APPLICATION OF POLYNOMIAL CORRECTIONS TO CONSTRUCT AN OPTIMAL ONE-DIMENSIONAL DENSITY MODEL OF THE MANTLE - Shumlianska, L.; Pigulevskiy, P. (Visnyk of Taras Shevchenko National University of Kyiv. Geology, 2025)
In this work, an optimal one-dimensional density model was obtained, corresponding to the velocity curve for one of the mantle domain under the Ukrainian shield. When obtaining a one-dimensional density model, only the Earth’s mass and seismic velocities are known physical parameters. The density is obtained by solving the Adams-Williamson equation, the use of which is possible under the assumption that the density is created only by the weight of the upper layers, with a homogeneous composition of the mantle. Some approximation to the real density distribution gives a seismic parameter that scales the obtained densities in accordance with the geometry of the seismic velocity distribution, while, as shown by our studies, the obtained density values are not absolute, but only an approximation corresponding to the equation is used. In order to obtain a density distribution we transform the first approximation obtained from the Adams-Williamson equation. This paper shows several options for transformation; based on the arithmetic mean correction for 5 reference mantle models (PEMC, PEMA, PREM, AK135, IASP91); using control points representing seismic boundaries to determine the intervals for computation of density using the Adams-Williamson equation; when introducing corrections in the form of the difference between the polynomials for the theoretical density curve and that obtained by the Adams-Wilmson equation for the IASP91 model. The density curve obtained by the last method is not distorted by the introduced density jumps from the IASP91 model, correspond to positions of seismic boundaries along the inflections of the P-velocity curve. The density curve obtained from the Adams-Williamson equation is transformed into a curve that is as close as possible to the geometry of the inherent curve seismic velocity of P and S waves. In our opinion, the density curve obtained using the difference polynomial shows the most approximate solution to the optimal density model for a given seismic velocity distribution, in our case, for the mantle domain under the Ukrainian shield with center coordinates 28.25Е 49N.