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The Richter scale [1] (/ ˈ r ɪ k t ər /), also called the Richter magnitude scale, Richter's magnitude scale, and the Gutenberg–Richter scale, [2] is a measure of the strength of earthquakes, developed by Charles Richter in collaboration with Beno Gutenberg, and presented in Richter's landmark 1935 paper, where he called it the "magnitude scale". [3]
According to this definition, if the amplitude of the seismic wave measured by the Wood Anderson torsion seismometer at the epicentral distance of 100 km is 1 mm, then the magnitude is 3. [Notes 6] Although Richter et al. attempted to make the results non-negative, modern precision seismographs often record earthquakes with negative scales due ...
The original "body-wave magnitude" – mB or m B (uppercase "B") – was developed by Gutenberg 1945c and Gutenberg & Richter 1956 [25] to overcome the distance and magnitude limitations of the M L scale inherent in the use of surface waves. mB is based on the P and S waves, measured over a longer period, and does not saturate until around M 8.
The formula to calculate surface wave magnitude is: [3] = + (), where A is the maximum particle displacement in surface waves (vector sum of the two horizontal displacements) in μm, T is the corresponding period in s (usually 20 ± 2 seconds), Δ is the epicentral distance in °, and
As an example, in the magnitude 7.9 Denali earthquake of 2002 in Alaska, the epicenter was at the western end of the rupture, but the greatest damage was about 330 km (210 mi) away at the eastern end. [7] Focal depths of earthquakes occurring in continental crust mostly range from 2 to 20 kilometers (1.2 to 12.4 mi). [8]
This page was last edited on 31 August 2023, at 11:46 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may ...
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
Suppose that the area C enclosed by the circle is greater than the area T = cr/2 of the triangle. Let E denote the excess amount. Inscribe a square in the circle, so that its four corners lie on the circle. Between the square and the circle are four segments. If the total area of those gaps, G 4, is greater than E, split each arc in