Ari Ben-Menahem (Schlanger) has been professor of mathematics and geophysics at the Weizmann Institute of Science since 1964 and visiting professor at MIT. He is a seismologist, author, polymath, and historian of science. He coauthored with Sarvajit Singh, "Seismic Waves and Sources: the mathematical theory of seismology", a pioneering treatise since the nascent of this discipline at the turn of the 20th century.
Ben-Menahem was born in Berlin, Germany on November 4, 1928. He received his master's degree in physics in 1954 from the Hebrew University of Jerusalem and his doctoral degree from the California Institute of Technology (CIT) in 1961. He did his post-doctoral research at CIT, where he worked with Hugo Benioff and Frank Press (1962-1965).
In his doctoral thesis he pioneered the birth of modern seismic-source elastodynamics based on his theory of wave radiation from a finite rupturing fault with subshear or supershear velocity. His theory was confirmed through the observed asymmetric radiation of long-period surface-waves from the great Chilean earthquake of May 22, 1960, where he introduced the fundamental concepts of 'Directivity' and 'Potency' from which the moment tensor is derived. Since then, rupturing fault length, rupture velocity, moment-magnitude and moment energy are routinely calculable from spectra of recorded seismic waves-forms.
In 1975, Ben-Menahem used seismic and barometric recording of the Tunguska event of June 30, 1908, to derive the height and energy of the explosion, demonstrating for the first time a feasible non-cometary mechanism of this extraterrestrial bolide encounter with earth.
Ben-Menahem is the sole author of a 6-volume, 6000 pages treatise: Historical Encyclopedia of Natural and Mathematical Sciences published in 2009 by Springer Verlag.
Selected publications
Seismic Waves and Sources, Springer Verlag N.Y 1981, 1108 pp.
Seismic Waves and Sources, 2nd edition, Dover Publications, NY, 2000
Vincint Veritas – A portrait of the life and work of N.A Haskell, Am. Geoph. Union, Washington D.C 209pp, 1990
An earthquake is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from those that are so weak that they cannot be felt, to those violent enough to propel objects and people into the air, damage critical infrastructure, and wreak destruction across entire cities. The seismic activity of an area is the frequency, type, and size of earthquakes experienced over a particular time period. The seismicity at a particular location in the Earth is the average rate of seismic energy release per unit volume. The word tremor is also used for non-earthquake seismic rumbling.
Heinrich Rudolf Hertz was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. The unit of frequency, cycle per second, was named the "hertz" in his honor.
Physics is a branch of science whose primary objects of study are matter and energy. Discoveries of physics find applications throughout the natural sciences and in technology. Physics today may be divided loosely into classical physics and modern physics.
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz, between the infrared and the ultraviolet.
Seismology is the scientific study of earthquakes and the propagation of elastic waves through the Earth or other planetary bodies. It also includes studies of earthquake environmental effects such as tsunamis as well as diverse seismic sources such as volcanic, tectonic, glacial, fluvial, oceanic, atmospheric, and artificial processes such as explosions. A related field that uses geology to infer information regarding past earthquakes is paleoseismology. A recording of Earth motion as a function of time is called a seismogram. A seismologist is a scientist who does research in seismology.
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. Waves are often described by a wave equation or a one-way wave equation for single wave propagation in a defined direction.
Seismic moment is a quantity used by seismologists to measure the size of an earthquake. The scalar seismic moment is defined by the equation , where
The moment magnitude scale is a measure of an earthquake's magnitude based on its seismic moment. It was defined in a 1979 paper by Thomas C. Hanks and Hiroo Kanamori. Similar to the local magnitude/Richter scale (ML ) defined by Charles Francis Richter in 1935, it uses a logarithmic scale; small earthquakes have approximately the same magnitudes on both scales. Despite the difference, news media often says "Richter scale" when referring to the moment magnitude scale.
In seismology, a hypocenter or hypocentre is the point of origin of an earthquake. A synonym is the focus of an earthquake.
The EarthScope project was an National Science Foundation (NSF) funded earth science program that, from 2003-2018, used geological and geophysical techniques to explore the structure and evolution of the North American continent and to understand the processes controlling earthquakes and volcanoes. The project had three components: USArray, the Plate Boundary Observatory, and the San Andreas Fault Observatory at Depth. Organizations associated with the project included UNAVCO, the Incorporated Research Institutions for Seismology (IRIS), Stanford University, the United States Geological Survey (USGS) and National Aeronautics and Space Administration (NASA). Several international organizations also contributed to the initiative. EarthScope data are publicly accessible.
Wave propagation is any of the ways in which waves travel. Single wave propagation can be calculated by second-order wave equation or first-order one-way wave equation.
Seismic magnitude scales are used to describe the overall strength or "size" of an earthquake. These are distinguished from seismic intensity scales that categorize the intensity or severity of ground shaking (quaking) caused by an earthquake at a given location. Magnitudes are usually determined from measurements of an earthquake's seismic waves as recorded on a seismogram. Magnitude scales vary on what aspect of the seismic waves are measured and how they are measured. Different magnitude scales are necessary because of differences in earthquakes, the information available, and the purposes for which the magnitudes are used.
The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:
The focal mechanism of an earthquake describes the deformation in the source region that generates the seismic waves. In the case of a fault-related event it refers to the orientation of the fault plane that slipped and the slip vector and is also known as a fault-plane solution. Focal mechanisms are derived from a solution of the moment tensor for the earthquake, which itself is estimated by an analysis of observed seismic waveforms. The focal mechanism can be derived from observing the pattern of "first motions", that is, whether the first arriving P waves break up or down. This method was used before waveforms were recorded and analysed digitally and this method is still used for earthquakes too small for easy moment tensor solution. Focal mechanisms are now mainly derived using semi-automatic analysis of the recorded waveforms.
In seismology, a supershear earthquake is an earthquake in which the propagation of the rupture along the fault surface occurs at speeds in excess of the seismic shear wave (S-wave) velocity. This causes an effect analogous to a sonic boom.
The Richter scale —also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale—is a measure of the strength of earthquakes, developed by Charles Francis Richter and presented in his landmark 1935 paper, where he called it the "magnitude scale". This was later revised and renamed the local magnitude scale, denoted as ML or ML .
Immanuel ben Jacob Bonfils was a French-Jewish mathematician and astronomer in medieval times who flourished from 1340 to 1377, a rabbi who was a pioneer of exponential calculus and is credited with inventing the system of decimal fractions. He taught astronomy and mathematics in Orange and later lived in Tarascon, both towns in the Holy Roman Empire that are now part of modern-day France. Bonfils studied the works of Gersonides, the father of modern trigonometry, and Al-Battani and even taught at the academy founded by Gersonides in Orange.
In seismology, an earthquake rupture is the extent of slip that occurs during an earthquake in the Earth's crust. Earthquakes occur for many reasons that include: landslides, movement of magma in a volcano, the formation of a new fault, or, most commonly of all, a slip on an existing fault.
An earthquake occurred in southern Mongolia on December 4, 1957, measuring Mw 7.8–8.1 and assigned XII (Extreme) on the Modified Mercalli intensity scale. Surface faulting was observed in the aftermath with peak vertical and horizontal scarp reaching 9 m (30 ft). Because of the extremely sparse population in the area, this event, despite its magnitude, was not catastrophic. However, 30 people died and the towns of Dzun Bogd, Bayan-leg and Baruin Bogd were completely destroyed.
Michel Campillo is a French seismologist and geophysicist who is currently a professor at Grenoble Alpes University.
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