Geophysical Gravity Exploration

Gravity exploration serves as a fundamental geophysical method that infers subsurface density distributions and geological structures by measuring and analyzing variations in Earth's gravitational field. In gravity anomaly data processing, forward modeling and inversion represent crucial steps, with least squares methods extensively employed for optimizing model parameters.

Forward Modeling Calculation Forward modeling computes surface gravity anomaly responses based on known subsurface density distribution models. This typically involves discretizing the subsurface space into multiple volumetric elements, each assigned specific density values. By superimposing gravitational contributions from all elements toward surface measurement points, theoretical gravity anomalies are derived. This step requires efficient handling of integral calculations or numerical approximation problems, often implemented through matrix operations where the sensitivity matrix maps subsurface density changes to surface measurements.

Inverse Problem Inversion conversely deduces subsurface density distributions from observed gravity anomaly data. Since inversion problems are often ill-posed (exhibiting non-unique solutions or sensitivity to data errors), least squares methods are applied to find optimal solutions. Core to least squares inversion lies in minimizing the sum of squared residuals between observed and theoretical data, while incorporating regularization terms to stabilize solutions. Implementation typically involves solving linear systems Ax=b through QR decomposition or singular value decomposition (SVD) for numerically stable solutions.

Least Squares Method Applications In inversion, objective functions generally comprise data fitting terms and model constraint terms. Least squares solutions are obtained through matrix operations or iterative optimization algorithms like conjugate gradient methods. To enhance computational efficiency, sparse matrix storage techniques or parallel computing approaches may be employed. Furthermore, prior geological information or smoothness constraints are commonly introduced to mitigate non-uniqueness issues, implemented via Tikhonov regularization where regularization parameters control solution smoothness.

Practical Application Challenges Major challenges in gravity exploration inversion include data noise, resolution limitations, and computational complexity. Appropriate initial model selection and regularization parameter tuning significantly impact inversion results. Code implementations often incorporate cross-validation techniques for optimal parameter selection. Additionally, integrating other geophysical data (such as magnetic or seismic data) for multi-parameter inversion enhances interpretation reliability, requiring joint inversion algorithms that handle different physical property relationships.

The integration of gravity forward/inversion procedures with least squares methods provides powerful tools for subsurface resource exploration and geological structure studies. Ongoing optimization and computational efficiency improvements remain active research areas, with recent advances focusing on machine learning-enhanced inversion and GPU-accelerated computations.