A number of relations connecting the physical properties of rocks (e.g., seismic velocity, density) with their porosity (ø) and porosity-related properties (e.g., permeability, strength, saturation) have been proposed in recent years, in step with advances in seismic methods and interpretations. The inferences most commonly used can be classified in (1) empirical relations that are obtained statistically for a given data set [see Mavko et al., 1998], (2) bounds that are rigorously derived from basic physical principles but do not give specific velocity estimates, only a range of possible values [e.g., Hashin and Shtrikman, 1963], and (3) “naïve” deterministic models that attempt a meaningful explanation of the experimental observations [e.g., Wyllie et al., 1956; Raymer et al., 1980]. Empirical relations for water-saturated sediment are numerous (see review by Erickson and Jarrard ), but are scarce for crystalline rocks. In the latter case, naïve deterministic models and bounds are most commonly used to estimate porosity from velocity. Most models assume that rocks behave identically regardless of the porosity volume (i.e., they are frame supported). A primary achievement of rock physics during the last decade has been, however, to demonstrate that this is not the situation. At porosities higher than a given threshold value (e.g., 30–40% for sediments), intergrain contacts are too weak to transmit applied load and the strength of the rock is low. Under those conditions the rock is disaggregated and behaves as a suspension (fluid supported). In this domain, seismic velocity is essentially not sensitive to changes in porosity. Below the porosity threshold the rock is frame supported, it is able to transmit loads and velocity is highly sensitive to porosity (see review by Nur et al. ). Nur et al.  referred to this threshold porosity value as critical porosity (øc). All types of rocks exhibit a critical porosity value, which can be as low as 5% for cracked igneous rocks [Nur et al., 1998]. For water-saturated basalt, representative of deep sea oceanic crust, the critical porosity is 10–15% (Figure 7). Several effective medium theories incorporating the concept of critical porosity have recently emerged [e.g., Mukerji et al., 1995]. Modifications typically made include the replacement of the inclusion phase by the critical phase and the renormalization of the porosity to ø/øc. A simple example of a critical porosity effective medium theory is the modified Voigt bound, which apparently provides a good estimate for velocities at porosities below øc [Nur et al., 1998]. In this circumstance, the original Voigt bound (i.e., a linear interpolation between the elastic properties of two constituents of a two-phase composite) is modified by replacing the water end-member (at 100% porosity) by the suspension end-member (at øc). By doing so, porosities below øc can be estimated from the compressional wave velocity, v, as follows:
where vR the velocity of the bulk rock and vS is the velocity of the suspension, which in turn can be approximated calculating the lower Reuss bound at the critical porosity:
where vw is water velocity.
 Figure 7 shows the compressional wave modulus, or M modulus (M = ρv2, where ρ is density) as a function of porosity for water-saturated basalt, based on experimental data extracted from the work of Nur et al. . If we use Carlson and Herrick's  relation for v-ρ conversion, ρ = 3.81–6.0/v, as we did in the gravity analysis, it is possible to express M in terms of v only:
 As is observed in Figure 7, the M modulus for zero-porosity basalt, MR, is ∼120 GPa, which based on (3) corresponds to a velocity, vR ≈ 6.5 km/s. This velocity is typical of lower oceanic crust, where porosity is believed to be negligible, and is similar to the velocity at the bottom of the upper plate beneath the coastline (Figure 4a). Substituting vR into (2) and using øc = 0.15 (i.e., 15%), we obtain an estimate of the suspension end-member velocity for the basement of the upper plate, vS ≈ 4.3 km/s. The M modulus for this phase is thus MS ∼ 43 GPa, apparently consistent with data from Figure 7 at a porosity higher than øc. Therefore interpreting that the basement of the overriding plate is effectively made of igneous rocks similar to oceanic basalt as indicated by the v-ρ relation, then the parts of the margin with velocity lower than ∼4.3 km/s (ø > 0.15) would have to be made of largely disaggregated material. For velocities higher than ∼4.3 km/s (ø < 0.15), we can approximate the rock porosity from (1), using the values of vR, vS, and øc referred to above:
 Figure 8 shows the upper plate porosity estimated from (4), using the velocities obtained in the tomography model (Figure 4a). Porosity uncertainties propagated from the Monte Carlo–derived velocity models are smaller than 1% within most of the upper plate, and 1–2% in the low-velocity zone, being the uncertainties negligible for the comparison of material physical properties and tectonic processes.