Multi-mode analysis of Rayleigh-type Lg. Part 1. Theory and applicability of the method

Rayleigh-type Lg propagating in a laterally homogeneous continental crust can be synthesized by adding only a few overtones at periods greater than 2 sec. Under minimal assumptions, we show that wavenumber analysis of Lg recorded on a several hundred kilometers long linear array of 10 stations allow us to isolate the different overtones, providing a tool to study crustal structures and excitation of the overtones at the source. In this first paper, we use synthetic Lg seismograms to investigate the applicability of a time-frequency-wavenumber analysis technique (UC diagram algorithm) to realistic arrays of stations. The behavior of the algorithm in the presence of lateral heterogeneities is studied numerically by introducing either random or coherent phase perturbations. We find that (1) the method is tractable if random phase fluctuations from station to station are spread over less than half a cycle, and (2) coherent velocity changes between two halves of a profile are spatially averaged if they are too small to be resolved by the array.