The far field displacements radiating from a rectangular fault with uniformly varying velocity are studied in this paper.An analytic solution to the general form of this problem is obtained.The assumptions are:
1)When 0 ≤ t ≤ V₂-V₀/a₁,the instantaneous Vt is:
V_t=V₀+a₁ t
where V₀ is initial rupture velocity,a₁ is rupture acceleration.(a₁= constant)
2)When V₂-V₀/a₁ ≤ t ≤ V₂-V₀/a₁+t_u⁽²⁾,V_t is V_t=V₂
t_u⁽²⁾=a₁(2a₁L-V₀²)-a₃(V₂²'-V₀²)/2a₁a₃V₂
where V₂ is maximum rupture velocity,a₂ is deceleration(a₂=const-ant),and L stands for the length of rupture.
3)When V₂-V₀/a₁+t_u⁽²⁾≤t ≤ V₂-V₀)/a₁+t_u⁽²⁾+V₂/a₃,V_t is:
V_t=V₂-a₃t
where a₁ is not equal to |a₃|.
4)Cracking starts from an initial length of which is considered as zero in this paper.
Above all,V₀,V₂,a₁,a₃ and L are parameters.