ON DIRECT RECOVERY OF THE IMPULSE RESPONSE*

The deconvolution equation is solved in the z-transform domain directly for an impluse response. The principal assumption is the odd-depth model: two-way traveltimes to the boundaries are constrained to be odd integers only. It is further assumed that the length of the wavelet sequence is known to be less than half the length of the data sequence. An inverse of the impulse response is constrained by the zero samples of the source function. The resulting underdetermined set of equations is supplemented with the equations provided by the odd-depth model. The impulse response is found from the inverse by polynomial division.