**Parameter Estimation of Velocity Function in Unconsolidated Sand Via Semblance Velocity Analysis**

**Abdullatif A. Al-Shuhail* and Abdulrahman A. Al-Shuhail**

*KFUPM, Saudi Arabia
*[email protected]*

Previous theoretical and field studies suggest the existence of continuous * velocity*-depth functions in unconsolidated sand layers. One such function is V(z) = V

_{0}√(1+kz

^{1/3}), where V

_{0}and k are the

*function parameters which depend strongly on the layer porosity (F) and water saturation (Sw), and to a lesser extent, on the properties of the sand matrix, pore water and air. To properly understand seismic wave propagation in an unconsolidated sand layer, it is important to know its*

**velocity***-function parameters. This study proposes a procedure to estimate the*

**velocity***-function parameters in unconsolidated sand layers.*

**velocity***-function parameters are generally independent. However, it was possible to relate V*

**Velocity**_{0}and k of the above V(z) function because both parameters depended strongly on F and Sw. The relation k(V

_{0})=278 – 1.4x10

^{4}/V

_{0}+ 4.9x10

^{5}/V

_{0}

^{2}was found to fit k-V

_{0}curves within 10% error for all F and Sw values lying within the ranges 0.1 < F < 0.65 and 0 < Sw < 0.9. Next, a table of V(z) functions corresponding to these F and Sw ranges was generated using F and Sw increments of 0.05. These V(z) functions were then used to calculate the corresponding time-offset (T-X) curves of the direct wave in the layer. The calculated T-X curves were fit to the observed T-X curve using the semblance

*method by scanning for the V*

**velocity**_{0}value that generated the highest semblance value. The corresponding value of k was finally calculated using the above k(V

_{0}) relation. The procedure was successfully applied to a synthetic T-X dataset.

AAPG Search and Discovery Article #90077©2008 GEO 2008 Middle East Conference and Exhibition, Manama, Bahrain