Threshold dynamic ranges for accuracy ra and precision rp at 95% confidence as a function of mc, m∞, and the assumed or estimated b-value and corner magnitude mθ. The bias or precision respectively are defined when they are equal to 0.05 units in |$\bar{m}$| and 0.1 units in b (Fig. 2). The accuracy cannot be estimated for the real data because the underlying values are not known.
| Figure . | Data . | |$r_a(\bar{m}$|) . | |$r_p(\bar{m}$|) . | ra(b) . | rp(b) . | mc . | Estimated |$\bar{m}_\infty$| . | Estimated b-value . | Estimated mθ . |
|---|---|---|---|---|---|---|---|---|---|
| 2(a) and (b) | Synthetic GR | 3.6 | 4.0 | 3.0 | 3.8 | 1.0 | 1.43 | 1.00 | 3.5 |
| 2(c) and (d) | Synthetic MGR | 1.7 | 2.6 | 1.7 | 2.0 | 1.0 | 1.42 | 1.00 | 3.5 |
| 3(a) and (b) | The Geysers | - | 2.0 | - | 2.2 | 1.25 | 1.66 | 1.02 | ∼ 4.6 |
| 3(c) and (d) | Southern California | - | 3.0 | - | 2.7 | 3.28 | 3.70 | 1.04 | ∼ 7.0 - 7.5 |
| Figure . | Data . | |$r_a(\bar{m}$|) . | |$r_p(\bar{m}$|) . | ra(b) . | rp(b) . | mc . | Estimated |$\bar{m}_\infty$| . | Estimated b-value . | Estimated mθ . |
|---|---|---|---|---|---|---|---|---|---|
| 2(a) and (b) | Synthetic GR | 3.6 | 4.0 | 3.0 | 3.8 | 1.0 | 1.43 | 1.00 | 3.5 |
| 2(c) and (d) | Synthetic MGR | 1.7 | 2.6 | 1.7 | 2.0 | 1.0 | 1.42 | 1.00 | 3.5 |
| 3(a) and (b) | The Geysers | - | 2.0 | - | 2.2 | 1.25 | 1.66 | 1.02 | ∼ 4.6 |
| 3(c) and (d) | Southern California | - | 3.0 | - | 2.7 | 3.28 | 3.70 | 1.04 | ∼ 7.0 - 7.5 |
Threshold dynamic ranges for accuracy ra and precision rp at 95% confidence as a function of mc, m∞, and the assumed or estimated b-value and corner magnitude mθ. The bias or precision respectively are defined when they are equal to 0.05 units in |$\bar{m}$| and 0.1 units in b (Fig. 2). The accuracy cannot be estimated for the real data because the underlying values are not known.
| Figure . | Data . | |$r_a(\bar{m}$|) . | |$r_p(\bar{m}$|) . | ra(b) . | rp(b) . | mc . | Estimated |$\bar{m}_\infty$| . | Estimated b-value . | Estimated mθ . |
|---|---|---|---|---|---|---|---|---|---|
| 2(a) and (b) | Synthetic GR | 3.6 | 4.0 | 3.0 | 3.8 | 1.0 | 1.43 | 1.00 | 3.5 |
| 2(c) and (d) | Synthetic MGR | 1.7 | 2.6 | 1.7 | 2.0 | 1.0 | 1.42 | 1.00 | 3.5 |
| 3(a) and (b) | The Geysers | - | 2.0 | - | 2.2 | 1.25 | 1.66 | 1.02 | ∼ 4.6 |
| 3(c) and (d) | Southern California | - | 3.0 | - | 2.7 | 3.28 | 3.70 | 1.04 | ∼ 7.0 - 7.5 |
| Figure . | Data . | |$r_a(\bar{m}$|) . | |$r_p(\bar{m}$|) . | ra(b) . | rp(b) . | mc . | Estimated |$\bar{m}_\infty$| . | Estimated b-value . | Estimated mθ . |
|---|---|---|---|---|---|---|---|---|---|
| 2(a) and (b) | Synthetic GR | 3.6 | 4.0 | 3.0 | 3.8 | 1.0 | 1.43 | 1.00 | 3.5 |
| 2(c) and (d) | Synthetic MGR | 1.7 | 2.6 | 1.7 | 2.0 | 1.0 | 1.42 | 1.00 | 3.5 |
| 3(a) and (b) | The Geysers | - | 2.0 | - | 2.2 | 1.25 | 1.66 | 1.02 | ∼ 4.6 |
| 3(c) and (d) | Southern California | - | 3.0 | - | 2.7 | 3.28 | 3.70 | 1.04 | ∼ 7.0 - 7.5 |
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