magnitude.
A number that characterizes the relative size of an earthquake. Magnitude is based on measurement of the maximum motion recorded by a seismograph. Several scales have been defined, but the most commonly used are (1) local magnitude (ML), commonly referred to as "Richter magnitude," (2) surfacewave magnitude (Ms), (3) bodywave magnitude (Mb), and (4) moment magnitude (Mw). Scales 13 have limited range and applicability and do not satisfactorily measure the size of the largest earthquakes. The moment magnitude (Mw) scale, based on the concept of seismic moment, is uniformly applicable to all sizes of earthquakes but is more difficult to compute than the other types. All magnitude scales should yield approximately the same value for any given earthquake. ( See also Earthquake ABC's & FAQ discussion.)
agnitude Magnitude is the most commonly reported measure of an earthquake's size. It began as a completely empirical measure defined by Beno Gutenberg and Charles Richter in the 1930's. They wanted a quantitative way to compare earthquakes, based on instrumental recordings, independent of the location of the observer. They borrowed the idea of a magnitude scale from astronomers, who used it to classify the brightness of stars. They defined it in terms of the amplitude of ground velocity recorded on a particular seismograph, scaled by the distance from the instrument to the earthquake.It has since been shown to be proportional to the energy released in the earthquake but the energy goes up with magnitude faster than the ground velocity, by a factor of 32. Thus, a magnitude 6 earthquake has 32 times more energy than a magnitude 5 and almost 1,000 times more energy than a magnitude 4 earthquake. This does not mean there will be 1,000 times more shaking at your house. Bigger earthquakes last longer and release their energy over a much larger area.
“How big was the earthquake? That should be easy. Why do the scientists always seem to have problems coming up with a simple answer to a simple question?”
Many Californians have felt some version of this frustration after each earthquake where one seismologist always seems to be contradicting another. In fact, earthquakes are very complex. Measuring their size is something like trying to determine the “size” of an abstract modern sculpture with only one use of a tape measure. Which dimension do you measure?
Seismologists have tried different dimensions leading to several magnitude scales. These include local (also sometimes called the Richter scale since it was the first one defined by Richter), surfacewave, bodywave, duration and coda. All these scales measure the amplitude of some aspect of ground motion (velocity or acceleration at different distances and in different frequency bands).
In recent years, seismologists have developed a new scale, called moment magnitude to describe the size of an earthquake. Unlike other magnitude scales that measure only one part of the ground motion, moment magnitude is based on a physical quantity, called moment, that can be determined either from the geometry of the fault plane or from the total energy recorded on a seismogram. It is equal to the area of the fault times the amount of slip across the fault times the rigidity of the rock. Several recent earthquakes have confirmed that moment determined by geologists measuring the fault in the field matches the moment determined by seismologists from a seismogram.
Moment magnitude has many advantages over other magnitude scales. First, because it uses the complete seismogram, it doesn't saturate, allowing us to measure the largest earthquakes. Second, because it can be determined either instrumentally or from geology, we can use it to measure the size of old earthquakes and compare them to instrumentally recorded events. Third, estimates tend to be more reliable so differences of 0.2 in moment magnitude do mean something (just don’t compare with some other type of magnitude.)
Q: How are earthquakes recorded? How are
earthquakes measured? How is the magnitude of an earthquake determined? 
A: Earthquakes are recorded by a seismographic network. Each seismic station in the network measures the movement of the ground at the site. The slip of block of rock over another in an EQ releases energy that makes the ground vibrate. That vibration pushes the adjoining piece of ground and cause it to vibrate and thus the energy travel out from the EQ in a wave. There are many different ways to measure different aspects of an earthquake. Magnitude is the most common measure of an earthquake's size. It is a measure of the size of the earthquake source and is the same number no matter where you are or what the shaking feels like. The Richter scale measures the largest wiggle on the recording, but other magnitude scales measure different parts of the earthquake. Intensity is a measure of the shaking and damage caused by the earthquake, and this value changes from location to location. See also the discussion in the Effects
section. 
bodywave magnitude, mb, and surfacewave magnitude, Ms. Each is valid for a particular frequency range and type of seismic signal. In its range of validity each is equivalent to the Richter magnitude. Because of the limitations of all three magnitude scales, ML, mb, and Ms, a new, more uniformly applicable extension of the magnitude scale, known as moment magnitude, or Mw, was developed. In particular, for very large earthquakes moment magnitude gives the most reliable estimate of earthquake size. New techniques that take advantage of modern telecommunications have recently been implemented, allowing reporting agencies to obtain rapid estimates of moment magnitude for significant earthquakes.
Q: What is "moment magnitude"? 
A: Moment is a physical quantity proportional to the slip on the fault times the area of the fault surface that slips; it is related to the total energy released in the EQ. The moment can be estimated from seismograms (and also from geodetic measurements). The moment is then converted into a number similar to other earthquake magnitudes by a standard formula. The results is called the moment magnitude. The moment magnitude provides an estimate of earthquake size that is valid over the complete range of magnitudes, a characteristic that was lacking in other magnitude scales. 
For further
information, see:
Magnitude
& Intensity, NEIC
Q: What are the earthquake magnitude
classes? 
A:

Q: What is a P wave? An S wave? 

A: When an earthquake occurs, it releases energy in the form of waves that radiate from the earthquake source in all directions. The different types of energy waves shake the ground in different ways and also travel through the earth at different velocities. The fastest wave, and therefore the first to arrive at a given location, is called the P wave. The P wave, or compressional wave, alternately compresses and expands material in the same direction it is traveling. The S wave is slower than the P wave and arrives next, shaking the ground up and down and back and forth perpendicular to the direction it is traveling. Surface waves follow the P and S waves.

Q: What is intensity? What is the
Modified Mercalli Intensity Scale? 
A: The Mercalli Scale is based on observable EQ damage. From a scientific standpoint, the Richter scale is based on seismic records while the Mercalli is based on observable data which can be subjective. Thus, the Richter scale is considered scientifically more objective and therefore more accurate. For example a level IV on the Mercalli scale would represent a small amount of observable damage. At this level doors would rattle, dishes break and weak or poor plaster would crack. As the level rises toward the larger numbers, the amount of damage increases considerably. The top number, 12, represents total damage. For further information, see: 
Q: How much energy is released in an
earthquake? 

A: Earthquakes release a tremendous amount of energy, which is why they can be so destructive. The table below shows magnitudes with the approximate amount of TNT needed to release the same amount of energy.

Q: What is acceleration, velocity, and
displacement? 
A: Acceleration is the rate of change in velocity of the ground shaking (how much the velocity changes in a unit time), just as it is the rate of change in the velocity of your car when you step on the accelerator or put on the brakes. Velocity is the measurement of the speed of the ground motion. Displacement is the measurement of the actual changing location of the ground due to shaking. All three of the values can be measured continuously during an earthquake. 
Q: What is spectral acceleration? 
A: PGA (peak acceleration) is what is experienced by a particle on the ground. SA is approximately what is experienced by a building, as modeled by a particle on a massless vertical rod having the same natural period of vibration as the building. For further information see: 