We use a modified form of the Burke et. al (2020) bottom hole temperature (BHT) method on a county-scale basis. The concept is that every BHT is too low because of unknown circulation and shutin times, as well as mud temperature after circulation. Our modification is to anchor the gradients at the 10-yr average surface temperature then set up a sweep of gradient lines on the high side of the BHTs and visually determine the highest gradient supported by the data. This is a lower bound on the geothermal gradient to the deepest support points, the gradient could be better (hotter) but not worse. Below is an example for Columbia County, Arkansas, where the data supports a gradient of > 40 C/km at 2500 m.
We suspect that the gradient is about the same for the 3500 m zone, but have insufficient number of BHTs to prove it. This is a statistical approach, it takes lots of BHTs to have a few that, through serendipity, approach the true geothermal gradient.
You might notice the very high gradients implied shallower in the plot. We see in all areas that geothermal gradients decrease with depth: in other words, 'the geothermal gradient' does not exist, there are many at any location. Geothermal gradient is a multivalued function of depth. Even so, a linear geothermal gradient is a useful approximation for estimating reservoir temperature at a given depth.
