Impulse Response

The purpose of Dip Move Out is to replace a nonzero offset data set by a zero offset data set. Both data sets are to be equivalent in the sense that both data sets result in the same subsurface picture after migration.

The prestack migration response to a nonzero offset impulse is the locus Q(x,z) for which all traveltimes SQR are equal. Such a locus is called isochrone. In a constant velocity medium an isochrone corresponding to the two-way traveltime t_n is an ellipse with its foci at the location of source and receiver. The major and minor axes (A and B) of the ellipse are  

$$A^{2} = {V^{2}{\cdot}t_{n}^{2}\over{4}},$$ (10)

 

B² = A²-h².

The ellipse equation is  

$${x^{2}\over{A^{2}}} + {z^{2}\over{B^{2}}} -1 = 0.$$ (12)

The poststack migration response to a zero offset impulse of time t_z is the wavefront at the time t_z/2 after initiation. In the case of constant velocity medium it is a circle with midpoint at the source receiver position B(b,0) and radius t_zV/2:  

$$(x^{2}-b^{2}) + z^{2} = {t_{z}^{2} V^{2}\over{4}}.$$ (13)