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a.<br />

200<br />

150<br />

V p (m/s)<br />

4000 2000<br />

1000<br />

SHALE<br />

Lama and Vutukuri (1978)<br />

Jizba (1991)<br />

Carmichael (1982)<br />

UCS (MPa)<br />

100<br />

15<br />

50<br />

12 13<br />

11<br />

14<br />

0<br />

0 100 200 300 400 500 600<br />

∆t (µs/ft)<br />

b.<br />

UCS (MPa)<br />

300<br />

200<br />

100<br />

SHALE<br />

Lama and Vutukuri (1978)<br />

Carmichael (1982)<br />

Jizba (1991)<br />

16<br />

0<br />

0 20 40 60 80 100<br />

E (GPa)<br />

c.<br />

200<br />

SHALE<br />

150<br />

Lama and Vutukuri (1978)<br />

Jizba (1991)<br />

UCS (MPa)<br />

100<br />

50<br />

17<br />

19<br />

18<br />

0<br />

0 0.1 0.2 0.3 0.4 0.5<br />

f<br />

Figure 4.15. Comparison between different empirical laws (Table 4.2) for the dependence of the<br />

strength of shale on (a) compressional wave velocity, (b) Young’s modulus and (c) porosity. After<br />

Chang, Zoback et al. (2006). Reprinted with permission of Elsevier.

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