Magnitude and Energy of Earthquakes

Abstract

Discrepancies arise among magnitudes as derived from local earthquake data (M L ), body waves (M B ) and surface waves (M S)This paper is in continuation of previous investigations Richter 1942, 1956].The earthquake magnitude has statistical and other uses independent of the relation between magnitude and energy. Indeed, it is possible that there is no complete one-to-one correlation between magnitude and energy for large and complex tectonic events. Even so, a mean or representative relation is a legitimate object of inquiry. In attempting to refine the magnitude-energy relation it was found [Gutenberg and Richter 1956] that three imperfectly consistent magnitude scales had been in use:M L determined from records of local earthquakes according to the original definition [Richter 1935]; M S from the amplitudes of surface waves for shallow teleseisms, [Gutenberg and Richter 1936;Gutenberg 1945a]; m B from the amplitude/period ratio of body waves for teleseisms, shallow and deep-focus [Gutenberg 1945b[Gutenberg , 1945c.The two latter were originally adjusted to coincide near M = 7, but were later found to diverge linearly so that The revision is based on a large body of data. Magnitudes have been derived by the senior author, from surface waves and from body waves separately, for a selection of better recorded large shallow earthquakes as listed by Gutenberg and Richter [1954]. Those for which there was suspicion of depth in excess of the normal (believed to be about 25 km) were rejected. Values of m B were plotted against those of M S , and (1) derived from the plot. The values a = 0.37, b = 6.76 are comparable with those found by Bath [1955] as follows:At Pasadena, a weighted mean is taken between m B as found directly from body waves, and m S , the corresponding value derived from M S by applying the relation (1), or still better from tables and charts set up to give m S directly from surface wave data. This weighted mean is designated the unified magnitude denoted by m.In Figure 1 residuals m B -m S on the basis a = 0.37, b = 6.76 are plotted against m, using amplitude and period data from all available station bulletins,

Statistics and topological changes in 2D foam from the dry to the wet limit

“…There is a variety of physical systems which exhibit avalanches, ranging from earthquakes [24] and random fuse networks [25] to piles of rice [26]. However, their statistics are usually described by power-laws of the form p(n) ∼ n −α , where the exponent α has a value between 1 and 2.…”

United States earthquakes, 1985

“…mb=log (A{f) + Q(D,h), (2) as defined by Gutenberg and Richter (1956), except that T, the period in seconds, is restricted to 0.1;;::: T;;::: 3.0, and A, the ground amplitude in micrometers, is not necessarily the maximum of the P-wave group. Q is a function of distance D and depth h, where D > 5°.…”

Simulation-Based Probabilistic Tsunami Hazard Analysis: Empirical and Robust Hazard Predictions

“…This minimum value of magnitude should also take into account that small-to-moderate earthquakes rarely generate significant tsunamis and their contributions to the tsunami hazard are negligible ).To describe the earthquake size in a target region, i.e., the term f(M) in Eq. (2), a truncated Gutenberg-Richter relationship (Gutenberg and Richter 1956) can be adopted:…”