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a)0b)depth (m)100020003000400050000 2000 4000 6000 8000depth (m)1800 2000 2200 2400 2600c)derived porosity0.06 0.10 0.14 0.18o o o oo oooo o o ooo ooooooo oooooooooooo o o ooo oo oo oooooo ooo ooooooo o oo ooo oooooooooo ooo o oo oooo ooooooooooooooo oo oooo oooooooo oo oo oooooooooo ooooo oo oooooooo oooooooooo ooooo ooo ooooofitted trendfitted trend +/− residual standard errorfitted trend +/− two residual standard errors3800 4000 4200 4400 4600 4800in−situ vp (m/s)ooo o oooo oooooo ooo oo oo o o oo oooooooooo o o oooooo ooooooooooooo oooooooooooooooooooooo ooooo oooooooo oo oooooo o ooooooooooooooooooooo o ooooofitted trendoooooglobal trendoo oo o o oo o o ofitted trend +/− residual standard error oooo oofitted trend +/− two residual standard errorsooo3800 4000 4200 4400 4600 4800in−situ vp (m/s)in−situ vp(m/s)Figure 3.1: Illustration of derivation of rock physics relationships relating porosity to depth. Figure (a)shows <strong>the</strong> Lake Preston in situ V P versus depth log. Figure (b) shows <strong>the</strong> linear regressionfor <strong>the</strong> in situ V P versus depth using and Figure (c) shows <strong>the</strong> derived porosity versus <strong>the</strong> insitu V P . In Figures (b) and (c), black crosses show <strong>the</strong> mean and standard deviations for <strong>the</strong>interval averages that were used in <strong>the</strong> regressions. To properly model <strong>the</strong> sand endmember,only data at depths indicated by <strong>the</strong> red markers in Figure (a) were used in <strong>the</strong> regressions.32 |

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