Multimode multioffset phase analysis of surface waves, a new approach to extend MOPA to higher modes

Multioffset phase analysis (MOPA) is a fairly recent technique for evaluating seismic surface wave dispersion and estimating the presence of lateral variations. The main limitation of MOPA is that it is based on the assumption of one predominant mode, usually the fundamental mode, in the wave propagation. However, MOPA can be extended (at least) to the two-mode case: this new technique will be called multimode MOPA (MMMOPA). The method employs both amplitude and phase spectral information. The analysis is performed for each frequency independently. The presence of two modes causes the amplitude to have an oscillating behaviour as a function of offset (beats): the spatial period of the oscillating amplitude is identified, amplitude maxima and minima are extracted, and the local wavenumber is computed via linear regression. The resulting multimodal dispersion curve is consequently derived. Model uncertainties can be estimated by propagating the experimental phase and amplitude error variances through the different steps of the analysis all the way to the final phase velocities. An algorithm running the process in an automatic way has been implemented and tested on both synthetic and real data, with success. This is the base for future developments that, in the MOPA framework, can take into account rapid lateral velocity variations within the same acquisition window and estimate the modal absorption, for the estimation of the damping ratio, even in the presence of multimode surface wave propagation.