Extending Eaton Exponents: beyond P-Wave Velocities

Ebrom, Daniel Andrew¹, Martin L. Albertin², Philip Heppard³ (1) BP, Houston, TX (2) BP America, Inc, Houston, TX (3) ConocoPhillips, Houston, TX

Pore pressure predictions are typically indirect, and require the transformation of measured geophysical proxies. One of the most popular transformations was invented by Ben Eaton: a normalized effective stress is given by a normalized geophysical quantity raised to a specified exponent. (“Normalized” means divided by the expected value for hydrostatic conditions. “Effective stress” means overburden minus pore pressure.) In log-log space (log effective stress on the y-axis; log geophysical measurement on the x-axis), the Eaton exponent describes a straight line with a slope equal to the exponent. For a specified geophysical quantity and constant lithology (pore pressure predictions are typically done on shale sections), all measurement/pressure pairs would hypothetically lie on this line. Eaton specified an exponent of 3 for P-wave velocities and 1.2 for resistivity measurements.

Published work by us (2003) using rock physics regressions has confirmed Eaton's P-wave exponent and has gone further to show that the exponent for S-wave velocities is 2, and for local mode conversions (C-wave velocities) is 2.5. Notable is that the exponents are measures of the insensitivity of a measured quantity to pressure changes: that is, the lower the exponent, the higher the pressure sensitivity. Although P-wave and S-wave velocities are obvious proxies for conversion to pressure, more natural quantities to use are P-wave modulus and shear modulus, since they correspond to mechanical properties of the earth. Moduli also have Eaton exponents more in line with resistivity measurements. Eaton exponents for P-wave modulus, resistivity, and shear modulus, are, respectively, 1.5, 1.2, and 1.0.