  An axisymmetric collapse of non-rotating gravitational waves is numerically
investigated in the subcritical regime where no black holes form but where
curvature attains a maximum and decreases, following the dispersion of the
initial wave packet. We focus on a curvature invariant with dimensions of
length, and find that near the threshold for black hole formation it reaches a
maximum along concentric rings of finite radius around the axis. In this regime
the maximal value of the invariant exhibits a power-law scaling with the
approximate exponent 0.38, as a function of a parametric distance from the
threshold. In addition, the variation of the curvature in the critical limit is
accompanied by increasing amount of echos, with nearly equal temporal and
spatial periods. The scaling and the echoing patterns, and the corresponding
constants, are independent of the initial data and coordinate choices.
