Origin-time and speed-ratio regression ($t_A=t_0+\Delta t/(r-1)$)

If $r=v_A/v_B$ and both phases share path length, arrival time of A is affine in the interphase delay. With unbiased independent clock errors, the intercept estimates earthquake origin time and slope estimates $1/(r-1)$. A common clock bias is indistinguishable from an origin-time shift; unrestricted station offsets also destroy speed-ratio identifiability. A statistical regression must state its clock-error assumptions.