GEOPHYSICS, VOL. 50, NO. 8 (AUGUST 1985); P. 1318-1334, 13 FIGS., 4 TABLES. Analysis of temperatures in sedimentary basins: the Michigan Basin Marvin A. Speece*, Timothy D. Bowen*, James L. Folcik*, and Henry N. Pollack* ABSTRACT We develop an analytical and numerical method- ology for the analysis of large bottom-hole temperature (BHT) data sets from sedimentary basins, and test the methodology using temperature, stratigraphic, and lithologic data from 411 boreholes in the Michigan Basin. Least-squares estimates of temperature gradients in the formations and lithologies present are calculated as solutions to a large system of linear equations. At each borehole the temperature difference between the bottom and top of the hole is represented as a sum of temperature increments through the various formations or lithologies penetrated by the borehole. Quadratic programming techniques enable bounds to be placed on the gradient solutions in order to suppress or exclude improbable gradient estimates. Numerical experiments with synthetic data reveal that the estimates of temper- ature gradients for a given formation or lithology are sensitive to the degree of representation of that unit; well represented units have more stable gradient esti- mates in the presence of noise than do poorly repre- sented units. The estimates of temperature gradients ob- tained for lithologies are more stable than those for formations and are believed to be good estimates of actual lithologic temperature gradients in the Michigan Basin. Formation temperature gradients obtained as a weighted sum of the estimates of the component litho- logic temperature gradients appear to be good estimates of the average temperature gradients for the formations of the basin. At each borehole a temperature residual exists corre- sponding to the difference between the observed BHT and the BHT predicted by the estimated interval tem- perature gradients. Residuals are far more stable than estimated temperature gradients. The values of residuals change little regardless of whether lithology, formation, bounded, or unbounded gradient estimates are used to calculate them. Maps of residuals indicate well-defined and spatially coherent patterns of positive and negative temperature residuals. Filtered subsets of large- magnitude residuals alone show a pattern of negative residuals coinciding with the mid-Michigan gravity high, a geophysical feature thought to delineate a Pre- cambrian (Keweenawan) rift zone in the crust beneath the basin. Thermal models of the Michigan Basin and the crust and upper mantle beneath the basin indicate that the suspected rift beneath the basin can cause a variation in basement heat flow sufficient to produce temperature residuals of the magnitude observed in the sediments, with negative temperature residuals over the area of the rift. INTRODUCTION The American Association of Petroleum Geologists (AAPG) recognized more than a decade ago that major oil companies The purpose of this paper is to: (1) present an analytical and had a great deal of potentially valuable temperature data. The numerical methodology for analysis of large bottom-hole tem- perature (BHT) data sets from sedimentary basins, and (2) demonstrate application of this methodology to the Michigan Basin, a Paleozoic intracratonic basin in the mid-continent of North America. In particular we address in some detail questions associated with noise and errors in, and the hetero- geneous quality of, the BHT data set, as well as the stability and robustness of the quantitative results obtained from the analysis. data had been obtained as BHT~ during logging following the completion of drilling. The AAPG undertook to collect, col- late, and assemble in machine-processable form BHTs from as many regions of North America as possible. The result was a data set of 28 187 temperatures from the United States, Canada, and Mexico, obtained at depths ranging to greater than 6 km (Am. Assn. Petr. Geol., 1976). The AAPG group devised a correction for nonequilibrium data that provided an estimate of the equilibrium BHT at each site, and then calcu- Manuscript received by the Editor June 11, 1984; revised manuscript received February 13. 1985. *Department of Geological Sciences, The University of Michigan, Ann Arbor, Michigan 48109. 0 1985 Society of Exploration Geophysicists. All rights reserved. Downloaded 10/23/14 to 150.131.130.14. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/