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Apparent density mapping is a technique to obtain lateral density distribution of subsurface layer by inverting gravity anomaly. In general, the subsurface layer can be divided into vertical, juxtaposed prisms in Cartesian coordinates. However, for continental and global scales, the curvature of the earth should be taken into account, and the subsurface layer should be divided into Tesseroids in spherical coordinates instead of rectangular prisms. In this paper, we present a modified Gauss-Legendre algorithm to forward the gravity anomaly generated by an arbitrary Tesseroid, and the precision can be improved vastly when the observation points in the near surface of the Tesseroid. The shell tests show that the relative maximum error can be controlled in 0.0009343% when the Gauss-Legendre nodes are set as (4, 4) in the longitude and latitude directions and the subdivision parameter W is set as 1.5. Then, an apparent density mapping approach is presented in spherical coordinates to minimize the difference between the observed gravity anomalies and calculated gravity anomalies. The synthetic model verified the feasibility and precision of our approach. In real application, we have obtained the crustal apparent density distribution of Chinese mainland with $0.25^{\circ }\times 0.25^{\circ }$ in longitude and latitude directions. The crustal apparent distribution of Chinese mainland is generally low in the western region and high in eastern region varying from 2.45-2.81 g/cm3 and closely related to lithologic units and geological boundaries.

The Apparent Density Mapping Approach in Spherical Coordinates and the Crustal Density Distribution of Chinese Mainland