Sediment with porous grains: Rock-physics model and application to marine carbonate and opal Franklin Ruiz 1 and Jack Dvorkin 1 ABSTRACT We offer an effective-medium model for estimating the elastic properties of high-porosity marine calcareous sedi- ment and diatomite. This model treats sediment as a pack of porous elastic grains. The effective elastic moduli of the po- rous grains are calculated using the differential effective-me- dium DEM model, whereby the intragranular ellipsoidal in- clusions have a fixed aspect ratio and are filled with seawater. Then the elastic moduli of a pack of these spherical grains are calculated using a modified scaled to the critical porosity upper Hashin-Shtrikman bound above the critical porosity and modified lower carbonates and upper opal Hashin- Shtrikman bounds below the critical porosity. The best match between the model-predicted compressional- and shear- wave velocities and Ocean Drilling Program ODP data from three wells is achieved when the aspect ratio of intra- granular pores is 0.5. This model assigns finite, nonzero val- ues to the shear modulus of high-porosity marine sediment, unlike the suspension model commonly used in such deposi- tional settings. The approach also allows one to obtain a satis- factory match with laboratory diatomite velocity data. INTRODUCTION Many empirical and theoretical rock-physics relations and mod- els deal with siliciclastic sediment composed of solid grains or car- bonates with inclusions. However, large areas on the earth are cov- ered with deposits of microscopic, hollow, calcareous or siliceous fossil skeletons. This study concentrates on velocity-porosity-min- eralogy relations for such sediment textures. Calcareous sediments cover about 68% of the area in the Atlantic Ocean, 36% in the Pacific Ocean, and 54% in the Indian Ocean. The total coverage is about 48% of the world’s seafloor Sverdrup et al., 1942. In most cases, calcium carbonate is transferred to the seafloor by biological activities. Organisms use dissolved calcium carbonate to construct their skeletons. The remains of the microorganisms set- tle to the seafloor and form a bed of calcareous sediment Mohamed- elhassan and Shang, 2003. In deep water, shallow buried calcareous marine sediment is composed largely of minute skeletons porous grains. When this sediment is deposited, its porosity may be as high as 0.7–0.8 Fabricius, 2003. Burial and the resulting compaction re- duce porosity to approximately 0.5–0.6 within the first few hundred meters below the seafloor. The elastic properties of this overburden and their relation to porosity, mineralogy, and stress are important for properly imaging targets located beneath this calcareous sedi- ment. Another widely distributed deposit with porous grains is diato- mite, which can be part of the overburden e.g., in the North Sea or hydrocarbon reservoirs Monterey Formation, California, U.S.A.. Diatomite is composed of the fossilized skeletal remains of micro- scopic plants called diatoms. Diatoms are made of siliceous skeleton and are found in almost every aquatic environment. Because their cell wall is composed of hydrated silica SiO 2 .nH 2 O, they are well preserved in the sediments Mohan et al., 2006. Diatoms have the unique ability to absorb water-soluble silica present in their natural environment to form a rigid, highly porous skeletal framework of amorphous silica. Atomic force microscopy AFM analysis of live diatoms reveals the nanostructure of the valve silica to be composed of a conglomerate of packed silica spheres Crawford et al., 2001; Losic et al., 2007. Hamm et al. 2003 perform real and virtual loading tests on diatom cells, using calibrated glass microneedles and finite-element analysis. They show that the frustules are remarkably strong by virtue of their archi- tecture and the material properties of the diatom silica. Diatomite is structurally close to calcareous sediment because both have a biogenic origin and thus are composed of the skeletal parts of organisms. Calcareous and diatomite materials have inter- granular and intragranular porosity. Diatoms precipitate silica from seawater as amorphous opal opal-A. After deposition, silica progresses from opal-A toward quartz, the stable phase, through an intermediate phase, opal-CT. Each transition occurs through disso- Manuscript received by the Editor 24 August 2007; revised manuscript received 15 July 2008; published online 10 December 2008. 1 Stanford University, Stanford, California, U.S.A. E-mail: fjruiz@stanford.edu; dvorkin@stanford.edu. © 2009 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 74, NO. 1 JANUARY-FEBRUARY 2009; P. E1–E15, 17 FIGS., 1 TABLE. 10.1190/1.3033212 E1 Downloaded 19 Apr 2011 to 216.198.85.26. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/