Introduction

There are two reasons for exploring imaging and velocity analysis with a frequency-dependent velocity model. First, significant dispersion may occur naturally in the volume of rock investigated by the seismic experiment. Second, the goal of Wave Equation Migration Velocity Analysis (WEMVA, Biondi and Sava (1999)) is image optimization, which some successful approaches Pratt (1999) perform by inverting one frequency at a time, from lower to higher frequencies. The velocity model that optimizes the image may vary with frequency within the physical error bar of the velocity analysis solution. In what follows, I will examine only whether dispersion from natural causes is strong enough to be considered in WEMVA.

Frequency dispersion of elastic waves is a frequent occurrence that is more noticeable in surface waves than in body waves Pedersen et al. (2003). Some authors Wang (2001) highlight its importance and the infrequency with which it is explored by rock physics. Other articles Marion et al. (1994) analyze the conditions in which dispersion appears. Techniques for modeling dispersion Robinson (1994), or for migration with a frequency and attenuation-dependent velocity model Mittet et al. (1995) are currently available.

Dispersive phenomena in the dataset on which FEAVO was originally defined are depicted in Figure 8 of Vlad and Biondi (2002). I further investigate quantitatively whether dispersion plays a large enough role to warrant performing the velocity analysis separately for each frequency, and migrating with a $v(x,z,\omega)$ velocity model. The expense and coding overhead associated with using a frequency-dependent velocity model in wave-equation migration would be negligible, because wave-equation imaging and migration velocity analysis are parallelized over frequencies.