Fig 1: Concatenated optimization results plotted as logs for the seven formations. The horizontal axis is the sample number which is a proxy for depth. Measured and optimized well logs are sampled every half foot (0.1524 m) over the depth range given for each formation in Table 1. The formation names and ranges are given above the top panel. Sample numbers are 1–414 for the Spraberry, 415–715 for the Wolfcamp, 716–1269 for the Avalon, 1270–1319 for the Woodford, 1320–1830 for the Eagle Ford, 1831–1986 for the Cline, and above 1987 for the Bakken. Top panel: optimized empirical coefficients m, ξ, and p for each formation. Second panel: the Xi are mineral solid volume fractions from volumetric log analysis such that ∑Xi = 1 for organic matter (XTOC), pyrite (XPyrite), calcite (XCalcite), dolomite (XDolomite), clay (XClay) and quartz plus feldspars (XQuartz). TOC is weight percent of total solid organic carbon. XTOC is the volume fraction of solid organic carbon derived from TOC using the Vernik27 relation. Third panel: red curve—dynamically measured Kud from sonic and density logs. Blue curve—predicted Kud using the semi-empirical Brown–Korringa model (Eqs. (2)–(5)), volumetric well log analysis, and the optimized coefficients for each formation. Bottom panel: predicted Brown–Korringa bulk moduli using the optimized coefficients in each formation. Red curve—dry frame modulus, Kfr. Blue curve—pore space modulus, Kφ. Green curve—effective solid constituent bulk modulus, Ks.