Solution (source code)

= Solution

The shorter, stronger northern pulses and broader southern pulses suggest propagation \b[from south to north], towards the northern station. The useful evidence is the difference in \b[pulse widths], not just the earlier northern arrivals: the latter chiefly reflect station distance.

As rupture reaches successively more northerly patches, each patch radiates a new <P wave> and <S wave> pulse. Towards the north, the later emission time is partly cancelled by a shorter propagation path; those contributions arrive closer together. Towards the south, later emission and a longer path add, stretching the signal. This is <rupture directivity>. It refers to the advance of the slipping region along the <fault>, not necessarily the direction of the local <fault slip> vector. A thrust can slip up-dip while its rupture front advances in a direction with a northward component.

More generally, emission from a patch at distance $s$ along the rupture arrives at
$$
t_{\mathrm{arr}}(s)=t_{\mathrm{start}}+\frac{s}{V_r}+\frac{R(s)}c,\qquad \frac{dt_{\mathrm{arr}}}{ds}\simeq\frac1{V_r}-\frac{\cos\psi}{c}.
$$
The forward direction has a smaller arrival-time spread. This is the same travel-time compression captured by isochrone-based <rupture directivity> calculations.<A formulation of directivity for earthquake sources using isochrone theory>[The primary report relates directivity to rupture geometry, seismic speed and the arrival-time distribution of radiation from successive fault patches.]{ref} Larger northern amplitude supports the interpretation but is not decisive on its own because <geometrical spreading>, <seismic attenuation>, <seismic radiation patterns> and site response also affect amplitude. With only two traces, propagation, filtering and site effects remain alternatives to test; the idealized exercise is most naturally explained by northward directivity.