Question

How much more energy is released by an M7.3 earthquake compared with an M5.3 earthquake?

Short answer

An M7.3 earthquake releases 1000 times more energy than an M5.3 earthquake.

Step-by-step solution

Identify the magnitudes of the earthquakes

The magnitudes of the two earthquakes are M1 = 7.3 and M2 = 5.3.

Apply the energy ratio formula

Using the energy ratio formula, we have: Energy Ratio = 10^(1.5*(M1-M2))

Substitute the magnitudes into the formula

Now, we substitute the values of M1 and M2 into the formula: Energy Ratio = 10^(1.5*(7.3-5.3))

Calculate the difference in magnitudes

Next, we calculate the difference in magnitudes 7.3 - 5.3 = 2.0 So, the equation becomes: Energy Ratio = 10^(1.5 * 2.0)

Multiply the exponent

Multiply the exponent: 1.5 * 2.0 = 3.0 The equation now becomes: Energy Ratio = 10^3.0

Calculate the energy ratio

Finally, we calculate the energy ratio: Energy Ratio = 10^3 = 1000 Thus, an M7.3 earthquake releases 1000 times more energy than an M5.3 earthquake.

Key concepts

Earthquake Magnitudes: Understanding the Richter Scale

When it comes to measuring the power of earthquakes, the Richter scale is a commonly used tool. Earthquake magnitudes are denoted by the letter 'M' followed by a number.

• The Richter scale is logarithmic, meaning each whole number increment represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.
• A small difference in magnitude numbers can signify a large difference in energy release.
• In our exercise, we compare an M7.3 earthquake to an M5.3 earthquake. The difference is 2.0 on the scale, highlighting a big discrepancy in energy released.

So, while M7.3 and M5.3 might seem close numerically, the energy release differs greatly. This large difference emphasizes the importance of the magnitude values when discussing earthquake impacts and potential damages.
Recognizing the significance of these numbers helps in understanding the potential for destruction an earthquake holds.

Energy Ratio Formula: Calculating Differences in Earthquake Energy

The energy ratio formula provides a way to compare how much more energy one earthquake releases compared to another. The formula is given by:
For two earthquakes with magnitudes M1 and M2, the energy ratio is:\[ Energy\ Ratio = 10^{(1.5 \times (M1 - M2))} \]This equation allows us to see that even a small difference in magnitude results in a significant difference in energy release.

Steps in using the formula involve:

• Calculating the difference between the two magnitudes (M1 - M2).
• Multiplying this difference by 1.5 to account for the logarithmic nature of the scale.
• Raising 10 to the power of the result to determine the energy ratio.

Using the example provided earlier, where M1 is 7.3 and M2 is 5.3:
- The difference in magnitude is 2.0.- Multiplying 2.0 by 1.5 gives us 3.0.- The energy ratio, therefore, is \(10^3 = 1000\).
Thus, the energy released by the M7.3 earthquake is 1000 times greater than that of the M5.3 earthquake.
Understanding this formula aids in grasping how differing magnitudes affect earthquake energy release drastically.

Seismology Calculations: Practical Implications for Earthquake Studies

Seismology calculations, like using the energy ratio formula, play an essential role in earthquake studies. They help scientists predict the potential energy release of seismic events and understand their potential impacts.

Here’s why these calculations matter:

• Helps in risk assessment, especially for structures and areas near active fault lines.
• Guides the design of buildings to withstand potential seismic energy impacts.
• Aids in the development of emergency readiness plans based on likely earthquake magnitudes and their potential energy releases.

These calculations, while often based on mathematical models and theoretical understanding, result in practical applications that significantly affect safety standards and preparedness strategies.
For students and researchers, comprehending these calculations helps frame the broader picture of earthquake preparedness and mitigation. Practice using these calculations can give one confidence in applying theoretical knowledge to real-world scenarios, ensuring more robust solutions and safety measures in seismic areas.