earthquake

Question about logarithm and earthquake

The formula used to find the measure of the magnitude of an earthquake is:

(x represents the seismographic reading in millimeters ,x0 represents a zero-level earthquake the same distance from the epicenter)

Q:

Suppose that you wanted to find the magnitude of the San Francisco Earthquake of 1906 given the data that a seismographic reading of 7,943 millimeters was registered 100 kilometers from the center.

First, we will need to use the logarithmic models formula for finding magnitude of an earthquake:

In the formula, we substitute 7943 mm for the value of x, and 0.001 for the value of x_o:

Now, we type into a calculator to evaluate the function and find M(x):

Therefore, the magnitude of the earthquake that hit San Francisco in 1906 was 6.9.

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Earthquakes Logarithms

This is how we get earthquake . There are two wave,first is compassional waves(called P-waves),second is shear waves(called S-waves)

The formula originally used by Richter is:

$M_L=\log_{10}(Amplitude)+(Distance Correction Factor)$
$M_L=\log_{10}(Amplitude)+3\log_{10}(8\Delta t)-2.92$
(Where $\Delta t$ is the S-P time interval.)
However,these formules are not 100 percent accurate ,It depends on different areas and stations.This is just a estimation based on varying data.

Nowadays,the earthquake is happening more and more frquently.Although human created some formulas to estimate it ,natural power is infinite.Do not destroy our earth any more!

The Flirtations - Earthquake

The Richter Scale

The Richter magnitudes are based on a logarithmic scale (base 10). What this means is that for each whole number you go up on the Richter scale, the amplitude of the ground motion recorded by a seismograph goes up ten times. Using this scale, a magnitude 5 earthquake would result in ten times the level of ground shaking as a magnitude 4 earthquake (and 32 times as much energy would be released). To give you an idea how these numbers can add up, think of it in terms of the energy released by explosives: a magnitude 1 seismic wave releases as much energy as blowing up 6 ounces of TNT. A magnitude 8 earthquake releases as much energy as detonating 6 million tons of TNT. Pretty impressive, huh? Fortunately, most of the earthquakes that occur each year are magnitude 2.5 or less, too small to be felt by most people.

Logarithms and Earthquake Magnitude

M = log10 (A / Azero)
A = Azero 10M
For each unit increase in M, the amplitude increases by a factor of 10.
Empirical studies have found that:
Energy is proportional to 10(1.5M)
Consider the energy (E1) from a magnitude M and from (E2) from magnitude M+1
E2/E1 = (10(1.5M + 1.5))/( 101.5M)
E2/E1 = 101.5 = 32
Thus, for each unit increase in magnitude, the energy increases by a factor of 32.
For two units of magnitude, the increase is a factor of 103 or one thousand.

What are the actual energies involved?
The equation relating energy (E) to magnitude is:
E = 10(1.5M + 4.8) Joules