MATLAB Implementation of Gravity Inversion with Code Examples

To implement gravity inversion effectively, we must first comprehend the fundamental principles of gravity inversion and its critical applications in geological exploration, mineral resource assessment, and petroleum geology. For instance, gravity inversion techniques enable precise localization of concealed mineral deposits and hydrocarbon reservoirs through subsurface density contrast analysis. In MATLAB implementations, this typically involves processing Bouguer gravity anomalies using specialized geophysical toolboxes. The subsequent phase involves constructing a robust forward model, which simulates gravity responses based on predefined subsurface density structures. MATLAB's gravity forward modeling can be implemented using analytical solutions for simple geometries or numerical methods like finite-difference approaches for complex structures. Key functions may include calculating gravitational acceleration using Newton's law of universal gravitation and incorporating terrain corrections through digital elevation models. Following forward modeling establishment, the inversion process utilizes optimization algorithms to estimate subsurface density distributions from observed gravity data. MATLAB implementations often employ linearized inversion techniques with Tikhonov regularization or stochastic methods like Markov chain Monte Carlo (MCMC) for uncertainty quantification. The core inversion algorithm typically minimizes the misfit between observed and calculated gravity anomalies through iterative least-squares optimization, possibly utilizing MATLAB's lsqnonlin function with appropriate constraint handling for realistic geological solutions. This integrated workflow demonstrates that gravity inversion constitutes a sophisticated computational procedure requiring systematic implementation of conceptual understanding, forward modeling formulation, and inverse problem resolution. Mastering MATLAB-based gravity inversion enables professionals to extract crucial subsurface information and enhance decision-making accuracy across exploration geophysics disciplines.