**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 velocity 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_{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 velocity method by scanning for the V_{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