Stanford Thermal Earth Model for the Conterminous United States

Provided here are various forms of the Stanford Thermal Earth Model, as well as the data and methods used for its creation. The predictions produced by this model were visualized in two-dimensional spatial maps across the modeled depths (0-7 km) for the conterminous United States. The thermal earth model is made available as an application programming interface (API) and as feature layers on ArcGIS, which are both provided via links below.

A data-driven spatial interpolation algorithm based on physics-informed graph neural networks was used to develop these national temperature-at-depth maps. The model satisfied the three-dimensional heat conduction law by predicting subsurface temperature, surface heat flow, and rock thermal conductivity. Many physical quantities, including bottomhole temperature, depth, geographic coordinates, elevation, sediment thickness, magnetic anomaly, gravity anomaly, gamma-ray flux of radioactive elements, seismicity, and electric conductivity were used as model inputs. Surface heat flow, temperature, and thermal conductivity predictions were constructed for depths of 0-7 km at an interval of 1 km with spatial resolution of 18 km2 per grid cell. The model showed superior temperature, surface heat flow and thermal conductivity mean absolute errors of 4.8C, 8.1 mW/m2 and 0.07 W/(C-m), respectively..

本处提供斯坦福热地球模型的多种形式，以及其构建所采用的数据与方法。该模型所生成的预测结果以二维空间地图的形式在模型模拟的深度范围内（0-7公里）进行可视化展示，范围覆盖美国大陆。热地球模型以应用程序编程接口（API）和ArcGIS上的功能层的形式提供，链接如下。采用基于物理信息图神经网络的空间插值算法，并结合物理原理，开发出这些国家温度深度图。模型通过预测地下温度、地表热流和岩石热导率，满足了三维热传导定律。众多物理量，包括井底温度、深度、地理坐标、高程、沉积物厚度、磁异常、重力异常、放射性元素伽马射线通量、地震性和电导率等，均作为模型输入。针对0-7公里的深度，以1公里的间隔构建了地表热流、温度和热导率的预测，每个网格单元的空间分辨率为18平方公里2。该模型在温度、地表热流和热导率的平均绝对误差方面表现出卓越性能，分别为4.8摄氏度、8.1毫瓦/平方米和0.07瓦/(摄氏度-米)。