This paper builds upon my work on Tesseroids and
extends the methodology to work for depth-variable densities. Santiago, a PhD student at
Universidad Nacional de San Juan whom I co-advise, led this
project and did most of the work and writing of the paper.

Abstract

We present a new methodology to compute the gravitational fields generated by tesseroids
(spherical prisms) whose density varies continuously with depth according to an
arbitrary function. It approximates the gravitational fields through the Gauss-Legendre
Quadrature along with two discretization algorithms that automatically control its
accuracy by adaptively dividing the tesseroid into smaller ones. The first one is a
preexisting adaptive discretization algorithm that reduces the errors due to the
distance between the tesseroid and the computation point. The second is a new
density-based discretization algorithm that decreases the errors introduced by the
variation of the density function with depth. The amount of divisions made by each
algorithm is indirectly controlled by two parameters: the distance-size ratio and the
delta ratio. We have obtained analytical solutions for a spherical shell with radially
variable density and compared them to the results of the numerical model for linear and
exponential density functions. These comparisons allowed us to obtain optimum values for
the distance-size and delta ratios that yield an accuracy of 0.1% of the analytical
solutions. The resulting optimal values of distance-size ratio for the gravitational
potential, its gradient, and Marussi tensor are 1, 2 and 8, respectively. A delta ratio
of 0.2 is needed for the computation of the gravitational potential and its gradient
components, while a value of 0.01 must be used for the Marussi tensor components.
Lastly, we apply this new methodology to model the Neuquén Basin, a foreland basin in
Argentina with a maximum depth of over 5000 m, using an exponential density function.

Application of the methodology to the Neuquén basin in the Andes. The sedimentary
pack was modeled using an exponential density function.

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