REHEATFUNQ 1.4.0: A model for regional aggregate heat flow distributions and anomaly quantification

Abstract. Surface heat flow is a geophysical variable that is affected by a complex combination of various heat generation and transport processes. The processes act on different lengths scales, from tens of meters to hundreds of kilometers. In general, it is not possible to resolve all processes for a lack of data or modeling resources, and hence the heat flow data within a region is subject to residual fluctuations.

We introduce the REgional HEAT-Flow Uncertainty and aNomaly Quantification (REHEATFUNQ) model, version 1.4.0. At its core, REHEATFUNQ uses a stochastic model for heat flow within a region, considering the aggregate heat flow to be generated by a gamma distributed random variable. Based on this assumption, REHEATFUNQ uses Bayesian inference to (i) quantify the regional aggregate heat flow distribution (RAHFD), and (ii) estimate the strength of given heat flow anomaly, for instance as generated by a tectonically active fault. The inference uses a prior conjugate to the gamma distribution for the RAHFDs, and we compute parameters for a uninformed prior from the global heat flow data base by Lucazeau (2019). Through the Bayesian inference, our model is the first of its kind to consistently account for the variability of regional heat flow in the inference of spatial signals in heat flow data. Interpretation of these spatial signals and in particular their interpretation in terms of fault characteristics (particularly fault strength) is a longstanding debate within the geophysical community.

We describe the components of REHEATFUNQ and perform a series of goodness-of-fit tests and synthetic resilience analyses of the model. While our analysis reveals to some degree a misfit of our idealized empirical model with real-world heat flow, it simultaneously confirms the robustness of REHEATFUNQ to these model simplifications.

We conclude with an application of REHEATFUNQ to the San Andreas fault in California. Our analysis finds heat flow data in the Mojave section to be sufficient for an analysis, and concludes that stochastic variability can allow for a surprisingly large fault-generated heat flow anomaly to be compatible with the data. This indicates that heat flow alone may not be a suitable quantity to address fault strength of the San Andreas fault.