Velocity depth trends are the key to seismic modeling and also important in seismic processing (velocity analysis and depth conversion, NMO and DMO corrections) and inversion of seismic data. A Comparison of a standard velocity-depth trend with an actual velocity-depth trend may lead to a variety of new information. For example, the deviation of an actual velocity-depth trend compared to a theoretical or an empirical trend may indicate uplift/erosion, cementation, over-pressure, and/or presence of hydrocarbons. The few methods in use today either employ empirical sand baselines or rock physics models. We present new empirical equations for porosity and velocity prediction as functions of sand grain-size, shape, sorting and mineralogy. These are based on data from experimental mechanical compaction of sands with different textural and mineralogical compositions. These data may help to predict properties of sandstones at a certain depth as a function of provenance and sedimentary facies.
Velocity-depth trends are important for seismic modeling and prediction of velocities at a particular depth. Expected brine-saturated velocity-depth trends can be used to detect overpressure (Mukerji, 2002), uplift and erosion (Al- Chalabi and Rosenkranz, 2002) and/or cementation and presence of hydrocarbon (Avseth et al., 2005). Velocitydepth trends are also applied to estimate velocities before drilling in a frontier region and velocity trends of different lithologies may yield an estimate of reflectivity at their possible interfaces. Earlier work (Avseth et al. (2005) has used Hertz-Mindlin theory (Mindlin, 1949) to compute the velocity trends as a function of depth in unconsolidated sands and shales and the contact cement model (Dvorkin and Nur, 1996) for cemented sands. Velocity trends for sandstones and shales based on modified Voigt relation and a constrained relation between time and depth, respectively has also been proposed (Japsen et al., 2007). In this paper we suggest a method to compute porosity and velocity-depth trends for a wide range of unconsolidated sands as function of grain size, shape, sorting and mineralogy using empirical equations based on multiple regression of mechanically compacted sands of various mineralogical and textural combinations.
A high stress uniaxial oedometer was used to compact eight different types of sands up to a maximum stress of 50 MPa. Detailed mineralogical analysis was carried out using the X-ray diffraction technique. Based on mineralogy the sands were divided into two main groups: a) quartz-rich sands containing more than 70% quartz with the remaining being feldspar and b) quartz-poor sands containing less than 55% quartz with feldspar combined with other minerals as the second major component and minor amounts (maximum 23% in sample FG-1) of clay minerals. The sands were separated into fine, medium and coarse grain sizes using a sieve method. Sorting was measured using the weight percentage of the different grain sizes obtained by sieving. Morphological parameters like roundness, sphericity and aspect ratio were computed using the public domain, Javabased image analysis program ‘Image J’. Most of the experiments were carried out on dry samples which are simpler and faster to test than fluid saturated samples.
