Multimode dispersion, attenuation and amplitude from line-shape fitting in the frequency-wavenumber plane

Elastic waves in materials and structures often carry multiple modes, each with a dispersion, an attenuation and an amplitude worth measuring. Two families of methods exist for such measurement based on a record taken at many positions along the propagation path. The first, in the frequency-wavenumber domain, takes one line shape at a time, recovering dispersion and attenuation but not amplitude. The second fits the frequency-space record and returns all three quantities, but relies on coherent measurement of the field. Here the line shape of multiple damped modes is derived exactly, and fitted for all three quantities at once. The resulting coherent model is exact and places no such requirement on the measurement. Neglecting the record length and the interference between modes reduces it to the incoherent Lorentzian model that the first family of methods assumes; the costs of both approximations are quantified and remedies given. Across three case studies spanning different application scenarios, the coherent model is accurate to a few per cent, behind the second family through fitting error alone. The models apply to any medium whose modes decay along the path, from guided waves to poroelastic and scattering media.