A new approach to the topographic correction for terrestrial heat flow measurements is presented. The approach features calculation of a Fourier series fit to the surface temperature‐surface elevation data where the surface temperatures are based on a model that includes surface temperature variations due to microclimate variations. The mathematics of the terrain correction problem are similar to the upward (away from source) continuation problem in gravity and magnetics so several solutions, in addition to the Fourier series approach, are available in the literature that allow an accurate calculation of the correction provided the surface boundary condition is properly specified. However, the usual boundary condition applied, a linear relation between ground surface temperature and elevation, is shown to be inadequate for drill holes in the depth range 30–200 m no matter how low the topographic relief. Thus a model of ground surface temperature is developed that includes the effects of elevation, slope orientation, and slope angle. Because of the effects of microclimate, the classical models that have isothermal surfaces that generally parallel the topographic surface are significantly in error in many cases, and the patterns of isotherms near the topographic surface are more complicated than was previously recognized. This complexity causes gradient variations with depth in 30‐ to 200‐m holes that have not been previously recognized as being related to topographic effects. Because the temperature effects of slope orientation and inclination do not scale with respect to the magnitude of the relief, significant terrain corrections may be required even in areas of relatively low relief. The application of the technique is illustrated by application to a line dipole hill and a group of drill holes near Wilbur, Washington. In addition, several examples of two‐dimensional terrain effects and one example of three‐dimensional terrain effects are illustrated for topographic sections in the northwestern United States. In the United States, most ‘anomalous’ gradients in the upper 100–200 m of drill holes in impermeable rocks can be explained by a combination of topographic and microclimatic effects, without resorting to temporal climatic changes or unknown types of water effects. The depth of the holes necessary for reliable heat flow measurements in such settings is a signal to noise problem where the noise is the effect at depth of the microclimatically related surface temperature variations, coupled with the topographic effect, and the signal is a temperature increase at any depth due to the background geothermal gradient. Typically, the noise has decreased to a few degrees centigrade per kilometer within the depth range 100–200 m. Thus the general conclusion has been that these depths of holes are required for reliable heat flow values. In fact, when linear temperature‐depth data are observed in shallower holes or when appropriate corrections are made, reliable measure ments in impermeable rocks may be consistently ma...

Geothermal data from 248 wells and drill holes, a thermal model for the effects of the Snake Plain aquifer on observed heat flow, an estimate of the regional heat flow in the eastern Snake River Plain, a detailed moving source, regional thermal model, and a discussion of the origin and the relationship of the eastern and western halves of the Snake River Plain are included in this paper. In order to determine the thermal structure of the eastern Snake River Plain, an extensive geothermal gradient and heat flow survey was carried out. Data from 248 holes show high heat flow values along the margins but low values along the center because of effects of the extensive Snake Plain aquifer. Based on a thermal model of the aquifer, a heat budget was derived from which a mean heat flow for the eastern Snake River Plain of 190 mW m -2 was calculated. This value can be compared to observed values along the margins of 120 mW m -2 and two values in deep holes along the northeastern margin of 110 and 109 mW m -•. The areas of highest expected values, in the Island Park caldera region, have not been sampled by heat flow measurements, however. Based on the heat flow results from the eastern and the western Snake River Plain and other geophysical and geological data, a finite-width movingsource-plane thermal model is developed for the Snake River Plain. Even though the geological and geophysical characteristics of the eastern and western Snake RiVer Plain are somewhat different, they are attributed to the same moving heat source, and the spatial geological and geophysical differences are explained by different stages in a time-related sequence of thermally driven geological and tectonic events. The Snake River Plain is due to a strong thermal source interacting with the crust with the resulting complete chemical reorganization of the crust. The major immediate driving mechanism is a thick mafic intrusive emplaced in the midlevels of the crust. Associated with this thermal event are regional uplift of a kilometer or sO as the heating occurs, associated melting of the upper crust, and subsequent rapid subsidence of approximately 1/2 to 1 km because of the change in density of the crust and upper mantle section associated with the emplacement of the basic intrusive and the disruption of the granitic upper crust. After the heat source moves eastward, continued subsidence occurs due to cooling of the lithospheric section (similar to that seen for oceanic regions). Along with the subsidence and soon after completion of the extensive silicic volcanism, basalts began to be extruded. Thermal contraction also generates faulting on the sides and perhaps in the center of the hot spot track. The subsidence causes reversal of the dips of the silicic ash flows from their initial away-from-the-source configuration, to the toward-the-source configuration observed in the Snake River Plain. Continued subsidence and cooling cause the formation of the basin which is then filled by sediments, causing additional subsidence due to isostatic adjustment ...

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A continuation technique for conductive heat flow in a homogeneous isotropic medium is presented which utilizes observe surface heat flow data. The technique uses equivalent point sources and is developed for transient or steady‐state conductive heat flow problems for a homogeneons half‐space with plane surface and a surface with topographic relief. The technique is demonstrated by comparison with a steady‐state fault model and the terrain correction problem; it is also compared to observed heat flow data in two geothermal areas (Marysville, Montana, and East Mesa, Imperial Valley, California). Calculated subsurface temperature distributions are compared to analytical models and the results of geophysical studies in deep drillholes in geothermal systems. Even in geothermal systems, where convection is involved in the heat transfer, the boundaries of the “reservoir” associated with the convective system can be treated as a boundary condition and the depth and shape of this boundary can be calculated, since many geothermal systems are controlled by permeability barriers. These barriers may either be due to the natural development of a trap or to self‐sealing. Continuation of surface heat flow data is a useful technique in the initial evaluation of geothermal resources as well as an additional tool in the interpretation of regional heat‐flow data.

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