应用多项式修正构造最优的地幔一维密度模型

L. Shumlianska, P. Pigulevski
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摘要

本文得到了一个最优的一维密度模型,对应于乌克兰盾下一个地幔域的速度曲线。在获得一维密度模型时,只有地球质量和地震速度是已知的物理参数。密度是通过求解Adams-Williamson方程得到的,在假设密度仅由上层的重量产生,并且地幔的成分均匀的情况下,可以使用该方程。对实际密度分布的一些近似给出了一个地震参数,该参数根据地震速度分布的几何形状对得到的密度进行缩放,而我们的研究表明,得到的密度值不是绝对的,而只是使用与方程相对应的近似。为了得到密度分布,我们对从Adams-Williamson方程得到的第一个近似进行变换。本文展示了几种转换选项;基于5个参考地幔模型(PEMC、PEMA、PREM、AK135、IASP91)的算术平均校正;用控制点表示地震边界,确定用Adams-Williamson方程计算密度的间隔;当以理论密度曲线的多项式与IASP91模型的Adams-Wilmson方程得到的多项式之差的形式引入修正时。最后一种方法得到的密度曲线不受IASP91模型中引入的密度跳变的影响,与沿p -速度曲线拐点的地震边界位置相对应。由Adams-Williamson方程得到的密度曲线被转换成尽可能接近P、S波固有地震速度曲线几何形状的曲线。在我们看来,使用差分多项式获得的密度曲线显示了给定地震速度分布的最佳密度模型的最近似解,在我们的例子中,对于中心坐标为28.25Å 49N的乌克兰盾下的地幔域。
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APPLICATION OF POLYNOMIAL CORRECTIONS TO CONSTRUCT AN OPTIMAL ONE-DIMENSIONAL DENSITY MODEL OF THE MANTLE
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 28.25Å 49N.
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HISTORY, CURRENT STATE AND FUTURE PROSPECTS OF GEOELECTROMAGNETIC RESEARCH IN UKRAINE HIGHLY PROSPECTIVE OBJECTS OF THE MINERAL AND RAW MATERIAL BASE OF UKRAINE. PART 1. METALLIC MINERALS CRETACEOUS RIFTING IN THE GEOLOGICAL HISTORY OF THE UKRAINIAN SECTOR OF THE BLACK SEA GEOPHYSICS OF PEDOSPHERE IN KYIV UNIVERSITY REGIONAL MINERAL AND RAW MATERIAL BASES AS A KEY FACTOR IN THE DEVELOPMENT OF UKRAINE DURING THE WAR AND POST-WAR PERIODS
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