Crustal reflection of plane<i>SH</i>waves

TLDR

Numerical computations were performed for a single‑layered continental crust model. The derived amplitude equation predicts that surface displacement from plane SH waves exhibits harmonic minima and maxima, is weak at grazing incidence except near Love‑wave cutoffs, casts doubt on the whispering‑gallery explanation for long‑period S waves, and accounts for large amplitudes in alluvial layers over hard rock.

Abstract

An equation has been derived for the amplitude of the free surface displacement due to plane SH waves incident at any angle at the base of a layered crust. Numerical computations have been carried through for the case of a single-layered model of the continental crust. At any given angle of incidence the surface amplitude goes through a series of minima and maxima at periods which, in the single layered case, are harmonically related. At nearly grazing angles of incidence the surface amplitude is relatively small except at periods in the neighborhood of the cutoff periods of the second- and higher-order Love-wave modes. The results throw some doubt on the ‘whispering gallery’ effect as an explanation of the mode of propagation of long-period (20 to 30 sec) S waves at Sn velocity. Applied to the case of an alluvial layer over a hard-rock basement, the theory appears to give an adequate explanation of the abnormally large amplitudes that occur on unconsolidated formations in the epicentral region of earthquakes.