David S. Chapman

On the regional variation of heat flow, geotherms, and lithospheric thickness☆

Pollack, H.N. and Chapman, D.S., 1977. On the regional variation of heat flow, geotherms, and lithospheric thickness. Tectonophysics, 38: 279-296. Geotherm families in which surface heat flow is the principal independent variable have been constructed for continental and oceanic lithospheres. The continental model is characterized by geotherms in which surface heat flow is in equilibrium with heat flowing into the lithosphere at its base plus heat generated by radioactive decay within the lithosphere. The model accommodates the regional variation of the surface heat flow with proportional variations in the radioactivity of the surficial enriched zone and in the deeper heat flow. The proportionality is dictated by a new and general linear relationship between reduced heat flow and mean heat flow for a region (o* r 0.6 ifo), which enables both q* and the mean heat production of the enriched zone to be estimated from knowledge of the mean surface heat flow of a province. The oceanic model is characterized by the transient cooling of a semi-infinite medium with an initial temperature gradient and some near-surface radiogenic heat production. The model yields a heat flow in satisfactory agreement with observations in the oldest ocean basins. The depth at which both the oceanic and continental geotherms reach -0.85 of the melting temperature is shown to be a consistent estimator of the depth to the top of the low-velocity channel, or the thickness of the high-velocity lid overlying the channel. We identify the lid as synonymous with the lithosphere, and produce a global map of lithospheric thickness based on the regional variation of surface heat flow. The lithosphere is less than 100 km thick over most of the globe, but thickens appreciably and becomes more viscous beneath the Precambrian shields and platforms, regions of low heat flow. These characteristics of shields are consistent with recently reported models of the driving mechanisms of the plate system, which require greater retarding forces beneath plates with large continental areas.

Regional geotherms and lithospheric thickness

Continental and oceanic geotherm families parametric in surface heat flow intersect the mantle solidus at a depth coincident with the top of the seismic low-velocity zone, thus allowing surface heat-flow variations to be used to map the thickness of the lithosphere on a global scale. Thermal models were developed that predict a lithospheric thickness of a few tens of kilometers in young oceans and continental orogenic provinces and more than 300 km in shield areas. The variable thermal structue of the mantle implies a greater viscosity beneath shields, which offers an explanation for the observed retarded motions of plates that bear shields.

Global heat flow: A new look

A global heat flow map has been derived from existing observations supplemented in areas without data by an empirical predictor based on tectonic setting and age. In continental areas the predictor is based on the observed correlation of heat flow with age of last tectono-thermal event, and in oceanic regions on the observed relation of heat flow to age of ocean floor. The predictor was used to assign mean heat flow values to 5° × 5° grid areas on the globe, weighted according to the relative area of tectonic provinces represented. A spherical harmonic analysis to degree 12 of the heat flow field yields a mean value of 59 mW m−2, a rms residual of 13 mW m−2, and an amplitude spectrum which decreases gradually and almost monotonically fromn = 1. The spherical harmonic representation of the heat flow field is free of the unreal distortions which have characterized earlier analyses based on a geographically sparse data set. Areas with residuals greater than 15 mW m−2 comprise less than 19% of the area of the globe, thus indicating that most heat flow provinces have characteristic dimensions adequately represented in a 12-degree analysis.

An unequivocal case for high Nusselt number hydrothermal convection in sediment-buried igneous oceanic crust

New observations of seafloor heat flow, precisely located along seismic reflection profiles crossing a buried ridge on the eastern flank of the Juan de Fuca Ridge, show a nearly exact inverse correlation between heat flow and sediment thickness, such that the basement-sediment contact appears isothermal to within 10 K, despite a factor of three local variation in sediment thickness. We have used these observations with numerical models to infer hydrothermal heat-transport properties of the upper oceanic crust at this 3.5 Ma site. Model results show that, while fluid circulation is stimulated by the effects of basement topography even at sub-critical Rayleigh number conditions, the creation of a nearly isothermal basement surface requires very high heat-transport efficiency. Lower limits for the Nusselt number ( Nu ≥ 25), for the Rayleigh number ( Ra ≥ 4000), and for the permeability (κ ≥ 10−11 m2), are provided by assuming that high permeability is distributed throughout the uppermost 600 m of relatively low-velocity igneous crust at this site. Relatively high permeability can also be inferred by considering the calculated fluid pressure regime in light of what is known about the relationship between fluid seepage through the sediment section and the underlying basement topography from geochemical data: Local super-hydro-static pressure and fluid discharge above buried basement ridges can occur only if basement permeability is higher than 10−13 m2. Unfortunately, no constraint on the actual distribution of high permeability below the top of the igneous crust is provided by the thermal regime based on the heat-flow and seismic observations. Equally uniform upper basement temperatures can be produced by fluid flow in a thinner layer (of thickness h) having a correspondingly higher Nusselt number and permeability. Only the products of Nu × h, and κ × h2 are constrained. Bulk permeabilities (averaged over intervals a few hundred meters thick) measured in boreholes that have penetrated the upper oceanic crust are typically less than 10−13 m2. The much higher formation-scale permeability we infer may be a consequence of the relative youth of the crust at this site, although it is more likely that the interconnected fractures and extrusive volcanic unit contacts and voids that contribute most to the bulk formation permeability are relatively infrequent and not representatively sampled by drilling.

Mid-Latitude (30°–60° N) climatic warming inferred by combining borehole temperatures with surface air temperatures

We construct a mid-latitude (30°–60° N) reduced temperature-depth profile from a global borehole temperature database compiled for climate reconstruction. This reduced temperature profile is interpreted in terms of past surface ground temperature change and indicates warming on the order of 1°C over the past 100 to 200 years. The combination of an initial temperature (the primary free parameter) with the last 140 years of gridded surface air temperature (SAT) data yields a synthetic temperature profile that is an excellent fit to observations, accounting for 99% of the observed variance and a RMS misfit of only 12 mK. The good correlation suggests that this reduced temperature profile shares much information with the mean SAT record over large areas and long time-scales. Our analysis indicates 0.7°±0.1°C of ground warming between pre-industrial time and the 1961–1990 mean SAT.

Heat flow in the Uinta Basin determined from bottom hole temperature (BHT) data

The thermal resistance (or Bullard) method is used to judge the utility of petroleum well bottom‐hole temperature data in determining surface heat flow and subsurface temperature patterns in a sedimentary basin. Thermal resistance, defined as the quotient of a depth parameter Δz and thermal conductivity k, governs subsurface temperatures as follows: TB=T0+q0∑z=0BΔzk, where TB is the temperature at depth z=B, T0 is the surface temperature, q0 is surface heat flow, and the thermal resistance (Δz/k) is summed for all rock units between the surface and depth B. In practice, bottom‐hole and surface temperatures are combined with a measured or estimated thermal conductivity profile to determine the surface heat flow q0 which, in turn, is used for all consequent subsurface temperature computations. The method has been applied to the Tertiary Uinta Basin, northeastern Utah, a basin of intermediate geologic complexity—simple structure but complex facies relationships—where considerable well data are available. Bot...

A geothermal climate change observatory: First year results from Emigrant Pass in northwest Utah

Temperature-depth profiles, measured in boreholes, contain a temporal record of past changes in surface ground temperature and provide valuable constraints on climatic variations over the last few centuries. However, the linkage between ground temperature and meteorological variables including air temperature is imperfectly known. To understand that linkage better and to document in detail how the surface ground temperature changes propagate into the subsurface where they are later measured in temperature-depth logs in boreholes, we have designed and installed a geothermal climate change observatory. Installed in arid northwest Utah, our Emigrant Pass Observatory (EPO) consists of an array of thermistor strings in the subsurface and a meteorological station at the borehole collar. Results from our first complete annual cycle, November 1, 1993, though October 31, 1994, are presented. Ground and air temperatures generally track each other but with important time-varying offsets. The mean surface ground temperatures for the period are 11.3°C on the granite outcrop and 9.5°C for the partially shaded regolith site; mean air temperature at a 2-m mast height above the ground is 8.8°C. The ground-air temperature differences are variable on timescales from days to seasons, largely governed by level of absorbed solar radiation. Marginal precipitation (8.6 mm) and ephemeral snow cover did not significantly disturb the ground-air temperature difference during the year monitored. Instrumental measurement of air temperature has nonrandom sampling biases that present problems for observing long term changes. The calculation of average annual air temperature at EPO decreases by 0.34 K as the sampling rate of air temperature is decreased from 60 s to every 12 hours. The attenuation and phase lag of thermal waves with depth confirm that heat conduction theory adequately describes the transient temperature field at this site, and yield in situ estimates of thermal diffusivity, a quantity needed to reconstruct surface ground temperature histories. Thermal diffusivity for the granite and regolith is 0.88 × 10−6 m2 s−1 and 0.45 × 10−6 m2 s−1, respectively. Energy flux calculations for the Emigrant Pass Observatory site suggest that a geothermal climate change observatory has the capability of detecting a century scale energy perturbation that is one part in a million of the instantaneous flux.

Climate change inferred from analysis of borehole temperatures: An example from western Utah

Temperature-depth profiles measured in a suite of boreholes in western Utah are used to infer climate change in the region over the past century and to document how effectively the solid earth records secular changes in surface air temperature. The data for this analysis consist of (1) high-resolution temperature logs from six sites where terrain, hydrologic, and cultural disturbances to the temperature field are minimal, (2) surface air temperature records for the period 1891–1990 from seven meteorological stations geographically interspersed with the borehole sites, and (3) ground and air temperature records available from four weather stations. Deviations from linear temperature-depth profiles in the boreholes, interpreted in terms of a linear change of surface temperature with time, suggest changes of −0.8°C to +0.6°C (average +0.3°C) in surface temperature for western Utah over the last several decades. These changes are consistent in trend but smaller in amplitude than the 100-year linear trends in the surface air temperature data (average +0.8°C) for the same region. If the last 100 years of surface temperature change is assumed to be given by a nearby meteorological station record, then borehole temperatures yield additional information about the mean temperature prior to 1891. For three western Utah borehole sites the pre observational means are within ±0.3°C of the mean air temperatures for this century, indicating that up to 50% of the temperature increase seen in the 100 year record constitutes recovery from a cold period toward the end of the last century. The veracity with which our observed borehole temperature profiles match synthetic temperature-depth profiles computed from air temperature records leaves little doubt that the solid earth is a valuable recorder of climatic change.

Estimating thermal conductivity in sedimentary basins using lithologic data and geophysical well logs

A method for estimating in-situ thermal conductivity profiles in oil and gas wells is advanced to rectify a major shortcoming in thermal analyses of sedimentary basins. Thermal conductivity estimates are made in a two-stage procedure and are based on a model for the conductivity of mixtures and input data from lithological and geophysical logs. First, rock matrix conductivity for an arbitrary depth interval (i.e., drill cuttings sample interval, which is about 3 m) is determined from the laboratory-calibrated conductivities and volumetric representation of its individual lithologic components using a geometric mean model. In-situ conductivity is then estimated by a second application of the model, correcting for temperature and porosity determined from geophysical logs. > The method is illustrated for three Uinta basin (Utah) wells that penetrate a series of Tertiary sandstones, shales, and muddy carbonates. Detailed lithologic descriptions, together with sonic and neutron logs, were digitized and used for estimating in-situ conductivity. The validity of the method was tested by comparing the prediction against laboratory measurements on 565 samples from the same wells. Rock matrix thermal conductivity ranges from 1.6 to 6.8 W/m/K and is predicted within 20% of the actual measurement for 90% of the samples. Both in-situ conductivity values and variations for a given lithologic unit are reduced at increased porosity and increased temperature. Thermal conductivity nomograms are presented as useful tools to predict directly the in-situ thermal conductivit of a formation from a well log signal.

Climate change on the Colorado Plateau of eastern Utah inferred from borehole temperatures

Temperature profiles from boreholes on the Colorado Plateau of southeastern Utah have been examined for evidence of climate change. Because these boreholes penetrate layered sedimentary rocks with different thermal conductivities, Bullard plots (temperature versus integrated thermal resistance) are used to estimate background heat flow and surface temperature intercepts. Reduced temperatures, which represent departures from a constant heat flow condition, are inverted for a surface ground temperature history at each borehole site using a singular value decomposition algorithm. Singular value cutoffs are selected by analyzing the spectral energy and the standard deviation of the model fit to the data as a function of the number of eigenvalues; solutions are constructed from areas of large spectral energy and a cutoff where additional eigenvalues fail to improve the solution significantly. The solution is parameterized in terms of 13 time steps increasing in duration and going back 400 years. Eight of nine borehole sites indicate between 0.4 and 0.8°C (±0.2° C) warming over the past 200 years with some evidence for accelerated warming in this century; one borehole indicates local cooling over the same time period. The amplitude of the warming inferred from borehole temperatures is less than that deduced from analysis of 100-year surface air temperature records at four of the five weather stations surrounding the borehole sites.