Characterization of hydrocarbon deposits and monitoring of tectonic stresses require understanding of stress dependences of elastic moduli of rocks The third-order non-linear elasticity theory, usually applied for this, is restricted for rocks to small stress variations. Another approach is the piezosensitivity theory explicitly considering strains of the rock pore space as the main reason of the elastic non-linearity. Here we generalize the piezosensitivity approach to arbitrarily anisotropic rocks. We assume the isotropy of the tensor describing sensitivity of elasticity to small strains of the pore space and derive explicit stress dependencies of the elastic compliances. The resulting stress dependencies are expected to be valid up to several 100 MPa. The theory's predictions of mutual relations between isotropic third-order elastic moduli is in a rather good quantitative agreement with literature data on corresponding laboratory measurements.
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