Stochastic inversion of thermal data in a sedimentary basin: resolving spatial variability

Abstract

The concept of spatial stochastic processes and the techniques of geostatistics and stochastic inversion are presented as a means for evaluating the spatial variability of thermal properties and temperature in sedimentary basins. Data from the Uinta Basin of NE Utah are used to demonstrate the analysis. Bottom hole temperatures from oil and gas wells provide the best opportunity for a spatial analysis because of the large number and wide distribution of data. Errors in bottom hole temperatures are not too large to preclude their use and stochastic inversion provides an optimum method for removing random noise while retaining spatial resolution. Corrected bottom hole temperatures from 235 wells in the Uinta Basin are used to estimate: (a) average geothermal gradient as a function of position in the basin and (b) temperature gradients in individual formations, also as a function of position in the basin. The latter analysis yields a high-resolution estimate of temperature gradient and temperature throughout the basin. The temperature field shows variations of up to 50°C at a depth of 4 km and is estimated to be accurate to better than 5 "C. This variation in temperature is consistent with conductive and advective mechanisms of heat transfer in a heterogeneous medium.

Thermal analysis of the southern Powder River Basin, Wyoming

“…Information recorded on well information cards often focuses on an exploration play and is incomplete for the re mainder of the vertical section; thus, formation top informa tion for any particular formation throughout the basin may be sparse or incomplete. Therefore, structure maps of the seven lithothermal units were constructed by a geostatistical approximation method known as kriging (Davis, 1986;de Marsily, 1986;Willett, 1990).…”

“…Two models (Speece et al, 1985;Willett andChapman, 1987a, 1987b) in conjunction with inversion techniques (Deming and Chapman, 1988b;Willett, 1990) developed to resolve spatial variation do appear to mitigate the effects of BHT data noise. However, because of the lack of available high-resolution temperature data, it is unclear which model best estimates actual temperature fields.…”

“…Over 3000 well information cards were collected from which 1807 BHTs were used. The temperature models presented in Speece et al (1985) and Willett and Chapman (1987a) were used with the in version methods of Deming and Chapman (1988b) and Willett (1990) to construct the present-day temperature field. The re sults of the different models were compared to each other and a preferred temperature field, in conjunction with measured thermal conductivities and other geologic data, was used to estimate heat flow for the region.…”

A linear inversion method to infer exhumation rates in space and time from thermochronometric data

“…Hence, exhumation rate,ė, has length M max N and the forward model operator, A, has size N ×M max N. The covariance matrix now contains the spatial correlation structure between the exhumation rates defined in Eq. (21) (Tarantola and Nercessian, 1984;Willett, 1990). For a single time interval, a block of the covariance matrix is constructed using the separation distance between the ith and jth data (u) and the correlation function, ρ(u):…”