一种适于近场理论地震图宽频域计算的矩阵分解算法

理论地震图方法在地震震源过程的研究中得到了广泛的应用。为了研究震源过程的细节,必须利用近场地震资料的高频信息,但是在应用Haskell矩阵法计算近场理论地震图时,格林函数的高频成分的数值不稳定性是计算宽频域理论地震图的一个基本困难。因此,目前仅有不超过10Hz的算例。本研究采用Haskell矩阵的一种新的分解组合形式,在数值计算时有效地避免了在计算过程中数值结果的溢出,实现了近场理论地震图的宽频域计算。同时,由于利用了矩阵运算中的解析关系,减少了运算的次数,从而提高了计算的速度。根据本算法建立的Fortran程序,在Univoc-1100计算机上进行了数值检验。结果表明,计算得到的格林函数至少在0-40Hz频率域范围内仍保持良好的数值稳定性。本文给出的这种Haskell矩阵分解组合形式的矩阵元素简单,且具有一定的对称性。对于这种分解所包含的物理意义,将有待进一步深入研究。

A NEW ALGORITHM FOR NEAR-FIELD SYNTHETIC SEISMOGRAM WITH A BROAD FREQUENCY BAND

Haskell layer matrix method for the propagation of elastic waves in layered media have a wide range of application. However, numerical instabilities are a problem at high frequencies for phase velocity smaller than layer velocity. In this paper a new algorithm is suggested for calculating the near-field synthetic seismogram with broad frequency band. This algorithm is based on a new analytical form of the layer matrix given here and applies a normalization to avoid overflow in numerical calculation. The problem of numerical instabilities at high frequency is solved. As a check of the accuracy of this algorithm, we have calculated the Green functions of a 4-layered half space up to 40 Hz, and found no indication of numerical instabilities on our UNIVAC 1100 computer. This result implies that the algorithm suggested in this paper is practical and useful if the nearfield synthetic seismogram with a broad frequency band is calculated to investigate the details of the earthquake source and the propeties of the media through which the waves pass.