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The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function M(x) = log (x/(x0)), where = 10^-3. What is the magnitude of an earthquake whose seismographic reading is 7.6 millimeters at a distance of 100 kilometers from its epicenter?

Question

The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function M(x) = log (x/(x0)), where = 10^-3. What is the magnitude of an earthquake whose seismographic reading is 7.6 millimeters at a distance of 100 kilometers from its epicenter?

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Solution

To solve this problem, we need to substitute the given seismographic reading into the function M(x) = log (x/x0).

Here, x is the seismographic reading and x0 is a constant equal to 10^-3.

Given that x = 7.6 millimeters, we first need to convert this measurement to the same units as x0, which are meters.

1 millimeter = 10^-3 meters, so 7.6 millimeters = 7.6 * 10^-3 meters.

Now we can substitute x = 7.6 * 10^-3 into the function:

M(x) = log (7.6 * 10^-3 / 10^-3)

This simplifies to:

M(x) = log (7.6)

The magnitude of the earthquake is therefore approximately 0.88 on the Richter scale.

This problem has been solved

Similar Questions

The Richter scale measure of the magnitude of the earthquake can be found by using 𝑅=log⁡(𝐴𝐴0),where 𝐴 is the measure of the intensity of the earthquake, and 𝐴0 is the intensity of a standard earthquake (the amplitude of the smallest detectable wave).Find the magnitude of an earthquake 20% of the intensity of a magnitude 7 earthquake.Give your answer correct to one decimal place.

You explained very well why the logarithm function is used to measure the magnitude of an earthquake. At least the earthquake was a moderate one it did not bring any damage to the people of Ghana. Work on your references and intext citations.

The Richter scale measures the magnitude of a seismograph because it  quantifies the amount of energy released at the earthquake's source, but we can determine the _______________, so we can see how much damage the earthquake will cause.

21. How does the Richter Magnitude Scale calculate its measurements?*1 pointEyewitnessesAmount of damage causedThe amount of time the earthquake lastedThe strength of the seismic waves recorded by a seismograph machine

Answer this using the PHIVOLCS Earthquake Intensity Scale (PEIS) *

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