The along-strike rupture time is , where is rupture velocity. Taking a representative crustal gives about s for a km unilateral finite-source rupture. A different assumed rupture velocity changes this estimate. The local slip rise time at one patch is not specified and need not equal the whole-fault rupture time.
For comparable distance and ground conditions, the eastern observer lies in the forward rupture directivity direction. Radiation from successive patches arrives closer together, producing a shorter, more concentrated and generally larger-amplitude ground-velocity pulse. The western observer receives the contributions spread over a longer interval, generally with less concentrated shaking. This concerns pulse duration and amplitude; it does not imply an equally large permanent displacement at the eastern site.[ref]
What is Directivity by United States Geological Survey. Explanation of constructive interference and the relation of rupture speed to S-wave speed
For distant observers approximately along strike, an elementary seismic travel time construction giveswhere is the shear-wave velocity. With and , these propagation contributions are about and s, respectively; finite local rise time broadens them. Double-couple radiation pattern, receiver geometry and local site response can change the observed amplitudes, so location east or west alone is not an unconditional intensity prediction.
The star is near the southwestern end of the main fault slip patch, so a much longer part of the finite-source rupture propagates northeastward. For comparable distances, ground conditions and buildings, the northeastern site receives the stronger, shorter direct pulse; the southwestern site receives the weaker, longer direct shaking. This is rupture directivity.[ref]
What is Directivity by United States Geological Survey. Explanation of focusing by successive rupture elements
For a segment of length , rupture velocity and seismic wave speed , successive arrival times span approximatelyForward arrivals overlap and concentrate energy into a shorter pulse. Backward arrivals spread out. The supplied finite-source rupture is not perfectly unilateral, so the prediction concerns the dominant contribution. Seismic radiation patterns, seismic attenuation, sediment amplification and building response can alter the ranking of actual damage or total coda duration.
For a unilateral finite-source rupture advancing at approximately constant rupture velocity , the along-fault propagation length isThere is no supplied or calibrated seismic source time function, so a unique spatial extent cannot be read directly from Figure 4. For illustration, and an assumed would give . Allowing – and assumed – gives lengths of order 8–15 km. These are explicitly conditional scale estimates, not measured fault dimensions.
If equal-and-opposite ray geometry and phase pulse durations were known, the directivity model in solution would instead constrain a projected length,where is the angle between the rupture direction and the northern ray. Distinct P and S wave speeds, unknown takeoff angles, smooth pulse boundaries and the clipped southern S tail prevent a reliable independent numerical inversion here. This observation is consistent with a few-kilometre projected extent while the actual along-fault length can be larger. A rupture length is not the accumulated fault slip, the width of the whole fault plane, or the approximately 50 km station distance.