ. The solution to this ordinary differential equation is:  
formula
where αmnq is given by:  
formula

Thus the Fourier coefficients for u can be directly computed by substituting equations 6, 7, and 8b into equation 8a. A Fortran 90 code was written to compute the series summation solution efficiently. At each time step, the temperature distributions corresponding to 6 depths between 1 km and 6 km, at 1 km intervals, were estimated over a computational grid of 51 × 26 nodes. In addition, the temperature profile along a vertical line perpendicular to the thrust plane, passing through the center of the thrust sheet (x = a/2, y = b/2), was computed at a depth resolution of ~50 m (141 nodes). To test for convergence of the solution, as well as accuracy, partial sums were estimated at a few sample locations using a spreadsheet. These partial sums were computed, using successively larger numbers of terms, until the solution converged to within 0.1 °C. The series summation converged after ~100,000 terms. In order to be conservative, however, the solutions presented here were computed using more than 250,000 non-zero terms (i.e., for m = 1 to 100, n = 1 to 100, and q = 0 to 100).

Acknowledgment is made to the donors of the Petroleum Research Fund (38965), administered by the American Chemical Society, for support of this research. Jack Pashin provided the graphics files for Figure 3 and the volatile-matter contour map in Figure 2, as well as helpful advice on sample selection and a review of a draft of the manuscript. Richard Carroll provided numerous core samples from boreholes. Brian Cook, Liz Dodson, and Carrie Kidd assisted in the compilation and computation for the tables and Figure 4. We thank John Costain, Rick Groshong, Bob Hatcher, and Sid Jones for helpful reviews of the manuscript.

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