subroutine slowfit( vsurface, alpha, t0,dt, s0,ds, scan,nt,ns, reg,    slow)
integer irange, it,is,                                  nt,ns
real num,den, t,s,  vsurface, alpha, t0,dt, s0,ds, scan(nt,ns),reg(nt),slow(nt)
do it= 1, nt {	t= t0 + dt*(it-1) + dt
	reg(it)  = 1./( vsurface * sqrt( (exp(alpha*t) - 1.)/(alpha*t) ))
	slow(it) = reg(it)
	}
do irange= ns/4, 5, -1 {				# shrink the fairway
do it=     1,   nt     {	t= t0 + dt*(it-1)
	do is= 1, ns   {	s= s0 + ds*(is-1)
		if( s > slow(it) + irange*ds)	scan(it,is) = 0.
		if( s < slow(it) - irange*ds)	scan(it,is) = 0.
		if( s > 1./1.6              )	scan(it,is) = 0.	# water
		}
	den= 0.0;	num= 0.0
	do is= 1, ns {	s= s0 + ds*(is-1)
		num = num + scan(it,is) * s
		den = den + scan(it,is)
		}
	slow(it) = num / ( den + 1.e-20)
	if( slow(it) == 0.)   slow(it) = 1./vsurface
	}}
return;	end