Gravity Profiles Research Articles

3D geophysical inversions of the north‐east Amer Belt and their relationship to the geologic structure

ABSTRACTThe Amer Lake area is located within the Churchill Structural Province in the Kivalliq Region of Nunavut, approximately 160 km north‐west of Baker Lake. Two distinct geophysical‐geological entities are structurally intercalated: an Archean mixed granitoid gneiss – metasedimentary‐metavolcanic basement and the unconformably overlying Paleoproterozoic Amer Group metasediments. From east of Amer Lake stretching toward the south‐west, these two entities form the Amer fold and thrust belt. At the north‐east end of this belt, high‐resolution aeromagnetic data define a distinctive oval shape that has been interpreted as a south‐west trending doubly plunging synform. The outcrop within the interior of this structure is sparse resulting in limited structural data and speculative geological interpretations with multiple geometries possible. The high‐resolution aeromagnetic data compiled through an industry‐government consortium and newly acquired detailed gravity profiles were modelled to provide constraints on the geometry of this synform.We document a geophysical‐geological feedback process whereby the available geological and geophysical data were used to derive constraints on inversion models for the synform. Starting with available limited litho‐structural data the presence of a double plunging synform was directly inferred from the aeromagnetic data. Segments of the aeromagnetic data have 2D morphology and so can be modelled using a simple parametric 2D dipping slab inversion approach. Models of profiles extracted from the aeromagnetic data were used to provide preliminary dip and magnetic susceptibility constraints for the Three Lakes mudstone with iron formation and the Five Mile Lake basalt. Landsat imagery outlined the spatial limits of the stratigraphically underlying, non‐magnetic Ayagaq quartzite. Incorporating these outputs as bounds in the input / reference model for a UBC‐GIF 3D magnetic inversion helped to accentuate the geological structure in the output mesh: an enhanced inversion that incorporates both geological and geophysical constraints. The validity of the resulting inversion model was tested by computing 2D forward models of the gravity profile data. The inversion model generated by this study emphasizes the importance of integrating information from as many knowledge sources as one can find. More trust can be placed on forward and inversion models where there is agreement among all data sets and a coherency of structural style.

Displacement along the Red River Fault constrained by extension estimates and plate reconstructions

Significant E‐W extension and/or compression must have been generated by displacements along the Red River Fault (RRF) since its curvature does not match a small circle centered at the Euler pole for the Indochina–south China plate pair. The amount of extension perpendicular to the RRF offshore Vietnam depends on the magnitude of left‐lateral displacement along the RRF. In general, the larger the left‐lateral displacement along the fault, the smaller the amount of E‐W extension. All purely strike‐slip models of the opening of the South China Sea that assume large displacements (>250 km) along the RRF encounter major problems because they imply little extension, or even considerable shortening, offshore east Vietnam. This is inconsistent with the presence of large elongated basins offshore Vietnam. Using a plate tectonic model, we compare continental extension values implied by different magnitudes of displacement along the RRF with crustal stretching estimates derived from 2‐D profiles modeled from gravity data. We utilize 2‐D gravity forward models to restore the extended continental margin crust to its original position prior to extension. We find that substantial amounts of extension for offshore Vietnam can only be modeled assuming moderate displacements along the RRF compatible with the presence of a southward subducting proto–South China Sea. The total amount of ENE‐WSW extension offshore northern Vietnam constrained by our 2‐D gravity profiles and gravity inversion increases southward from 36 to 89 km along the Yinggehai Basin. These values of ENE‐WSW extension are consistent with 250 km of left‐lateral displacement along the RRF.

New methods for depth determination to horizontal cylinder

Three procedures can be utilized to determine the depth to the center of the horizontal cylinder from gravity profile. Firstly, the gravity profile is subjected to a simple filtering technique. Then, the maximum slope lines are drawn along the flanks of the filtered profile. The horizontal distances between the two slope lines for the positive part are measured at various amplitude levels. A plot of the horizontal distances against amplitude values will give an inclined straight line. The first procedure of depth estimation consists of measuring the distance between the points of intersection of the maximum slope lines at zero level background. This distance, for the positive or negative part, after it is multiplied by the empirical factor, gives directly the depth to the center of the horizontal cylinder. The other two procedures involve fitting a least square line to the inclined straight line of horizontal distances against amplitude values. Then, the maximum amplitude value of the filtered profile multiplied by an empirical factor is used to determine the depth, either graphically or through a simple equation. Accurate results have been achieved with low error percentages for a large number of gravity profiles due to synthetic horizontal cylinders having various depths and radii.

Analysis of the risk of karst collapse in Lapão, Bahia, Brazil

On October 2008, the large extent of dissolution of limestone in the Irecê Basin resulted in the occurrence of minor ground shakes and the enhancement of fractures along the surface of the ground and on the walls of buildings in the urban and periurban area of the city of Lapão. After preliminary geological and geotechnical studies to analyse the danger of collapse of underground caves, we have carried out gravity and electro-resistivity profiles in order to map the concealed caves and to help the determination of the level of groundwater within them. The interpretation of the results provided useful information both for the immediate safety of the population and for subsequent hydrological and geotechnical work. We have defined five risk areas based on the variations of the Bouguer and of the electrical resistivity data, by correlating the distribution of gravity lows with the presence of caves and the less resistive zones with the presence of brine water underground.

Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a $ {\mathbb{Z}_2} $ orbifold singularity supporting $ \mathcal{N} $ = 2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is “dual” to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

Fine Crustal Structure Beneath the Capital Area of China Derived from Gravity Data

AbstractIn this paper the multi‐scale wavelet method is used to separate gravity field. Moho topography of Capital area is determined using 3D Parker density interface inversion method and variable density model, constrained by deep seismic data. And at last, two typical gravity profiles are modeled. The results indicate that the crustal structure of Capital area rebuilded by multiple tectonic movements is very complicated, with adjoining depressions and uplifts, alternating basins and hills, and inhomogeneous density. Influenced by strong extension, thinning and erosion of North China Craton lithosphere, Moho topography around Capital area fluctuates greatly. The dominating tectonic direction of the Moho topography strikes from NE to NNE. Two steep slopes exist between North China Basin and Western Taihang uplift and Northern Yanshan uplift, respectively. Moho depth in North China Basin varies greatly, with the largest difference of 5 km, but the average thickness of crust in the basin is small. The thinnest is about 29 km, beneath Beijing and Tangshan area. The thickest crust is about 34 km in Wuqing depression. Adjusted by gravity equilibrium, crust thickness of western Taihang uplift area increases greatly. However, the density of western area is lower than the eastern basin. Gravity anomalies in upper and middle crusts are related to surface relief and topographic features. Affected by Cenozoic rifting, crustal structure of Capital area is very complicated in upper and middle crusts. Many geological tectonic units striking NNE are formed in different tectonic movements. Most faults cut through to the middle crust. Fold structures are formed in lower crust. High and low density anomalies are distributed alternatively. Crustal density in Capital area is remarkably inhomogeneous. Research concludes that occurrences of strong earthquakes in Capital area are probably related to upwelling of asthenosphere and uppermost mantle high density materials.

Dense gas-particle flow in vertical channel by multi-lattice trajectory model

A multi-lattice deterministic trajectory (MLDT) model is developed to simulate dense gas-particle flow in a vertical channel. The actual inter-particle collision and particle motion are treated by a Lagrangian model with three sets of lattices to reduce computational time. Cluster formation and motion near the wall are successfully predicted with mean particle volume fraction and velocity, showing quantitatively agreement with experimental results. The mechanism of particles concentrated near the wall is investigated by considering effects of gravity, particle-wall collisions, inter-particle collisions and velocity profiles of the gas phase. It is shown that the inter-particle collision and gas-phase velocity distribution are the essential factors for cluster formation near the wall, while gravity and particle-wall collision only have minor effects on particle concentration near the wall. Particles are unable to remain in the high velocity region due to the strong inter-particle collisions, while they tend to stay in the low velocity region for weak inter-particle collisions. In addition, the effects of channel width and particle sizes on cluster formation are also investigated and it is found that particle concentration near the wall reduces with the decrease of channel width and increase of particle size.

The continent-ocean transition at the southeastern margin of the South China Sea

The South China Sea formed by magma-poor, or intermediate volcanic rifting in the Paleogene. We investigate the structure of the continent-ocean transition (COT) at its southern margin, off NW Palawan between the continental blocks of Reed Bank and the islands of Palawan and Calamian. Several surveys, recorded by the BGR from 1979 to 2008, established a comprehensive database of regional seismic lines, accompanied with magnetic and gravity profiles. We interpret two major rifted basins, extending in the NE direction across the shelf and slope, separated by a structural high of non volcanic origin. The continent-ocean transition is interpreted at the seaward limit of the continental crust, when magnetic spreading anomalies terminate some 80–100 km farther north. The area in between displays extensive volcanism - as manifest by extrusions that occasionally reach and cut the seafloor, by dykes, and by presumed basaltic lava flows - occurring after break-up. The COT is highly variable along the NW Palawan slope: One type shows a distinct outer ridge at the COT with a steep modern seafloor relief. The other type is characterised by rotated fault blocks, bounded by listric normal faults ramping down to a common detachment surface. Half-grabens developed above a strongly eroded pre-rift basement. The seafloor relief is smooth across this other type of COT. We suggest the pre-rift lithospheric configuration had major influence on the formation of the COT, besides transfer zones. Volcanic domains, confined to the north of competent crustal blocks correlate with the style of the COT. Gravity modelling revealed an extremely thinned crust across the shelf. We propose a depth-dependent extension model with crust being decoupled from mantle lithosphere, explaining the discrepancy of subsidence observed across the South China Sea region.

Adaptive filtering in airborne gravimetry with hidden Markov chains.

AbstractThe paper studies filtering of airborne gravimetry data on a survey line. The aim is to build a filter that adapts to the nonhomogeneous gravity structure, which is induced by the unknown structure of Earth core, topography, etc. Gravity is modeled by a hidden Markov chain with finite number of states, each state corresponds to a certain type of gravity profile. Filtering is done in three steps: estimate the parameters of the Markov chain, determine moments of transitions between states, and construct the corresponding non-stationary Kalman filter. The algorithm takes into account the type of noise of the global positioning system. Tests on simulated and experimental data show that the filter diminishes over-smoothing and under-smoothing effects.

Geophysical and geological imprints of southern Neotethyan subduction between Cyprus and the Isparta Angle, SW Turkey

The present-day eastern Mediterranean region is characterized by two main arc systems: the western Hellenic arc and the eastern Cyprian arc, the latter having no significant trench unlike the former. Therefore, plate interactions in the western-northwestern side of the island of Cyprus is a matter of debate concentrating mainly on subduction or wrench systems. In order to understand the plate interactions within the area between the Isparta Angle and western segment of the Cyprus arc, the epicenter distribution of earthquakes, b-values and gravity anomalies for 5 depth intervals (0–35 km, 35–55 km, 55–75 km, 75–95 km, >95 km) have been analyzed on NE-SW trending regional profiles, and compared with geological structures. Although there are no earthquakes with depths greater than 50 km (i.e. crustal scale earthquakes) in the northern part of the Isparta Angle, all earthquake epicenters lie on a linear zone from southwest of Cyprus to the northwest, nearly parallel to the NW-SE trending Florence Rise. The b-value distribution shows a very good consistency with the epicentral and tectonic maps of Antalya Bay. The b-value maps, deeper than 55 km, show that low b-values depicting a NW-SE trending linear pattern correspond to seismic zones. Furthermore, this pattern shifts to the northeast and resembles the epicenters of the deep-focus earthquakes on the northeast dipping plane supporting the existence of a subduction zone. The gravity profiles show low gravity anomalies along the Florence Rise, high gravity anomalies at a certain distance interval to the NE direction which presumably resulted from subducting oceanic lithosphere, and again low gravity anomalies corresponding to the end of subducting slab and continental eastern limb of the Isparta Angle. On the other hand, the observed gravity anomalies are found to be consistent with the earthquake distribution patterns in the area. As a conclusion, for the area between the apex of the Isparta Angle and the western Cyprian arc, the distribution of earthquake epicenter locations, b-values, and gravity data suggest the presence of a subduction zone inclined to the northeast beneath the eastern limb of the Isparta Angle.

Shallow and Deep Structure of a Supradetachment Basin Based on Geological, Conventional Deep Seismic Reflection Sections and Gravity Data in the Buyuk Menderes Graben, Western Anatolia

The Buyuk Menderes Graben is a depression in the Menderes core complex of western Turkey. The region is one of the most rapidly deforming regions of continental crust in the world and has exceptionally high seismic activity. In this study, shallow and deep seismic studies were conducted at the Buyuk Menderes graben. These studies included surface geological mapping and two seismic reflection sections. Detailed modelling was performed with the seismic study. In addition to these, a moving windows power spectrum was applied to the Bouguer gravity profile data of the study area. Since no deep well is available in this area, the geological interpretation of the seismic stratigraphy is based on the correlation with the surface geology, this was combined with the major reflections and the seismic facies observed along the profiles, and, thus, four main seismic units can be distinguished in the basin fill. Structural features of the basin is driven by a complex extensional faults system, consisting of a low-angle, S-dipping Buyuk Menderes detachment and by its synthetic and antithetic splays, bordering the opposite flanks of the basin. As a result of conventional deep seismic reflection sections and gravity data, three layers were defined in the study area. The first layer occurs at a thickness of 6 km, and the second layer is between 13 and 18 km. The third layer is at ~33 km and may also emphasize Moho depth. The Buyuk Menderes graben has three clear reflectors which are base sediments, brittle-ductile transition, Moho and faults that show a half-graben floored by a detachment. The Moho depth is comparable with previous estimates. According to the results obtained, Bouguer gravity and seismic results are very much consistent with each other. It was observed that at the depths determined from seismic and gravity data, the distribution percentage of earthquake focal depths also rises.

Interpretation and modelling of regional gravity data of the Aveiro Basin (Northwest Portugal)

The gravity map of the Aveiro Basin, North West Portugal was produced in 2000/2001 and some limited two dimensional (2D) interpretation was carried out. It is intended in this article to advance the interpretation and modelling of the original Aveiro basin gravity data. Thus, the data were processed and the horizontal gradient, the second vertical derivative and downward continued field computed. The corresponding maps have been processed and a new interpretation of the basin tectonic features has been proposed. This is compared with the previous geological and tectonic information obtained from former surveys and local boreholes. As the next step a more detailed modelling of the Aveiro Basin took place. Bearing the interpretation of the basin tectonic features in mind, several north–south and east–west gravity profiles were established and modelled. The proposed models were presented and discussed. As a result, a comprehensive mass distribution model for the basin was proposed. Finally, comparison was made between the new gravity model and the previously published tectonic features map. This modelling is particularly useful for groundwater protection, exploration and exploitation and also for the dimensioning of drilling operations. Bearing in mind the geomorphology of the basin the gravity method is a very economical tool for the investigation of basin structures.

Geophysical investigation in the lower Benue Trough of Nigeria using gravity method

Gravity survey in parts of Akataka and the environs in Abakaliki area of the Lower Benue trough was conducted over an area between longitudes 8°42′ E to 8°47′ E and latitudes 6°35′ N to 6°45 ′ N. Ninety eight gravity stations were occupied and the data collected were reduced relative to a base station. The geometry of the buried body was determined from the interpretation of residual anomaly data. Spherical model was assumed for the anomalous body based on the local geology and the residual gravity anomaly. A density contrast of 0.32 gcm-3 was calculated for the body. The residualized and interpreted gravity profiles yielded results that reveal low Bouguer gravity anomalies with magnitudes ranging from –2.5 to 3.8 mgals and with abrupt changes at intervals thereby suggesting a fault. The low-density anomalous body suspected to be salt deposit was buried at depths of between 868 and 2618 m. Its diameter ranging between 2,126 and 3,322 m, mass ranges from 1.18 to 4.52 × 1013 kg. The low Bouguer gravity anomaly over the area suggests a zone of basic to intermediate igneous intrusions, deep basement and crustal thinning. These calculated values are in agreement with other works carried out within Abakaliki areas in particular and the Lower Benue trough in general. Key words: Gravity survey, profiles, Benue trough, intrusions, salt deposit, density.

Generation and study of satellite gravity over Gujarat, India and their possible correlation with earthquake occurrences

High-resolution satellite gravity data have been generated and utilized to infer subsurface geological structures in the area of devastating earthquake that struck the Bhuj region in Gujarat on 26 January 2001. Latitudinal gravity profiles have been generated in the Bhuj, Anjar and IBF regions across the epicentres (23.5° N, 69.8° E/Mw 7.0 in 2001; 23.2° N, 70° E/Mw 7.0 in 1956; 24.2° N, 69.2° E/Mw 7.8 in 1819). Substantial differences in gravity anomaly patterns as high as 37 mGal could be observed existing near the epicentre regions. These gravitational differences might have caused due to the plate tectonic processes and due to the changes in densities of different lithospheric zones/sedimentary layers. Temporal variations of the satellite-derived gravity and their probable relations with already occurred major earthquakes in this region have been studied. Hence we conclude that drastic changes in gravity anomalies can be considered as a precursor for occurrences of substantially large earthquakes.

Crustal structure of the western part of the Southern Granulite Terrain of Indian Peninsular Shield derived from gravity data

The Southern Granulite Terrain (SGT) is composed of high-grade granulite domain occurring to the south of Dharwar Craton (DC). The structural units of SGT show a marked change in the structural trend from the dominant north–south in DC to east–west trend in SGT and primarily consist of different crustal blocks divided by major shear zones. The Bouguer anomaly map prepared based on nearly 3900 gravity observations shows that the anomalies are predominantly negative and vary between −125 mGal and +22 mGal. The trends of the anomalies follow structural grain of the terrain and exhibit considerable variations within the charnockite bodies. Two-dimensional wavelength filtering as well as Zero Free-air based (ZFb) analysis of the Geoid-Corrected Bouguer Anomaly map of the region is found to be very useful in preparing regional gravity anomaly map and inversion of this map gave rise to crustal thicknesses of 37–44 km in the SGT. Crustal density structure along four regional gravity profiles cutting across major shear zones, lineaments, plateaus and other important geological structures bring out the following structural information. The Bavali Shear Zone extending at least up to 10 km depth is manifested as a plane separating two contrasting upper crustal blocks on both sides and the gravity high north of it reveals the presence of a high density mass at the base of the crust below Coorg. The steepness of the Moyar and Bhavani shears on either side of Nilgiri plateau indicates uplift of the plateau due to block faulting with a high density mass at the crustal base. The Bhavani Shear Zone is manifested as a steep southerly dipping plane extending to deeper levels along which alkaline and granite rocks intruded into the top crustal layer. The gravity high over Palghat gap is due to the upwarping of Moho by 1–2 km with the presence of a high density mass at intermediate crustal levels. The gravity low in Periyar plateau is due to the granite emplacement, mid-crustal interface and the thicker crust. The feeble gravity signature across the Achankovil shear characterized by sharp velocity contrast indicates that the shear is not a superficial structure but a crustal scale zone of deformation reaching up to mid-crustal level.

Gravity and magnetic modelling of crustal structure in central Victoria: what lies under the Melbourne Zone?

Three gravity and magnetic profiles through the central and eastern part of the Melbourne Zone, Lachlan Fold Belt, have been modelled, with tight control from surface geology to investigate the deep crust. The largely non-magnetic upper crust (folded Ordovician to Lower Devonian strata of the Melbourne Zone intruded by Devonian granite plutons) has been modelled using recently acquired density measurements, providing a good match with the gravity profiles. The top of the basement is modelled at ∼10–15 km depth in the centre of the zone, and ∼8–10 km depth in the south of the zone, reflecting a thinning of the folded cover sequence toward the south, consistent with outcrops of basement Cambrian rocks on the south coast of Victoria. Long-wavelength magnetic anomalies in the Melbourne Zone are modelled as highly magnetic tabular bodies lying in the basement below the folded strata of the Melbourne Zone. The only rock type that matches the density and magnetic susceptibility is serpentinised ultramafic rock. Thus, a large ophiolitic body is thought to exist in the upper part of the basement to the Melbourne Zone, at depths of 15–25 km in the central part of the zone, and 10–15 km in the south of the zone. This unit is correlated with the Cambrian mafic–ultramafic complex of Tasmania, agreeing with previous correlations of the Selwyn Block with Tasmania.

Evidence for upper mantle intrusion in the west African coastal sedimentary basins from gravity data: the case of the southern part of the Douala basin, Cameroon

The Bouguer anomaly map of the region between latitudes 30N and 3045’N and longitudes 9030’E and 10010’E and which forms the southern part of the Douala Basin, shows ring-like positive contour lines. The Bouguer gravity profiles obtained across the gravity anomaly contour lines in the region have been interpreted using 2D1/2 gravity modelling. The results reveal that in the southern part of the Douala Sedimentary Basin, two major structures exist: a half-dome of mantle material explained by isostatic compensation and a pillar of high density rocks probably representing an upper mantle intrusion down to a depth of about 14 km. The similarities of these results with those obtained in the coastal sedimentary basin of Mauritania-Senegal suggest a more extensive movement that would have affected the whole of West African coast.KEYWORDS: Bouguer anomaly, dome, graben.

The Millungera Basin—new geoscience supporting exploration

An unknown sedimentary sequence was first recorded during a Geoscience Australia/ Geological Survey of Queensland/ pmd*CRC deep seismic reflection survey in the Mount Isa Inlier and adjacent undercover terrains, during 2006/07. The sequence occurs unconformably underneath the Carpentaria Basin succession in the Julia Creek area, east of Cloncurry in north Queensland, and is named the Millungera Basin. A section through the basin is recorded along seismic line 07GA–IG1, recorded between north of Cloncurry to east of Croydon. In this section three internal sequences are noted—with two strongly reflective units separated by a poorly reflective unit. As well as deep crustal seismic reflection profiles, magnetotelluric profiles were collected along the same traverse. These data show a moderately conductive Millungera Basin underlying the strongly conductive Carpentaria Basin. Zones of limited reflectors beneath the basin in the seismic sections have been interpreted as granites, raising the possibility of raised geothermal gradients. The Millungera Basin may comprise a potential geothermal target. The Millungera Basin sequence is interpreted to overlie granites. Adjacent Proterozoic granites of the Williams Batholith are known to be high heat producing granites, containing high levels of potassium thorium and uranium. The hydrocarbon potential of the basin is similarly uncertain. Strong reflectors in the seismic sections may be coal beds. Although the depth of the basin in the seismic section is insufficient to have reached the oil window, interpretation of gravity profiles by Geoscience Australia suggest the basin deepens to the south, possibly reaching 4,000 m. If fertile beds have reached the oil window, the structurally more complex eastern side of the basin may contain petroleum traps. The age of the rocks in the Millungera Basin is not known. Constraints from the seismic suggest between the early Mesoproterozoic and the Middle Jurassic. Investigations into the nature of the basin are continuing. A more detailed magnetotellurc survey is being undertaken to better define the shape of the basin. In order to reliably describe the basins components, a deep drilling program is required.

The use of gravity methods in the internal characterization of landfills—a case study

Some examples of the use of gravity exploration methods in landfills were published recently. However, density contrast between the landfill and the host media as well as the cost involved may be limiting factors to the application of gravimetry to this problem. Herein a case study of the application of gravity methods to the internal characterization of a sealed landfill is presented. This landfill is installed in recent low-density quaternary sand formations. Two north–south gravity profiles were carried out. The first profile crossed the landfill at its centre, whilst a second profile was done some distance away from the landfill to provide general regional information. The first profile was modelled in order to obtain lateral variations of density within the landfill that might be caused by different types of waste and/or the age of the waste deposits. Gravity modelling and interpretation were supported with data from resistivity profiles carried out in the immediate vicinity of the gravity measurements, i.e. the resistivity profiles interpretation results constrained the thickness of landfill deposits.

TURBULENT STRESSES IN LOCAL SIMULATIONS OF RADIATION-DOMINATED ACCRETION DISKS, AND THE POSSIBILITY OF THE LIGHTMAN-EARDLEY INSTABILITY

We present the results of a series of radiation-MHD simulations of a local patch of an accretion disk, with fixed vertical gravity profile but with different surface mass densities and a broad range of radiation to gas pressure ratios. Each simulation achieves a thermal equilibrium that lasts for many cooling times. After averaging over times long compared to a cooling time, we find that the vertically integrated stress is approximately proportional to the vertically-averaged total thermal (gas plus radiation) pressure. We map out--for the first time on the basis of explicit physics--the thermal equilibrium relation between stress and surface density: the stress decreases (increases) with increasing surface mass density when the simulation is radiation (gas) pressure dominated. The dependence of stress on surface mass density in the radiation pressure dominated regime suggests the possibility of a Lightman-Eardley inflow instability, but global simulations or shearing box simulations with much wider radial boxes will be necessary to confirm this and determine its nonlinear behavior.