Fathom Geophysics Newsletter 25
Rock Mechanics News: Rotational seismic waves burst onto the scene
ROTATIONAL seismic waves are becoming better understood thanks to more realistic modeling of layered solids, a category that includes rock masses and various composite materials used in civil-engineered structures.
Western Australian-based rock mechanics researchers Elena Pasternak and Arcady Dyskin looked at how seismic waves travel through a hypothetical layered material in which its layers can slide relative to each other and can bend.  Sliding and bending are ignored in traditional models.
Pasternack and Dyskin looked at the behavior of the longitudinal waves (also known as primary waves, P waves, and compressional waves), the transverse waves (also known as secondary waves, S waves, and shear waves), and the rotational waves traveling through their modeled rock.
Just as longitudinal and transverse strain at an earthquake's source generates longitudinal and transverse components within the resulting seismic waves propagating away from the event, so too rotational strain naturally generates rotational components within the waves. 
As part of their model, the researchers assumed that the stacked, elastic material is of infinite height and its individual layers are isotropic and of equal thickness; that the material is compressed normal to its layers; that the layers stay together and undergo no delamination; and that seismic wavelengths are much greater than the thickness of one layer.
"A prominent feature of the rotational wave is its extremely high velocity," Pasternack and Dyskin said in their peer-reviewed paper.
They found that the longer the rotational wave's wavelength, the greater the wave's velocity. The velocity can even be "considerably greater" than the velocity of longitudinal waves propagating through layers, they said.
They also found that rotational wave velocities — unlike the velocities of longitudinal waves and transverse waves — were not heavily dependent on their propagation direction.
All of these attributes gave rotational waves a recognizable, and potentially useful, fingerprint.
"The fact that rotational waves propagate in material with sliding layers with very high velocity in all directions [could] be used to detect sliding zones," they said.
According to Pasternack and Dyskin, mysterious zones of anomalously high seismic-wave velocities had already been noted in the scientific literature.  These cases might be explained by rotational waves being generated when sliding occurred within layered rock masses and foliated rocks.
Pasternack and Dyskin's work is part of a nascent field of geoscience research called rotational seismology.
Those in the observational seismology arena have only relatively recently warmed to the idea of directly measuring rotational waves, because of a long-held belief that ground motions arising from them were negligible. Rotational waves are not only real, but also their observed amplitudes can be 10-100 times larger than what traditional seismic theory predicted. 
Since the development of sufficiently sensitive rotation-recording instruments, rotational waves have been recorded in Japan, Taiwan, Poland, Germany and New Zealand.   In theory it's possible to calculate rotational ground motion from translational ground motion recordings, but evidence suggests that the results aren't accurate enough. 
The effects of pure rotational waves on anthropological structures may be significant in ground dominated by soft sediments, which can experience liquefaction.   Some building types, such as skyscrapers, may be particularly susceptible to rotational waves.  So this is an important issue for densely populated, highly developed urban areas that are built on alluvial basins.
What are rotational waves?
As with other types of seismic waves and waves in general, rotational waves transmit energy from one location to another without a net movement of the material through which the wave passes. So rotational waves are the means by which rotational energy is transmitted through a material.
Rotational waves are a phenomenon predicted in materials classed as Cosserat continuums, which are named after two brothers who in 1909 published work that was overlooked until the 1950s and 1960s.  Pasternack and Dyskin's modeled rock falls into the Cosserat continuum category.
This arena of study is also known as micropolar elasticity. It factors in the reality that materials composed of rigid small-scale grains or voids (such as rocks, soils, bones, polymers, and foams) are made up of tiny units — micropoles — that have the ability to undergo rotation about themselves in three independent directions as well as translation in three independent directions.   Rotation around either of the two horizontal axes is called tilt, while rotation around the vertical axis is called torsion.
The micropoles are capable of responding to torque (turning force) as well as to translational force.  A micropole transmits its rotation to neighboring micropoles due to the cohesive forces existing among them. 
Rotations occurring at a micropscopic level all add up across a given volume of material, to become discernible at the macroscopic level. For instance, an easily visualized example of how rotational waves can contribute to macroscopic changes in a material is the snapping of a whole stack of balsam wood planks that have been karate-chopped just right.  Another example that is found in rocks is zig-zag chevron folding. 
In contrast, the modeling of tradtional elastic materials, which are known as classical continuums, involves: (1) the material is continuous and homogeneous, (2) its elastic limit is never exceeded, and (3) no drastic stress concentrations, such as bending, can occur in the material.  Classical continuum theory is unable to cope with certain features that can arise in a material whose microscopic structure is important. For example, the presence of geometric discontinuities, such as cracks and dislocations, violates the classical theory's basic assumptions and leads to problematic infinities in the stress field being modeled. 
One of the more esoteric spinoffs of exploring non-classical continuums could one day involve the acoustic cloaking (i.e., shielding) of objects, such as nuclear power plants , from seismic transverse waves by surrounding the objects with specially designed Cosserat/micropolar materials.   The materials are granular lattices known as phononic crystals, and because transverse and rotational waves interact inside them, they can be formulated in a way to either transmit or block a specific range of vibrations.  Manipulation of the lattice's properties permits variations in how exactly the two wave types mix within the structure.
Turning acoustic shielding on and off is theoretically doable at the very small scale as well as the very large scale. In fact, we may currently be in the early stages of a miniaturized-acoustic-circuits industry that is analogous to the infancy of the semiconductor industry, which employs semiconductor crystals to manipulate electron flow. It looks like seismic waves (i.e., acoustic/phononic waves) can potentially be guided, focused, band gapped, refracted, polarized, switched, amplified, and so on.  We may one day see an array of acoustic waveflow-based versions of today's electrical transistors, resistors and capacitors.  There has even been research into phononic crystals that respond to an externally applied magnetic field. 
It's hard to overstate the influence that science's embrace of rotational waves may eventually have on society.
A better understanding of rotational waves is relevant to improving the recording of ground motion caused by earthquakes , especially given that traditional instruments have their recordings infiltrated by rotational ground motion-related signal.   Over the past decade, applied geoscientists have been racing to come up with suitable seismometers.   It follows that improved earthquake recordings will pave the way to a better understanding of earthquakes themselves.
Traditionally, building code design formulas have only considered translational components of ground motion.  Incorporation of the impact of rotational seismic waves on built structures would help maximize the earthquake-resistance of buildings, bridges, tunnels, nuclear power plants, dams, pipelines, and other civil engineering structures and utility networks.    According to a study of a 2011 earthquake affecting Christchurch, New Zealand, models suggest that ignoring the effect of ground rotation on buildings could lead to a 15 percent underestimation of interstory drift, which in turn would produce greater-than-expected damage. 
In the realm of materials engineering, there might be rotational wave-related applications in the quality control of laminated materials, Pasternack and Dyskin said.
Knowledge of rotational waves could also lead to improved modeling of how seismic waves propagate through the earth,  which in turn could lead to better seismic imaging of the earth  , which is used in arenas such as mineral exploration and petroleum exploration.
And by recording the full gamut of seismic wave types, staff responsible for the structural integrity of underground mines and the health and safety of workers would have access to more complete monitoring of seismic events. 
 E. Pasternak and A.V. Dyskin (2018) "Rotational waves in layered solids with many sliding layers", International Journal of Engineering Science, 125, 40-50.
 M. Takeo and H.M. Ito (1997) "What can be learned from rotational motions excited by earthquakes?", Geophysical Journal International, 129, 319-329.
 See, for example: R.M. Kebeasy (1969) "On the anomaly of travel time of P waves observed at Japanese stations. Part 1", Bulletin of the Earthquake Research Institute, 47, 467-486.
 W.H.K. Lee, M. Celebi, M.I. Todorovska and M.F. Diggles (eds) (2007) "Rotational Seismology and Engineering Applications: Proceedings for the 1st International Workshop, Menlo park, California, USA — September 18-19, 2007", US Geological Survey, Open-File Report 2007-1144 (version 2.0), 46 pages.
 M.I. Todorovska, H. Igel, M.D. Trifunac and W.H.K. Lee (2008) "Rotational earthquake motions: International working group and its activities", 14th World Conference on Earthquake Engineering, Beijing, China, 8 pages.
 H.-C. Chiu, F.J. Wu and H.-C. Huang (2013) "Rotational motions recorded at Hualien during the 2012 Wutai, Taiwan earthquake", Terrestrial, Atmospheric and Oceanic Sciences, 24, 1, 31-40.
 J. Yin, R.L. Nigbor, Q. Chen and J. Steidl (2016) "Engineering analysis of measured rotational ground motions at GVDA", Soil Dynamics and Earthquake Engineering, 87, 125-137.
 N.D. Pham (2009) "Rotational motions in seismology: Theory, observation, modeling", Doctoral Dissertation, Ludwig Maximilian University of Munich, 108 pages.
 R. Guidotti (2012) "Near-field earthquake ground motion rotations and relevance on civil engineering structures", Doctoral Dissertation, Politecnico di Milano, 178 pages.
 A.M. Awad and J.L. Humar (1984) "Dynamic response of buildings to ground rotational motion", Canadian Journal of Civil Engineering, 11, 48-56.
 W. Nowacki and W. Olszak (1974) "Micropolar elasticity", International Centre for Mechanical Sciences, Courses and Lectures No. 151, Symposium Organized by the Department of Mechanics of Solids, June 172, Springer-Verlag.
 A.C. Eringen (1967) "Theory of micropolar elasticity", Princeton University Department of Aerospace and Mechanical Sciences, Technical Report No. 1 for Office of Naval Research, 193 pages.
 Microstretch elasticity and micromorphic elasticity take realistic modeling of materials even further. See, for example: R. Abreu, C. Thomas and S. Durand (2018) "Effect of observed micropolar motions on wave propagation in deep Earth minerals", Physics of the Earth and Planetary Interiors, 276, 215-225.
 R. Lakes (1995) "Experimental methods for study of Cosserat elastic solids and other generalized elastic continua", In: H. Muhlhaus (ed.), "Continuum models for materials with micro-structure", J. Wiley, Chapter 1, 1-22.
 Some versions of micropolar theory even take into consideration the thermodynamics of micropoles (e.g., microtemperatures) and electromagnetic phenomena of micropoles. See introductory discussion of this in: S. Dilbag (2008) "Some dynamical problems in micropolar elasticity", Panjab University, Chandigarh, Department of Mathematics, Engineering Sciences, 172 pages.
 D. Bigoni and P.A. Gourgiotis (2016) "Folding and faulting of an elastic continuum", Proceedings of the Royal Society A, 472, 20160018, 22 pages.
 Y. Sompornjaroensuk, W. Boonchareon and P. Kongtong (2013) "Elementary mathematical theory for stress singularities at the vertex of plane infinite wedges", Advance Studies in Theoretical Physics, 7, 423-446.
 A. Khlopotin, P. Olsson and F. Larsson (2015) "Transformational cloaking from seismic surface waves by micropolar metamaterials with finite couple stiffness", Wave Motion, 58, 53-67.
 B.B. Alagoz and S. Alagoz (2011) "Towards earthquake shields: A numerical investigation of earthquake shielding with seismic crystals", Open Journal of Acoustics, 1, 63-69.
 S.R. Sklan, R.Y.S. Pak and B. Li (2018) "Seismic invisibility: Elastic wave cloaking via symmetrized transformation media", New Journal of Physics, 20, 063013, 14 pages.
 H. Pichard, A. Duclos, J.-P. Groby and V. Tournat (2012) "Two-dimensional discrete granular phononic crystal for shear wave control", Physical Review B, 86, 134307, 12 pages.
 O.B. Wright and S. Matsuda (2015) "Watching surface waves in phononic crystals", Philosophical Transactions of the Royal Society A, 373, 20140364, 18 pages.
 G.Y. Lee, C. Chong, P.G. Kevrekidis and J. Yang (2016) "Wave mixing in coupled phononic crystals via a variable stiffness mechanism", Journal of the Mechanics and Physics of Solids, 95, 501-516.
 F. Allein (2017) "Linear and nonlinear waves in magneto-granular phononic structures: Theory and experiments", PhD Thesis, Acoustics Laboratory, Universite du Maine, 124 pages.
 R. Pillet and J. Virieux (2007) "The effects of seismic rotations on inertial sensors", Geophysical Journal International, 171, 3, 1314-1323.
 See, for example: J. Brokesova, J. Malek and J.R. Evans (2016) "Rotaphone-D: A new six-degree-of-freedom short-period seismic sensor: Features, parameters, field records", 4th International Working Group on Rotational Seismology, Tutzing, 20-23 June, presentation slides.
 L.R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marc, J. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz and R. Jankowski (2016) "Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications", Sensors, 16, 2161, 22 pages.
 E. Kalkan and V. Graizer (2007) "Coupled tilt and translational ground motion response spectra", Journal of Structural Engineering, 133, 5, 609-619.
 A. Cochard, H. Igel, B. Schuberth, W. Suryanto, A. Velikoseltev, U. Schreiber, J. Wassermann, F. Scherbaum and D. Vollmer (2006) "Rotational motions in seismology: Theory, observation, simulation", In: R. Teisseyre, E. Majewski and M. Takeo (eds) "Earthquake source asymmetry, structural media and rotation effects", Springer.
 R. Abreu, J. Kamm, A. Ferreira, C. Thomas, A.-S. Reiss, A. Madeo and P. Neff (2016) "Modeling rotational waves in seismology", University of Duisberg-Essen, poster.
 R. Abreu, J. Kamm and A.-S. Reiss (2017) "Micropolar modeling of rotational waves in seismology", Geophysical Journal International, 210, 1021-1046.
 A. Kurzych, L.R. Jaroszewicz, Z. Krajewski, J.K. Kowalski and M. Dudek (2018) "Torsion and tilt registration by two correlated interferometric optical fiber systems", 26th International Conference on Optical Fiber Sensors, Optical Society of America Technical Digest, Paper ThE99.
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In early 2008, Amanda Buckingham and Daniel Core teamed up to start Fathom Geophysics. With their complementary skills and experience, Buckingham and Core bring with them fresh ideas, a solid background in geophysics theory and programming, and a thorough understanding of the limitations of data and the practicalities of mineral exploration.
Fathom Geophysics provides geophysical and geoscience data processing and targeting services to the minerals and petroleum exploration industries, from the regional scale through to the near-mine deposit scale. Among the data types we work on are: potential field data (gravity and magnetics), electrical data (induced polarization and electromagnetics), topographic data, seismic data, geochemical data, precipitation and lake-level time-lapse environmental data, and remotely-sensed (satellite) data such as Landsat and ASTER.
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