Geophysical Gravity Exploration with Least Squares Method Applications

In geophysical gravity exploration, researchers develop programs utilizing the least squares method for both forward modeling and inversion of gravity anomalies. These programs serve as computational tools based on mathematical models to determine the position, properties, and distribution of subsurface materials. Through precise calculations and analysis, researchers can obtain more accurate information about subsurface geological structures, which holds significant application value in fields such as petroleum exploration and mineral resource development. The implementation typically involves matrix operations for solving linear systems, where the objective function minimizes the difference between observed and calculated gravity data. Key algorithmic components include: - Gravity field calculation using density contrast models - Jacobian matrix computation for sensitivity analysis - Regularization techniques to stabilize ill-posed inversion problems - Iterative optimization algorithms (e.g., Gauss-Newton or Levenberg-Marquardt) for parameter estimation Consequently, the least squares method has gained widespread application in geophysics, with researchers continuously refining and optimizing this algorithm through techniques like preconditioning and parallel computing to better meet the demands of exploration and research requirements.