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Seismology, Rotational, Complexity

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Encyclopedia of Complexity and Systems Science

Definition of Subject and Its Importance: Rotational Seismology

… note the utility of measuring rotation …, but as of this writing seismology still awaits a suitable instrument for making such measurements (Aki and Richards 2002)

Most seismological studies are built on the observation of ground translational motions (up–down, N–S, E–W, using seismometers as velocity sensors, accelerometers, or GPS). This concerns the study of the Earth’s interior by seismic tomography; the understanding of earthquake processes, crustal deformation, and the seismic cycle; the quantification of shaking hazard; the analysis of the structural health of buildings; and the seismic exploration for resources. Despite the fact that theoreticians have pointed out for decades that – to fully understand seismic sources and ground motion – the associated rotationalmotions (around three orthogonal axes) should also be observed, this has until recently been impossible due to the limited sensitivity of rotation...

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Abbreviations

Cross-axis sensitivity:

Translation sensors such as standard seismometers are not only sensitive to translations but also to rotational motions (in particular tilt). In some situations (strong ground motions, long-period seismology, ocean-bottom observations), this substantially deteriorates the quality of observations. It is generally not possible to separate the motion components (e.g., translations and rotations). Another example is the sensitivity of tiltmeters to transverse accelerations or the sensitivity of the vertical component of ring laser measurements to local tilts (tilt-ring laser coupling).

Ground motion:

The measurement of ground motions is at the heart of seismology and all its associated applications. These include the understanding of the damaging part of earthquake-induced strong ground motions, the recovery of structural information of Earth’s interior by tomographic means, the understanding of the earthquake source process, and the generation of seismic waves from sources such as the oceans, atmosphere, volcanoes, landslides, and anthropogenic sources. The theory of (linear) elasticity tells us that to completely characterize ground motions, we need to measure three components of translations, six components of strain, and three components of rotations.

Ring laser:

Ring lasers are active optical interferometers based on the Sagnac effect. They measure the interferogram of two internally generated counter-propagating monomode laser beams. Local ground rotations or the Earth’s rotation around the normal vector of the plane of the laser beams causes a change of the beat note. Ring lasers can have square or triangular-shaped cavities in which the light beams propagate. Ring lasers provide currently the most accurate and most sensitive measurements of ground rotations.

Rotation:

Rotational motions are related to the curl of the deformation field containing linear combinations of the space derivatives of translations. Rotation is a vectorial quantity with three orthogonal components, two horizontal components (also called tilt at the Earth’s surface), and a vertical component (sometimes referred to as twist or spin). Rotation sensors may measure angles, angular velocity, or angular acceleration.

Strain:

Strain is a tensorial quantity describing the change in length and direction of a vector inside an elastic body before and after (linear) deformation. The elements of strain are linear combinations of the space derivatives of translations.

Translation:

Standard seismometers or GPS instruments measure translations (displacements, velocities, or accelerations) in two orthogonal horizontal directions (usually N–S, E–W) and the local vertical direction. Almost everything we know about Earth’s interior, tectonics, earthquakes from ground motion observations is based on translational measurements.

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Authors and Affiliations

  1. Department of Earth and Environmental Sciences, Ludwig-Maximilians-University, Theresienstr. 41, 80333, Munich, Germany

    Heiner Igel, Moritz Bernauer & Joachim Wassermann

  2. Technische Universität München Forschungseinrichtung Satellitengeodäsie Fundamentalstation Wettzell, 93444, Bad Kötzting, Germany

    Karl Ulrich Schreiber

Authors
  1. Heiner Igel
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  2. Moritz Bernauer
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  3. Joachim Wassermann
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  4. Karl Ulrich Schreiber
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Correspondence to Heiner Igel .

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Igel, H., Bernauer, M., Wassermann, J., Schreiber, K.U. (2015). Seismology, Rotational, Complexity. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_608-1

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