No processing step changes seismic data more than 3-D imaging. Imaging techniques such as 3-D migration and dip moveout (DMO) generally change the position, amplitude, and phase of reflections as they are converted into reflector images. Migration and DMO may be formulated in many different ways, and various algorithms are available for implementing each formulation. These algorithms all make physical approximations, causing imaging software to vary with algorithm choice. Imaging software also varies because of additional implementation approximations, such as those that trade accuracy for efficiency. Imaging fidelity, then, generally depends upon algorithm, implementation, specific software parameters (such as aperture, antialias filter settings, and downward-continuations step size), specific acquisition parameters (such as nominal x- and y-direction trace spacings and wavelet frequency range), and, of course, the velocity model. Successfully imaging the target usually requires using appropriate imaging software, parameters, and velocities. Impulse responses provide an easy way to quantitatively understand the operators of imaging software and the predict how specific imaging software will perform with the chosen parameters. (An impulse response is the image computed from a data set containing only one nonzero trace and one arrival on that trace.)
I have developed equations for true-amplitude impulse responses of 3-D prestack time migration, 3-D zero-offset time migration, 3-D exploding-reflector time migration, and DMO. I use these theoretical impulse responses to analyze the operators of actual imaging software for a given choice of software parameters, acquisition parameters, and velocity model. The procedure is simple : compute impulse responses of some software; estimate position, amplitude, and phase of the impulse response events; and plot these against the theoretical values. The method is easy to use and has proven beneficial for analyzing general imaging software and for parameter evaluation with specific imaging software.