Estimation of the shear wave speed in mud based on a card‐house theory with elastic platelets.

Abstract

Principal constituents of mud ocean sediments are small platelets of minerals such as smectite and kaolinite. Isomorphous substitution produces negative charges on platelets, and salt water ions rearrange to cause an effective quadrupole moment per unit area of platelet. A card‐house structure results, where an edge of one platelet is bonded to the face of another and where each platelet is in a state of electrostatic equilibrium. Platelets are idealized as elastic plates, with a bending modulus proportional to Eh3. The elastic modulus E can be estimated from chemical physics principles as a dimensionless constant times ℏ2/(meaB5), where aB is the Bohr radius. When an elastic platelet is perturbed from its equilibrium position, the restoring forces near a contact point (joined edge) are exceptionally large so that an appropriate boundary condition is that the platelet is cantilevered. Shearing forces cause the platelet to bend like a cantilevered beam with distributed electrostatic restoring forces. Solution for the platelet deformation leads to estimates of the shear modulus and shear speed, which compare favorably with existing data. [Work partially supported by the ONR and NSWC PCD.]