Earthquake Shock Waves

3 Key excerpts on "Earthquake Shock Waves"

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  eBook - ePub

  Lees' Process Safety Essentials

  Hazard Identification, Assessment and Control

  • Sam Mannan(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The earth’s crust has a degree of elasticity and when subject to stress due to the earth’s forces, it undergoes crustal strain. This property is the basis of the elastic rebound theory of Reid. Reid suggests that ‘the crust, in many parts of the earth, is being slowly displaced, and the difference between displacements in neighboring regions sets up elastic strains, which may become greater than the rock can endure. A rupture then takes place, and the strained rock rebounds under its own elastic stresses, until the strain is largely or wholly relieved’.

  The origin of an earthquake is termed the focus, or hypocentre, and the point on the earth’s surface directly above the focus the epicenter. Earthquakes are classified as shallow focus (focus depth <70 km), intermediate focus (depth 70–300 km), and deep focus (depth >300 km).

  During an earthquake, waves pass through the earth and impart motion to the ground. There are two broad types of wave: body waves and surface waves. Body waves are classified as primary, or P, waves and secondary, or S, waves. The other main type of wave is surface waves. Surface waves, long waves or L waves.

  An instrument for the recording of the ground motion caused by an earthquake is known as a seismometer and the record that it produces a seismogram.

  Measurements may be made of any of the three main time-domain parameters: displacement, velocity, and acceleration. The measurement of ground motion is well developed and records have been obtained for the amplitude and for the acceleration of a large number of earthquakes.

  28.2 Earthquake Characterization

  The quantitative characterization of earthquakes is largely in terms of magnitude and intensity scales and of empirical correlations. Earthquakes are a geographical phenomenon and hence in many cases the original correlations have been derived for a specific region, often California. This should be borne in mind in respect of the relationships quoted. The relation of focus and epicenter, magnitude and magnitude scales, wave energy and the surface wave magnitude, frequency and return period, intensity and intensity scales are demonstrated in the full version Lees’ book (fourth edition).

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  Unearthing Fermi's Geophysics

  • Gino C. Segrè, John D. Stack(Authors)
  • 2022(Publication Date)
  • University of Chicago Press

    (Publisher)

  - 10 Hz range, with corresponding wavelengths ranging from a few hundred meters to several thousand meters.

  12.11 Snell’s Law for Elastic Waves

  Seismic waves, like optical waves, are refracted and reflected when they strike a boundary between two media. Their wave vectors are determined by a generalized form of Snell’s law, familiar from optics. Suppose the boundary between the two media is the plane x 3 = 0, and the wave vectors of all waves are in the 1 – 3 plane. Fig. (12.4) shows three such waves: (1) an incident wave at angle

  Øa

  with respect to the normal; (2) a reflected wave also making an angle

  Øa

  with respect to the normal; and (3) a transmitted wave making an angle

  Øb

  with respect to the normal. In optics, Snell’s law is usually expressed in terms of indices of refraction,

  It can equally well be written using the velocity of light propagation in the media a and b ,

  where we use

  va

  =

  c/na , vb

  =

  c/nb

  . Fig. (12.4) shows a case where

  Øb < Øa

  , corresponding to

  vb < va

  . This is an illustration of the familiar phrase in optics that “going from a fast medium to a slow medium, the transmitted wave is bent toward the normal.”

  Seismic waves also obey Snell’s law, but in general seismic waves cannot be described by the situation of elementary optics where a single reflected wave and a single transmitted wave are sufficient The main difference is that requiring the continuity of displacement and of the stress tensor leads to four boundary conditions at the interface. Given an incident wave of known amplitude, four waves must be present: reflected S and P waves, and transmitted S and P waves. In Fig. (12.5) we illustrate the situation for an incident P wave. The situation illustrated in the figure is for the case where x 3 > 0 is the “slow” medium, and x 3 < 0 is the “fast” medium. In going from slow medium to fast medium, waves are bent away from the normal. In each medium the longitudinal velocity is greater than the transverse velocity, so transverse waves are closer to the normal. If

  vl , vtr

  are the velocities of P and S waves in the upper medium, and

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  Mining of Mineral Deposits

  • Genadiy Pivnyak, Volodymyr Bondarenko, Iryna Kovalevs'ka, Mykhaylo Illiashov(Authors)
  • 2013(Publication Date)
  • CRC Press

    (Publisher)

  The third time band differs by the character and magnitude of changes in the energy index of the waves with time. This index decreases at first (from cycle 1 to cycle 2) and then increases (from cycle 2 to cycle 3). Its value changes two-threefold. Such large range of changes in the energy index speaks for high sensitivity of low-velocity low-frequency waves. High sensitivity of these waves is specified by the characteristics of their propagation in conditions of the original seismic channel. The upper boundary of the channel is ground surface; the lower boundary is top of rocks with increased elastic parameters. In this case a seismic wave is generated as a result of sequential reflection of signals from the above boundaries at the angle near to 90° at which elastic waves undergo small refraction. Due to such path waves pass a distance that exceeds the sounding base (source point interval/spacing) by many times and accumulate the impact of the stress state of rock mass.

  Figure 5. Low-velocity low-frequency wavetrain in the time band of 400–600 ms at seismic records obtained based on the different sounding bases.

  Low-velocity low-frequency waves as a low-frequency wavetrain (11–18 Hz) are notably traced at seismic records obtained at the sounding bases of 30 and 60 m (Figure 5 ).

  Amplitude levels of these waves in regard to the surface and refracted waves with the increase in the sounding base practically do not change. This feature shows that low-velocity low-frequency waves propagate in the seismic channel. In favor of their channel nature speaks also comparatively narrow spectrum and existence of dispersion (Figure 6 ).

  Hence, taking into account the mode of propagation and significant changes in the energy index we can consider the low-frequency waves as the most sensitive indicator of the changes in stress state of rock mass.

  It should also be stated that in spite of different nature of their generation the refracted and low-velocity low-frequency waves are characterized by correlation of energy indices changing with observation time (see Figure 2 and 4

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