The paper by Gutenberg and Richter investigates the physical elements of earthquakes, including magnitude \(M\), energy \(E\), intensity \(I\), and acceleration \(a\), and their relationships to depth \(h\) and radius of perceptibility \(r\). The authors extend the magnitude scale to cover short distances and develop empirical relations for California shocks. Key findings include: 1. **Empirical Relations**: - \( \log a = \frac{I}{3} - \frac{1}{2} \) - \( \frac{A D^2}{T^2} = \text{constant} \) - \( M = 2.2 + 1.8 \log a_0 \) - \( M = 1.3 + 0.6 I_0 \) 2. **Energy and Magnitude**: - For California shocks at usual depth (18 km), \( \log E = 11.3 + 1.8 M \) - For other depths, \( \log E = 9.5 + 3.2 \log h + 1.1 I_0 \) - \( \log E = 11.1 + 6.4 \log R - 3.2 \log h \) 3. **Intensity and Radius of Perceptibility**: - \( I_1 - I_2 = 6 \log \frac{D_2}{D_1} \) - \( I_0 - 1.5 = 6 \log \frac{R}{h} \) 4. **Apparent Depths**: - Equations are used to calculate apparent depths for earthquakes in the United States and Europe, confirming the relatively shallow origin of shocks on the Pacific Coast compared to those in other regions. 5. **Summary**: - The paper provides a comprehensive framework for understanding the physical elements of earthquakes, including their magnitudes, energies, intensities, and accelerations, and their relationships to depth and perceptibility.The paper by Gutenberg and Richter investigates the physical elements of earthquakes, including magnitude \(M\), energy \(E\), intensity \(I\), and acceleration \(a\), and their relationships to depth \(h\) and radius of perceptibility \(r\). The authors extend the magnitude scale to cover short distances and develop empirical relations for California shocks. Key findings include: 1. **Empirical Relations**: - \( \log a = \frac{I}{3} - \frac{1}{2} \) - \( \frac{A D^2}{T^2} = \text{constant} \) - \( M = 2.2 + 1.8 \log a_0 \) - \( M = 1.3 + 0.6 I_0 \) 2. **Energy and Magnitude**: - For California shocks at usual depth (18 km), \( \log E = 11.3 + 1.8 M \) - For other depths, \( \log E = 9.5 + 3.2 \log h + 1.1 I_0 \) - \( \log E = 11.1 + 6.4 \log R - 3.2 \log h \) 3. **Intensity and Radius of Perceptibility**: - \( I_1 - I_2 = 6 \log \frac{D_2}{D_1} \) - \( I_0 - 1.5 = 6 \log \frac{R}{h} \) 4. **Apparent Depths**: - Equations are used to calculate apparent depths for earthquakes in the United States and Europe, confirming the relatively shallow origin of shocks on the Pacific Coast compared to those in other regions. 5. **Summary**: - The paper provides a comprehensive framework for understanding the physical elements of earthquakes, including their magnitudes, energies, intensities, and accelerations, and their relationships to depth and perceptibility.