Update abstract on README.md

README.md

@@ -24,29 +24,36 @@ homogeneous density.*
 
 ## Abstract
 
-We present a new methodology to compute the gravitational fields generated by tesseroids
-(spherical prisms) whose density varies with depth according to an arbitrary continuous
-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 two
-dimensional 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,
-exponential, and sinusoidal density functions. These comparisons allowed us to obtain
-optimal 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 and its gradient are 1 and 2.5, respectively. The density-based
-discretization algorithm produces no discretizations in the linear density case, but a
-delta ratio of 0.1 is needed for the exponential and the sinusoidal density functions.
-These values can be extrapolated to cover most common use cases. However, the
-distance-size and delta ratios can be configured by the user to increase the accuracy of
-the results at the expense of computational speed. 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.
+We present a new methodology to compute the gravitational fields generated by
+tesseroids (spherical prisms) whose density varies with depth according to
+an arbitrary continuous 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 two dimensional 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,
+exponential, and sinusoidal density functions.
+The heavily oscillating density functions are intended only to test the algorithm to its
+limits and not to emulate a real world case.
+These comparisons allowed us to obtain optimal 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 and
+its gradient are 1 and 2.5, respectively.
+The density-based discretization algorithm produces no discretizations in the linear
+density case, but a delta ratio of 0.1 is needed for the exponential and most sinusoidal
+density functions.
+These values can be extrapolated to cover most common use cases, which are simpler than
+oscillating density profiles.
+However, the distance-size and delta ratios can be configured by the user to increase
+the accuracy of the results at the expense of computational speed.
+Lastly, we apply this new methodology to model the Neuquén Basin, a foreland basin in
+Argentina with a maximum depth of over 5000m, using an exponential density function.
 
 
 ## Reproducing the results