The seismic response of sediment-filled valleys. Part 2. The case of incident P and SV waves

We present the extension to incident P and SV waves of our previous study (Bard and Bouchon, 1980) concerning the seismic response of sediment-filled bidimensional valleys to incident SH transient signals. The reliability of the Aki-Larner method is briefly discussed and the domain is estimated within which it provides accurate results. Then we investigate the response of three different valleys, having various geometrical and elastic parameters, to vertically incident P and SV waves, in both the frequency and time domains. The behavior of the valleys is shown to be qualitatively similar to their behavior for SH waves: the nonplanar interface causes surface waves (here Rayleigh waves) to be generated on valley edges, and to propagate laterally inside the basin. The amplitude of these Rayleigh waves depends greatly on the velocity contrast, the valley shape, and the incident wave type ( P or SV ), but it may be significantly higher than the disturbance associated with the direct incident signal. The frequency and direction of incident motion determine partly whether the fundamental or first higher mode will be predominantly excited, depending on the main component (vertical or horizontal) of the Rayleigh mode motion. Although the reflections of these Rayleigh waves on valley edges do not appear as clearly as in the SH case, a very long duration of the ground shaking inside the valley is still observed. In deep valleys, these laterally propagating Rayleigh waves may degenerate into a lateral resonance pattern, involving high-amplitude surface motion. These latter resonance modes, however, begin to appear in shallower valleys for incident SV waves than for incident P ones.