Use of a power law relation to describe field measurements of compressional and shear velocity in a sediment

A sediment is assumed as a percolation network described by a “Swiss cheese” continuum model. A scaling law for a sediment is applicable to describe field measurements of compressional and shear velocity with porosity. The experimental data obtained by Deep Sea Drilling Project of three sites 288, 289, and 316 on the Ontong–Java Plateau in the western Pacific Ocean is available for calculations. The approximate expression of the variation of sound velocity with porosity (p) obtains when satisfied with the conditions of pc>p, where pc is the critical porosity. This expression is analogous to that of the frame bulk modulus obtained by Hamilton.