Lamé parameters of common rocks in the Earth's crust and upper mantle

Lamé parameter ( λ ) and shear modulus ( μ ) are the most important, intrinsic, elastic properties of rocks. The Lamé parameter λ , which relates stresses and strains in perpendicular directions, is closely related to the incompressibility and contains a high proportion of information about the resistance to a change in volume caused by a change in pressure. Recent studies have emphasized the roles played by λ in the discrimination of gas sands from carbonates and shale in sedimentary basins and in the seismic reflection of crustal fault zones. Here we analyze the equivalent isotropic elastic data of 475 natural rocks in order to characterize λ values for common types of crystalline rocks in the Earth's crust and upper mantle and their variations with pressure (P), temperature (T), and mineralogical composition. When no partial melting, metamorphic reaction, dehydration, or phase transformation occurs, λ of a crystalline rock as a function of P and T can be described by λ = a + (d λ /d P ) P − c exp(− kP ) − (d λ /d T ) T , where a is the projected λ value at zero pressure if microcracks were fully closed; d λ /d P is the pressure derivative in the linear elastic regime; c is the initial λ drop caused by the presence of microcracks at zero pressure; k is a decay constant of the λ drop in the nonlinear poroelastic regime; and d λ /d T is the temperature derivative. The parameter λ increases nonlinearly and linearly with increasing pressure at low (<∼300 MPa) and high (>∼300 MPa) pressures, respectively. In the regime of high pressures, λ decreases quasi‐linearly with increasing temperature with d λ /d T values in the range of 1–10 × 10 −3 GPa/°C. Approaching the α ‐ β quartz transition temperature, quartzite displays negative λ values. In the λ ‐ ρ (density) and μ ‐ λ plots, the main categories of lithology can be clearly distinguished. The ultramafic rocks display systematic decreases in both μ and λ with increasing the degree of serpentinization. Eclogites, mafic rocks (gabbro, diabase, mafic granulite, and mafic gneiss), and felsic rocks (granite, diorite, felsic gneiss, intermediate gneiss, and metasediments) are characterized by high, moderate, and low μ and λ values, respectively. For pyroxene and olivine, both λ and ρ increase, but μ decreases with increasing the Fe/Mg ratios. In the plagioclase series, both λ and μ increases with increasing the anorthite content. Increases in the contents of garnets, sillimanite, rutile, zircon, ilmenite, and spinel result systematically in an increase in rock's λ and μ values. The present results provide improved constraints on the discrimination of composition for crustal and upper mantle rocks in terms of λ and μ .

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