Introduction

Interval velocity estimation requires picking in many circumstances. For example, one might pick parameters indicating the flatness of a common depth point (CDP) gather for an initial velocity model Al-Yahya (1989); Etgen (1990) or how well an image focuses after residual migration Biondi and Sava (1999). Stereotomography Billette et al. (2003) requires picking slopes and traveltimes for the velocity estimation process. Other imaging techniques such as common-focus-point migration involve semblance analysis for updating focusing operators Berkhout and Verschuur (2001). Moreover, for most of these methods, specifically those based on tomography, several reflectors need to be selected (picked) for the velocity inversion Clapp (2001).

Very few velocity estimation techniques do not require any picking. For instance, Toldi (1989) derives a relationship between interval and stacking slowness perturbations that is valid for flat geology with constant velocity background. Closest to our approach, Symes and Carazzone (1991) directly invert time shifts between adjacent traces to estimate interval velocities.

It is our belief that picking is inherently flawed and should be replaced by more robust techniques requiring as little human interpretation as possible. The major shortcomings of human intervention are unrepeatability and subjectivity. Results of velocity analysis invariably differ from one person to another based on the tools used to perform the picking or on the experience of the interpretor. Our conjecture is as follows:

It is difficult to pick arrivals or events at different spatial locations reliably. However, it is easy to estimate local stepouts between adjacent traces. Event picking should always be replaced by dip estimation.

Therefore, we propose a fully automated interval velocity estimation technique based on (1) dip estimation, (2) dip integration and (3), tomographic inversion. The ultimate goal of this work is to be able to provide a robust technique that affords a first order estimate of interval velocities.

The initial velocity, or starting guess, is a v(z) model. From this simple model we apply a NMO correction to the CMP gathers. In general, NMO is unable to completely flatten CMP gathers because of laterally varying velocity. Flat gathers are then obtained by estimating a trace-by-trace local stepout from the NMO corrected gathers. Local stepouts are then integrated to form absolute time shifts at every time, offset, and midpoint location. If data are noise-free (bad traces, random noise), estimated time shifts flatten gathers regardless of the subsurface complexity.

Time shifts are then used to perform a tomographic inversion in $(x,\tau)$ space Clapp and Biondi (2000), where x is the mid-point position and $\tau$ the zero-offset travel time. Straight rays are assumed between the subsurface location and the source/receiver positions; however, this assumption is evidently violated for any realistic geological setting. We none-the-less show that this simplistic model leads to a reasonable velocity update.

Once the interval velocity is updated, more iterations of tomography are usually required. Because of the assumptions made in the tomographic inversion, we stop at the first velocity update. One way to check whether the estimated velocity perturbations flatten the gathers or not is by applying the forward modeling operator to the estimated velocity perturbations; the modeled time shifts can then be applied to the NMO corrected gathers. From this approach we are able to obtain updated interval velocities and flat CMP gathers. In the next two sections, the time-shifts estimation step and the tomographic inversion are described.