# Seismic velocity

seismic velocity: The speed with which an elastic wave propagates through a medium. For non-dispersive body waves, the seismic velocity is equal to both the phase and group velocities; for dispersive surface waves, the seismic velocity is usually taken to be the phase velocity. Seismic velocity is assumed usually to increase with increasing depth and when measured in a vertical direction it may be 10–15% lower than when measured parallel to strata.

The velocities of various rock types vary rather widely so it is usually difficult to determine rock type based only upon velocities. The table below shows rough ranges of velocities in units of kilometers per second for several types of earth materials. Therefore seismic surveys are most effective at delineating structure, .i.e boundaries where rock type changes.

The relations between elastic properties and velocity, introduced under "Fundamentals", are given again here.

Seismic measurements of velocity are averaged over the horizontal distance through which the seismic energy travels. Sediment velocities generally increase with depth due to increased pressure of the overburden. Fluids within pores tend to make the rocks less compressible and lead to higher interval velocities for P-waves. The adjacent figure summarizes typical velocities for differing lithologies and porosities. Carbonates in particular show a large range in velocities depending on porosity. Generally is its correct to stack the data with seismic velocity but little else. Nevertheless seismic velocity is often used for depth conversion and migration purposes and can be calibrated to well information or used where well information is particularly sparse.

### Seismic Velocity types

• Density and P-wave velocity in gas increase with pressure and temperature. Seismic velocity types

Seismic velocity types commonly considered, are:

1. Interval

2. Average

3. NMO

4. RMS

5. Stacking

6. Dix

1. The interval velocity (Vi) is the velocity in a single layer, which can be determined from sonic logs or laboratory measurements on cores from the layer.

2. The average velocity (V N ) to the Nth layer is defined in terms of the layers properties as:

where N: the total number of layers, Vi: the interval velocity in the i-th layer, and T0i = T0i – T0i-1; where T0i-1 and T0i are the zero-offset travel times to the top and bottom of the i-th layer, respectively (T00 = 0).

• The average velocity is the velocity that we get by dividing the depth (ZN) over the zero-offset one-way traveltime (T0N/2) to the bottom of the Nth layer:

3 . The NMO velocity (VNMO) to the bottom of the Nth layer is the velocity found using the approximate NMO correction formula.

• VNMO is found practically by searching for the velocity that will align the true T-X curve horizontally using the approximate NMO correction formula.
• This is usually done through the constant velocity stack (CVS) method during the velocity analysis phase of the seismic data processing flow.
• It can be found directly from TNMON(X) as

4. The root-mean-square velocity (VRMS) to the bottom of the Nth layer is defined, in terms of layers properties, as:

• It is defined, in terms of the true T-X curve, as the reciprocal of the square root of the X2 coefficient we get by fitting a polynomial to the true 2 T - 2 X curve. That is, fitting a polynomial of the form:
• Note that VRMS is also the reciprocal of the square root of the slope of the tangent to the true 2 T - 2 X curve at X = 0:

5. The stacking velocity (VS) to the bottom of the Nth layer is defined as the velocity

found by fitting a hyperbola to the true T-X curve of the form:

• Note that the stacking velocity is a special case of the RMS velocity.
• By fitting a hyperbola to the true nonhyperbolic T-X curve, we are lumping all the layers above the Nth reflector into a single virtual layer and assigning this virtual layer a velocity of VSN.
• VS is determined practically by searching for the velocity that will produce the best-fit hyperbola to the true T-X curve.
• This is usually done through the velocity spectrum method during the velocity analysis phase of the seismic data processing flow.
• At small offsets (X/ZN < 1),VRMSN ≈ VSN ≈ VNMON.

6. Dix velocity (VN) of the Nth layer is the interval velocity calculated from the RMS velocities to the top and bottom of the Nth layer (VRMSN-1 and VRMSN) using Dix’s following formula:

• Out of VRMSN, VSN, and VNMON, only VRMSN can be related directly to the interval velocities of subsurface layers through Dix velocity formula.
• However, if only small offsets are used, we can use VSN-1 and VSN or VNMON-1 and VNMON in place of VRMSN-1 and VRMSN in Dix’s velocity formula .



1. file:///C:/Users/Asa/Desktop/Asa's%20job%20hunting/Chapter3.pdf