), shale fraction (vsh), and consolidation history are (Erickson and Jarrard, 1998) as follows. Normal consolidation (Fig. F8):
The Shikoku Basin and Nankai accretionary prism sediments have been well imaged using seismic reflection methods (Bangs et al., 1999; Moore et al., 1999). Seismic velocity data are important for providing information about the large-scale structure of the prism. Other physical properties of the sediments are important for understanding prism hydrology, sediment mechanical properties, and deformation styles (see Shipboard Scientific Party, 2001b). A conversion between seismic velocity and porosity would provide information about regional porosity variations in the underthrust sediments by allowing a conversion of marine seismic reflection data to porosity.
Numerous studies have been conducted in order to determine a relationship between compressional velocity (or acoustic velocity) and porosity for a variety of sediment and rock types. One of the earliest and most widely used transforms is the Wyllie time-average equation (Wyllie et al., 1958). This relationship is only reliable for consolidated sandstones over a small porosity range of 25%–30% (Raymer et al., 1980). However, corrections need to be made to apply the transform to unconsolidated sediments. An improved version of the time-average equation, developed by Raymer et al. (1980), eliminates the need for a compaction factor correction but requires the use of a separate equation for each of three porosity ranges. As neither the Wyllie time-average equation nor the formulation suggested by Raymer et al. (1980) adequately fit the Nankai sediments, Hyndman et al. (1993) used the results of Jarrard et al. (1989) and Han et al. (1986) to fit a smooth polynomial to Site 808 data. This fitted polynomial is applicable for a porosity range of ~30%–60% using a clay content of 50%.
In order to improve further on previous studies and to determine a relationship that accurately predicts over a large range of porosity, Erickson and Jarrard (1998) completed a statistical analysis of unconsolidated, high-porosity siliciclastic sediments from the Amazon Fan to develop a global velocity-porosity relationship. They identified three dominant variables affecting compressional wave velocity: porosity, shale fraction, and consolidation history. A key element of their formulation is the presence of a critical porosity, or a porosity threshold, across which the relationship between velocity and porosity fundamentally changes.
Raymer at al. (1980) recognized the concept of two separate porosity domains in which velocity exhibits different behaviors. The suspension domain for high-porosity rocks describes a medium where solid particles are suspended in the fluid. The consolidated rock domain for low-porosity rocks describes a medium with a continuous frame-supported matrix. Nur et al. (1998) define this transition from a suspension to a continuous matrix as the critical porosity. Most importantly, the critical porosity transition divides the relationship between velocity and porosity into two domains. For porosities greater than the critical porosity, velocity is not strongly dependent on porosity. For values below the critical porosity, velocity depends strongly on porosity and increases significantly with a small decrease in porosity.
It is important to note that the existence of a critical porosity transition does not indicate the transition from a zero-strength suspension to a frame-supported regime, but rather a transition where the frame modulus increases beyond a threshold and causes a substantial velocity increase (Erickson and Jarrard, 1998).
Clay content was evaluated by Erickson and Jarrard (1998) as a possible third-order factor affecting compressional wave velocity. The physical dependence is indirect: clay content can affect porosity, which, in turn, affects velocity. Also, lithology directly affects velocity through matrix density and matrix velocity. By removing the effects of porosity and pressure to calculate residual velocities, Erickson and Jarrard (1998) determined that clay content has no direct influence in high-porosity sediments. They suggest for high-porosity sediments that the bulk modulus is dominated by the pore fluid modulus and lithology-dependent variations in the matrix bulk modulus are overwhelmed. However, clay content is assumed to be an important control on velocity for porosities of <30% through its direct effect on the aggregate and frame bulk moduli (Erickson and Jarrard, 1998).
Because quantitative clay content data were not generally available for their logging-based study, Erickson and Jarrard (1998) used an empirical "shale fraction" log that is loosely predictive of clay content. The shale fraction log (vsh) can be calculated by using the gamma ray log and the nonlinear response function for Tertiary rocks (Dresser Atlas, 1982):
where IGR = (GRlog – GRsand)/(GRshale – GRsand). The terms GRlog, GRsand, and GRshale are the gamma ray (GR) values in API units. The sand (GRsand) and shale (GRshale) baselines are the minimum and maximum values, respectively, in the gamma ray log.
Consolidation is known to affect the compressional velocities for high-porosity sediments (Blangy et al., 1993) by not only affecting the porosity but also the shear and frame bulk moduli by increasing intergrain contacts (Erickson and Jarrard, 1998). To account for this, separate velocity-porosity relationships have been determined for what are termed "normally" and "highly" consolidated sediments. High consolidation is often seen with accretionary prism deformation, early cementation, or deep burial. Sedimentary basins are an example of a normal consolidation environment.
The global empirical relationships for compressional wave velocity (VP) in terms of fractional porosity (), shale fraction (vsh), and consolidation history are (Erickson and Jarrard, 1998) as follows. Normal consolidation (Fig. F8):
+ 0.305/[( + 0.13)2 + 0.0725]
where X1 = tanh[40( – c)] – |tanh[40( – c)]|; critical porosity (c) = 0.31.
High consolidation (Fig. F8):
+ 0.305/[( + 0.135)2 + 0.0775]
where X2 = tanh[20( – c)] – |tanh[20( – c)]|; critical porosity (c) = 0.39.
