Earthquake frequency and amplitude relationship

Earthquakes and Seismology

earthquake frequency and amplitude relationship

The relationship between the seismic moment and magni- tude calculated from displacement amplitudes has been stud- ied mainly in the frequency domain. Attenuation of the waves in rock imposes high-frequency limits, and in small to The amplitude range of seismic waves is also great in most earthquakes. . phase, such as P, by correlation of waveforms from parallel network channels. Seismic waves travel outward from the portion of the fault that broke, like expanding Richter magnitude: The Richter magnitude is a measure of the amplitude of While the frequency of earthquakes is much greater in areas around tectonic.

Short-period instruments are used to record P and S body waves with high magnification of the ground motion. For this purpose, the seismograph response is shaped to peak at a period of about one second or less.

Gutenberg–Richter law

The intermediate-period instruments of the type used by the World-Wide Standardized Seismographic Network described in the section Earthquake observatories had a response maximum at about 20 seconds. Recently, in order to provide as much flexibility as possible for research work, the trend has been toward the operation of very broadband seismographs with digital representation of the signals.

This is usually accomplished with very long-period pendulums and electronic amplifiers that pass signals in the band between 0. When seismic waves close to their source are to be recorded, special design criteria are needed. Instrument sensitivity must ensure that the largest ground movements can be recorded without exceeding the upper scale limit of the device.

For most seismological and engineering purposes the wave frequencies that must be recorded are higher than 1 hertz, and so the pendulum or its equivalent can be small.

earthquake frequency and amplitude relationship

For this reason accelerometers that measure the rate at which the ground velocity is changing have an advantage for strong-motion recording. Integration is then performed to estimate ground velocity and displacement.

earthquake frequency and amplitude relationship

The ground accelerations to be registered range up to two times that of gravity. Recording such accelerations can be accomplished mechanically with short torsion suspensions or force-balance mass-spring systems. Because many strong-motion instruments need to be placed at unattended sites in ordinary buildings for periods of months or years before a strong earthquake occurs, they usually record only when a trigger mechanism is actuated with the onset of ground motion.

Solid-state memories are now used, particularly with digital recording instruments, making it possible to preserve the first few seconds before the trigger starts the permanent recording and to store digitized signals on magnetic cassette tape or on a memory chip. In past design absolute timing was not provided on strong-motion records but only accurate relative time marks; the present trend, however, is to provide Universal Time the local mean time of the prime meridian by means of special radio receivers, small crystal clocks, or GPS global positioning system receivers from satellite clocks.

The prediction of strong ground motion and response of engineered structures in earthquakes depends critically on measurements of the spatial variability of earthquake intensities near the seismic wave source. In an effort to secure such measurements, special arrays of strong-motion seismographs have been installed in areas of high seismicity around the world.

Large-aperture seismic arrays linear dimensions on the order of 1 to 10 km, or 0. Particularly important for full understanding of seismic wave patterns at the ground surface is measurement of the variation of wave motion with depth.

To aid in this effort, special digitally recording seismometers have been installed in deep boreholes. Field tests have established the feasibility of extensive long-term recording by instruments on the seafloor.

earthquake frequency and amplitude relationship

Japan already has a semipermanent seismograph system of this type that was placed on the seafloor off the Pacific coast of central Honshu in by means of a cable. Because of the mechanical difficulties of maintaining permanent ocean-bottom instrumentation, different systems have been considered. They all involve placement of instruments on the bottom of the ocean, though they employ various mechanisms for data transmission.

Signals may be transmitted to the ocean surface for retransmission by auxiliary apparatus or transmitted via cable to a shore-based station. Another system is designed to release its recording device automatically, allowing it to float to the surface for later recovery. The use of ocean-bottom seismographs should yield much-improved global coverage of seismic waves and provide new information on the seismicity of oceanic regions. Ocean-bottom seismographs will enable investigators to determine the details of the crustal structure of the seafloor and, because of the relative thinness of the oceanic crustshould make it possible to collect clear seismic information about the upper mantle.

Such systems are also expected to provide new data on plate boundaries, on the origin and propagation of microseisms, and on the nature of ocean-continent margins. Measuring microseisms Small ground motions known as microseisms are commonly recorded by seismographs.

These weak wave motions are not generated by earthquakes, and they complicate accurate recording of the latter. Some microseisms have local causes—for example, those due to traffic or machinery or due to local wind effects, stormsand the action of rough surf against an extended steep coast. Another class of microseisms exhibits features that are very similar on records traced at earthquake observatories that are widely separated, including approximately simultaneous occurrence of maximum amplitudes and similar wave frequencies.

These microseisms may persist for many hours and have more or less regular periods of about five to eight seconds. The amplitudes also depend to some extent on local geologic structure.

Earthquake - Properties of seismic waves |

Some microseisms are produced when large standing water waves are formed far out at sea. The period of this type of microseism is half that of the standing wave. Observation of earthquakes Earthquake observatories Worldwide during the late s, there were only about seismographic stations, which were equipped with seismographs of various types and frequency responses.

Few instruments were calibrated; actual ground motions could not be measured, and timing errors of several seconds were common. Each station of the WWSSN had six seismographs—three short-period and three long-period seismographs. Timing and accuracy were maintained by crystal clocks, and a calibration pulse was placed daily on each record.

By the s a further upgrading of permanent seismographic stations began with the installation of digital equipment by a number of organizations. Among the global networks of digital seismographic stations now in operation are the Seismic Research Observatories in boreholes metres feet deep and modified high-gain, long-period surface observatories.

The Global Digital Seismographic Network in particular has remarkable capability, recording all motions from Earth tides to microscopic ground motions at the level of local ground noise.

Earthquake seismology is the best tool to study the interior of the earth. When an earthquake or explosion occurs, part of the energy released is as elastic waves that are transmitted through the earth.

The waves are then detected and recorded by seismograms, which measure, amplify and record the motion of the ground. The information is then used to determine earthquake locations, the subsurface structures and etc.


This pendulum-mounted seismograph records horizontal motion. The mass is coupled to the Earth by means of a pendulum and a pivot is attached to a rod to constrain the mass to move in the horizontal direction only.

The spring-mounted seismograph records the vertical ground motion. A spring is attached to the mass which is connected to a rod. The rod is attached to a pivot to constrain the mass to move in an up and down direction only. Basic Physics There is some basic terminology and physics that describe the various aspects of wave form and motion. Amplitude A of the wave is the maximum displacement of the particle motions, or the height of the ripple crest.

Period T is the time it takes for two successive waves to pass a reference point or the motion to complete one cycle. The cycle of seismic waves or repetitions in a given unit of time is called frequency f.

Frequency and period are related by this relationship: The manner and speed of seismic waves travel through material is controlled by their elastic properties.

We are concerned with two types of deformation — uniform compression or expansion, and shear deformation: The maximum or "peak" ground motion is defined as the largest absolute value of ground motion recorded on a seismogram.

In the example above the surface wave has the largest deflection, so it determines the peak amplitude.

earthquake frequency and amplitude relationship

It was natural for these instrumental measures to be used to compare earthquakes, and one of the first ways of quantifying earthquakes using seismograms was the magnitude. Richter's Magnitude Scale In a Japanese seismologist named Kiyoo Wadati constructed a chart of maximum ground motion versus distance for a number of earthquakes and noted that the plots for different earthquakes formed parallel, curved lines the larger earthquakes produced larger amplitudes.

The fact that earthquakes of different size generated curves that were roughly parallel suggested that a single number could quantify the relative size of different earthquakes.

In Charles Richter constructed a similar diagram of peak ground motion versus distance and used it to create the first earthquake magnitude scale a logarithmic relationship between earthquake size and observed peak ground motion. He based his scale on an analogy with the stellar brightness scale commonly used in astronomy which is also similar to the pH scale used to measure acidity pH is a logarithmic measure of the Hydrogen ion concentration in a solution.

Sample of the data used by Richter to construct the magnitude scale for southern California. The symbols represent observed peak ground motions for earthquakes recorded during January of different symbols represent different earthquakes. The dashed lines represent the reference curve for the decrease in peak-motion amplitude with increasing distance from the earthquake. To complete the construction of the magnitude scale, Richter had to establish a reference value and identify the rate at which the peak amplitudes decrease with distance from an earthquake.

He established a reference value for earthquake magnitude when he defined the magnitude as the base-ten logarithm of the maximum ground motion in micrometers recorded on a Wood-Anderson short-period seismometer one hundred kilometers from the earthquake. Richter was pragmatic in his definition, and chose a value for a magnitude zero that insured that most of the earthquakes routinely recorded would have positive magnitudes. Also, the Wood-Anderson short-period instrument that Richter chose for his reference records seismic waves with a period of about 0.

Example seismogram recorded on a Wood-Anderson short period seismogram. The top waveform shows the broad-band displacement, the lower trace shows the corresponding ground motion that would register on a Wood-Anderson seismograph.

Richter also developed a distance correction to account for the variation in maximum ground motion with distance from an earthquake the dashed curves shown in the above diagram show his relationship for southern California.

The precise rate that the peak ground motions decrease with distance depends on the regional geology and thus the magnitude scale for different regions is slightly dependent on the "distance correction curve". Thus originally, Richter's scale was specifically designed for application in southern California. Richter's method became widely used because it was simple, required only the location of the earthquake to get the distance and a quick measure of the peak ground motion, was more reliable than older measures such as intensity.

It became widely used, well established, and forms the basis for many of the measures that we continue to use today. Generally the magnitude is computed from seismographs from as many seismic recording stations as are available and the average value is used as our estimate of an earthquake's size.

We call the Richter's original magnitude scale ML for "local magnitude"but the press usually reports all magnitudes as Richter magnitudes.