Test of rock physics models for prediction of seismic velocities in shallow unconsolidated sands: a well log data case^‡

Abstract

A B S T R A C TThis paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz-Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point.Using either the Hertz-Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over-prediction of the velocities. The P-velocity is overpredicted by a factor of ∼1.5 and the S-velocity by a factor of ∼1.8 for highly porous gas-sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz-Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences.The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab-derived results.

Characterization of seabed properties from Scholte waves acquired on floating ice on shallow water

“…Bachrach, Dvorkin and Nur (), Zimmer et al . (2007a,b), Walton (), Andersen and Johansen () and Moyano et al . () have discussed rock physics of underconsolidated sediments.…”

Experimental mechanical compaction of sands and sand–clay mixtures: a study to investigate evolution of rock properties with full control on mineralogy and rock texture

“…). Andersen and Johansen () showed that the velocities calculated from a combination of this model and Hashin–Shtrikman lower bound interpolation give a good agreement with acquired log‐derived acoustic velocity measurements from shallow unconsolidated gas sand. Although the calculated dry elastic moduli are close to the measured values, still, the dry elastic moduli are slightly overestimated by the contact models.…”

“…The validity and applicability of these contact models have been discussed in several studies, and some modifications are suggested (Bachrach, Dvorkin, and Nur ; Zimmer et al . ; Andersen and Johansen ; Dutta, Mavko, and Mukerji ). Moreover, the friable sand model developed by Dvorkin and Nur () can describe the effect of sorting on dry effective elastic properties of unconsolidated sands, and the model helps to predict rock properties at porosities between zero (non‐porous mineral phase) and initial depositional porosity (critical porosity).…”

Geophysical Properties of the Near Surface Earth: Seismic Properties

“…The moduli increase more rapidly in Makse et al's (1999) model because the number of grain contacts is also increasing with pressure. Recently, Andersen and Johansen (2010) found that Walton's (1987) model overpredicts the observed sonic log wave speeds in unconsolidated sands by more than a factor of 1.5, and they suggested empirically derived curves (e.g., Fam and Santamarina, 1997) may be best. Although the theory illustrated in Figure 21 captures some of the elements of the pressure dependence of the moduli, real measurements on granular materials give different moduli and velocities (Hardin and Blandford, 1989).…”