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We present a formal inverse procedure to extract exhumation rates fromspatially distributed low temperature thermochronometric data. Our method isbased on a Gaussian linear inversion approach in which we define a linearproblem relating exhumation rate to thermochronometric age with rates beingparameterized as variable in both space and time. The basis of our linearforward model is the fact that the depth to the "closure isotherm" can bedescribed as the integral of exhumation rate, ..., from the cooling ageto the present day. For each age, a one-dimensional thermal model is used tocalculate a characteristic closure temperature, and is combined with aspectral method to estimate the conductive effects of topography on theunderlying isotherms. This approximation to the four-dimensional thermalproblem allows us to calculate closure depths for data sets that span largespatial regions. By discretizing the integral expressions into time intervalswe express the problem as a single linear system of equations. In addition,we assume that exhumation rates vary smoothly in space, and so can bedescribed through a spatial correlation function. Therefore, exhumation ratehistory is discretized over a set of time intervals, but is spatiallycorrelated over each time interval. We use an a priori estimate of the modelparameters in order to invert this linear system and obtain the maximumlikelihood solution for the exhumation rate history. An estimate of theresolving power of the data is also obtained by computing the a posteriorivariance of the parameters and by analyzing the resolution matrix. Themethod is applicable when data from multiple thermochronometers andelevations/depths are available. However, it is not applicable when therehas been burial and reheating. We illustrate our inversion procedure usingexamples from the literature

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