Calculation of normal mode spectra in laterally heterogeneous earth models using an iterative direct solution method

SUMMARY Normal mode observations play an important role in studying broad‐scale lateral variations in the Earth. Such studies require the calculation of accurate synthetic spectra in realistic earth models, and this remains a computationally challenging problem. Here, we describe a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. In this iterative direct solution method , the mode‐coupling equations are solved in the frequency‐domain using the preconditioned biconjugate gradient algorithm, and the time‐domain solution is recovered using a numerical inverse Fourier transform. A number of example calculations are presented to demonstrate the accuracy and efficiency of the method for performing large ‘full coupling’ calculations as compared to methods based on matrix diagonalization and the traditional direct solution method.