Impulse response

The form of the shot continuation operator varies dramatically depending on the distance the shot is shifted. For illustration, Figure 5 depicts a shot gather s₁, which is shifted various distances. The original shot gather contains a single event at (t₁ = 1.0, h₁ = 0.25) and it is shifted to s₂ at the center of the geophone spread. The distance shifted varies from frame to frame as the shot location of s₁ advances from the right to the left of the geophone spread.

Each thin line in Figure 5 represents the kinematic solution as it is derived and rendered by Mathematica. The background raster plot is computed by the Ratfor routine shct.rst incorporating amplitude variations along the operator.

 

shct
Figure 5 Impulse Response. The kinematic operator derived by the Mathematica script smile.ma agrees with the raster-plot output of the corresponding Ratfor program shct.rst. The operator varies strongly with the relative position of the original and the extrapolated shot. The impulse response collapses to a point when the original and extrapolated shot position is identical or reciprocal.

The operator is a symmetric DMO-like smile when s₂ coincides with the midpoint associated with the input impulse at (t₁, h₁). However, the operator skews sideways and finally collapses to a point as the shot location s₁ or the geophone g₁ approaches s₂. Beyond the identical and reciprocal shot position, the operator turns into a frown. In addition to the variations induced by varying shift distances, the operator also varies with different impulse event times t₁.