INTRODUCTION

We use seismic velocities for many important purposes. The most important is to convert travel-times to depths and to migrate reflection data. Besides these geometric uses we also can use seismic velocities to infer lithology; what kind of rocks are present? In addition we can use velocity values to learn about the condition of rocks, the nature of pore fluids, rock temperatures and so on.

In seismic reflection there are many different kinds of velocity and terminology is not standardized. We’ll learn about some velocities that are fundamentally properties of forward models and others that are derived from field data.

VELOCITIES IN FORWARD MODELS

Many models consist of layers, each with a uniform velocity. We call these "layer velocities". They may be given as part of a forward model or may be estimated in an interpretation of field data. The numerical values of layer velocities in models are usually based on tables in textbooks or handbooks of physical properties.

The harmonic mean velocity is simply the vertical distance through a set of flat layers divided by the travel-time on a vertical ray. This mean velocity is also called the time-average velocity. We sometimes use this to calculate travel-times using the hyperbolic formula. As source-receiver separation increases with respect to depth, the calculated times become inaccurate. As with any average velocity it can be expressed as a function of vertical travel time at zero separation or as a function of depth.

The root-mean-square or rms velocity is another average velocity defined for a set of flat, uniform layers and a vertical raypath. The individual velocities are weighted according to the distance traveled in each layer and the definition can be modified to account for non-vertical rays. The rms velocity is never less than the harmonic mean velocity. It is often assumed that average velocities from field data can be interpreted as rms velocities.

The x^2-t^2 average velocity is given by the square root of the slope of a straight line fit to refection data plotted on an x-squared versus t-squared graph. The value depends strongly on the largest source-receiver separation used to collect the data. Processing data to get this velocity is only feasible if there are just a few distinct reflectors.

The stacking velocity is generally determined using computer processing of digital data. This average velocity (versus either time at zero separation or depth) is the one that yields the best stack. It’s the velocity needed to make the best normal moveout correction. It is often assumed that we can treat the stacking velocity as a harmonic mean velocity or an rms velocity.

Interval velocities are somewhat similar to layer velocities in that they are uniform velocities between reflectors. Whereas layer velocities are given for forward models, interval velocities are computed from field data using the Dix equation applied to stacking velocities.

ESTIMATION OF STACKING VELOCITIES BY COMPUTER

Stacking velocities are computed from uncorrected CMP gathers. The basic algorithm uses three nested loops to test every plausible velocity at every time on every trace.

The outer loop cycles over every travel-time step along the zero-separation trace. The middle loop cycles over a range of stacking velocities from low to high. The inner loop applies a normal moveout correction to each trace using the candidate stacking velocity. Now the amplitudes on each trace at the corrected time are added (stacked). If the candidate velocity is too large the corrections will be too small and the echoes will still show positive moveout. If the velocity is too small the traces will be overshifted upwards. If the velocity is correct, all the traces will shift correctly and the echoes will add in phase to give a strong peak.

When all times, velocities and traces have been tested, the result is a "velocity spectrum". This plots stacked amplitude as a function of vertical travel-time (zero separation) on one axis and candidate stacking velocity on the other. From this plot we see the stacking velocity as the line connecting the peak amplitude.

In cases where the velocity varies significantly in the horizontal direction we can estimate velocities by optimizing the migrated image. That is we use velocities as a function of depth and horizontal location to make the sharpest, most focused image.

READINGS

Poley et al., 1989, Geophysics, 54, 1114-

Taner and Kochler, 1969, Geophysics, 34, 859-