**Measuring the Size of an Earthquake**

**Magnitude **

_{L}) was then extended to observations of earthquakes of any distance and of focal depths ranging between 0 and 700 km. Because earthquakes excite both body waves, which travel into and through the Earth, and surface waves, which are constrained to follow the natural wave guide of the Earth's uppermost layers, two magnitude scales evolved - the $m$

_{b}and $M$

_{S}scales.

_{b}= log

_{10}(

*A/T*) + Q(

*D*,

*h*) ,

*A*is the amplitude of ground motion (in microns);

*T*is the corresponding period (in seconds); and Q(

*D*,

*h*) is a correction factor that is a function of distance,

*D*(degrees), between epicenter and station and focal depth,

*h*(in kilometers), of the earthquake. The standard surface-wave formula is

_{S}= log

_{10}(

*A/T*) + 1.66 log

_{10}(D) + 3.30 .

_{L}. Negative magnitude values are permissible.

$M$_{S}Earthquakes per year ---------- ----------- 8.5 - 8.9 0.3 8.0 - 8.4 1.1 7.5 - 7.9 3.1 7.0 - 7.4 15 6.5 - 6.9 56 6.0 - 6.4 210

_{b}scale utilized compressional body P-wave amplitudes with periods of 4-5 s, but recent observations are generally of 1 s-period P waves. The $M$

_{S}scale has consistently used Rayleigh surface waves in the period range from 18 to 22 s.

**Fault Geometry and Seismic Moment, $M$ _{O} **

$$M_{O} = µS9 d: ,

_{W}, based on seismic moment, where

_{W}= 2/3 log

_{10}(M

_{O}) - 10.7 .

_{S}8.5; $M$

_{W}9.6) and 7.5 X $1029$ dyn·cm for the 1964 Alaska earthquake($M$

_{S}8.3; $M$

_{W}9.2). $M$

_{S}approaches it maximum value at a moment between $1028$ and $1029$ dyn·cm.

**Energy, E **

_{10}

*E*= 11.8 + 1.5M

_{S}

*E*, is expressed in ergs. The drawback of this method is that $M$

_{S}is computed from an bandwidth between approximately 18 to 22 s. It is now known that the energy radiated by an earthquake is concentrated over a different bandwidth and at higher frequencies. With the worldwide deployment of modern digitally recording seismograph with broad bandwidth response, computerized methods are now able to make accurate and explicit estimates of energy on a routine basis for all major earthquakes. A magnitude based on energy radiated by an earthquake, $M$

_{e}, can now be defined,

_{e}= 2/3 log

_{10}E - 9.9.

For every increase in magnitude by 1 unit, the associated seismic energy increases by about 32 times.

Although $M$_{w} and $M$_{e} are both magnitudes, they describe different physical properites of the earthquake. $M$_{w}, computed from low-frequency seismic data, is a measure of the area ruptured by an earthquake. $M$_{e}, computed from high frequency seismic data, is a measure of seismic potential for damage. Consequently, $M$_{w} and $M$_{e} often do not have the same numerical value.

**Intensity **

The increase in the degree of surface shaking (intensity) for each unit increase of magnitude of a shallow crustal earthquake is unknown. Intensity is based on an earthquake's local accelerations and how long these persist. Intensity and magnitude thus both depend on many variables that include exactly how rock breaks and how energy travels from an earthquake to a receiver. These factors make it difficult for engineers and others who use earthquake intensity and magnitude data to evaluate the error bounds that may exist for their particular applications.

An example of how local soil conditions can greatly influence local intensity is given by catastrophic damage in Mexico City from the 1985, $M$_{S} 8.1 Mexico earthquake centered some 300 km away. Resonances of the soil-filled basin under parts of Mexico City amplified ground motions for periods of 2 seconds by a factor of 75 times. This shaking led to selective damage to buildings 15 - 25 stories high (same resonant period), resulting in lossed to buildings of about $4.0 billion and at least 8,000 fatalities.

The occurrence of an earthquake is a complex physical process. When an earthquake occurs, much of the available local stress is used to power the earthquake fracture growth to produce heat rather that to generate seismic waves. Of an earthquake system's total energy, perhaps 10 percent to less that 1 percent is ultimately radiated as seismic energy. So the degree to which an earthquake lowers the Earth's available potential energy is only fractionally observed as radiated seismic energy.

**Determining the Depth of an Earthquake **

Earthquakes can occur anywhere between the Earth's surface and about 700 kilometers below the surface. For scientific purposes, this earthquake depth range of 0 - 700 km is divided into three zones: shallow, intermediate, and deep.

Shallow earthquakes are between 0 and 70 km deep; intermediate earthquakes, 70 - 300 km deep; and deep earthquakes, 300 - 700 km deep. In general, the term "deep-focus earthquakes" is applied to earthquakes deeper than 70 km. All earthquakes deeper than 70 km are localized within great slabs of shallow lithosphere that are sinking into the Earth's mantle.

The evidence for deep-focus earthquakes was discovered in 1922 by H.H. Turner of Oxford, England. Previously, all earthquakes were considered to have shallow focal depths. The existence of deep-focus earthquakes was confirmed in 1931 from studies of the seismograms of several earthquakes, which in turn led to the construction of travel-time curves for intermediate and deep earthquakes.

The most obvious indication on a seismogram that a large earthquake has a deep focus is the small amplitude, or height, of the recorded surface waves and the uncomplicated character of the P and S waves. Although the surface-wave pattern does generally indicate that an earthquake is either shallow or may have some depth, the most accurate method of determining the focal depth of an earthquake is to read a depth phase recorded on the seismogram. The depth phase is the characteristic phase pP-a P wave reflected from the surface of the Earth at a point relatively near the hypocenter. At distant seismograph stations, the pP follows the P wave by a time interval that changes slowly with distance but rapidly with depth. This time interval, pP-P (pP minus P), is used to compute depth-of-focus tables. Using the time difference of pP-P as read from the seismogram and the distance between the epicenter and the seismograph station, the depth of the earthquake can be determined from published travel-time curves or depth tables.

Another seismic wave used to determine focal depth is the sP phase - an S wave reflected as a P wave from the Earth's surface at a point near the epicenter. This wave is recorded after the pP by about one-half of the pP-P time interval. The depth of an earthquake can be determined from the sP phase in the same manner as the pP phase by using the appropriate travel-time curves or depth tables for sP.

If the pP and sP waves can be identified on the seismogram, an accurate focal depth can be determined.

*by William Spence, Stuart A. Sipkin, and George L. ChoyEarthquakes and VolcanoesVolume 21, Number 1, 1989 *