Gravity inversion plays a crucial role in estimating subsurface structural information. This process typically involves dividing the subsurface into numerous rectangular prisms and determining the parameters for each one. However, applying the method to large-area model parameters inversion is challenging due to high memory demands and computational costs associated with the extensive sensitivity matrix. To address this problem, a new gravity anomaly analytical expression has been developed to reduce the computational cost of the sensitivity matrix for gravity inversion. The compressed matrix technique, which eliminating the need to store and calculate redundant sensitivity matrix, further reduces storage and computation time. Additionally, depth and horizontal weighting functions have been introduced to alleviate inherent ambiguity and enhance the resolution of gravity inversion. The conjugate gradient approach is utilized as the fundamental solver leveraging the fast forward modeling that comes from the fast calculation of the sensitivity matrix and compressed matrix techniques. Model tests and real data applications demonstrate that the proposed approach effectively resolves large-scale precise gravity inversion challenges.

Medium-depth geothermal energy mainly consists of two types, hydrothermal and dry-heat rock. With huge resource reserves, its exploration and development are of great significance to the transformation of China’s energy structure and the realization of the goal of “Double-Carbon”. From the differences in the electrical characteristics between hydrothermal and hot dry rock geothermal resources, this project uses the numerical modeling of the wide field electromagnetic (WFEM) method as a tool to design a model of typical geothermal resources. Then, we summarize and analyze the detection capability of the WFEM by calculating the WFEM response under the conditions of different depths, resistivity values, thickness-to-depth ratios and other parameters. Moreover, aiming at the key problems faced by the WFEM in real applications, we discuss the factors affecting the detection accuracy and give solutions to improve the reliability of the detection results. Finally, the medium-depth geothermal energy detection in the Jiyang Depression of Shandong is presented as an example, showing how the WFEM detection technique was used with the inversion result profile obtained. By comparing the results of geomagnetic and seismic detection on the same survey line, it is demonstrated that the WFEM method has great potential in the exploration of medium-depth geothermal energy and can be the preferred method.