Ray theory is used to investigate the effect that irregular crustal interfaces have on the different phases that comprise Lg. We concentrate on the effects of a variable Moho in this initial study, while keeping the surface flat. The Moho models considered are a cosinusoid, a model of the Moho below the German part of the European Geo-Traverse (EGT) and a model representing an ocean-continent transition.
It is found that even slight undulations of the Moho give rise to extensive multipathing. This affects the amplitudes of the supercritically reflected crustal multiples comprising Lg in a dramatic way. Two different types of ray behavior are distinguished. The first type, corresponding to regular or weakly chaotic ray behavior, occurs at smaller values of the ray parameter and gives rise to large amplitudes at distinct epicentral distances due to focusing, accompanied by “gaps” containing very little energy due to defocusing in between. The second type, corresponding to strongly chaotic ray behavior, occurs at larger values of the ray parameter. Small changes in the take-off angle in this chaotic regime produce large fluctuations in the epicentral distance of arrivals. The Moho below Germany, for example, produces 140 supercritically reflected arrivals at an epicentral distance of 400 km. Since the amplitudes of arrivals in the chaotic region are smeared out over a large epicentral distance range, they are much less prominent than the arrivals from the regular region, even though they are supercritically reflected.
Travel-time fluctuations are less sensitive to the undulations in the Moho than amplitude variations. They are more affected by the magnitude than by the wavelength of the undulations. Amplitude undulations of more than 3 km produce multiple arrivals that have differences in travel time of up to 10 sec.