Fitting Earth's Gravitational Field Using EGM96 Data

The EGM96 Earth Gravitational Model is a globally recognized high-precision model containing complete spherical harmonic coefficients. Using MATLAB for processing and analyzing this model enables calculation of gravitational field parameters at any location on Earth's surface. This fitting approach primarily relies on spherical harmonic expansion theory, utilizing normalized spherical harmonic coefficients provided by EGM96 to complete computational tasks.

In practical implementation, the first step involves loading EGM96 coefficient data, typically stored in text files. Then, a mathematical computation model based on spherical harmonics is constructed, where key steps include Legendre polynomial calculations and spherical harmonic summation. For given latitude and longitude coordinates on Earth's surface, the gravitational potential can be computed, subsequently deriving parameters like gravity anomalies, height anomalies, and deflection of the vertical.

The gravity anomaly calculation reflects the difference between actual gravity and normal gravity, while height anomaly represents the distance between the geoid and reference ellipsoid. Deflection of the vertical indicates the angle between the actual gravity direction and the reference ellipsoid normal. These parameters have significant applications in geodesy, geophysical exploration, and satellite orbit determination.

With its powerful matrix operation capabilities and comprehensive mathematical function library, MATLAB is particularly suitable for handling such complex calculations involving high-degree spherical harmonic expansions. By organizing the computational workflow efficiently, the entire gravitational field parameter fitting process can be implemented effectively, providing reliable foundational data support for subsequent Earth science research.