VELOCITY POROSITY RELATIONSHIPS IN THE UPPER OCEANIC-CRUST - THEORETICAL CONSIDERATIONS

We consider here the application of rock physics theories to investigate relationships between seismic velocities and porosities in the shallow oceanic crust. Classical Hashin-Shtrikman limits ignore void shapes and are too broad to provide useful constraints on velocities and porosities. Making some assumptions about the distribution of void shapes improves the constraints. Theories which ignore crack-crack interactions underestimate the effects of porosities on velocities, thus providing upper bounds on velocities and porosities. "Self-consistent" theories overestimate crack-crack interactions and so provide lower bounds. At the high porosities required to reduce basalt from a P velocity of 7 km/s in massive form to the 2.2 km/s observed in zero-age oceanic crust, however, the bounds are too far apart to be useful. The theories are strictly valid only for very small porosities. Using an algorithm proposed by Cheng for iteratively building up porosity to create a highly porous medium, analogous to differential computation methods traditionally used to improve upon the self-consistent approach, we have devised two hybrid theories, which we term extended Walsh and extended Kuster-Toksoz. These two theories remain approximately valid at the high porosities of oceanic crustal layer 2A to provide useful upper and lower bounds on velocity for a given porosity and pore aspect ratio distribution. We attempt the inverse problem, determining porosity from a given velocity, using on-bottom refraction data collected on the flank of the East Pacific Rise. For 120 ka material with a P velocity of 2.5 km/s, if our assumptions regarding the aspect ratio distribution are correct, porosity lies somewhere between 24 and 34%. Resolution on slower, zero-age crust (2.2 km/s) is poorer: there we predict a porosity between 26 and 43%. Use of shear-wave information would tighten these bounds.