Moment magnitude scale

The moment magnitude scale (MMS; denoted explicitly with Mw or Mw, and generally implied with use of a single M for magnitude) is a measure of an earthquake's magnitude ('size' or strength) based on its seismic moment (a measure of the 'work' done by the earthquake), expressed in terms of the familiar magnitudes of the original 'Richter' magnitude scale. The moment magnitude scale (MMS; denoted explicitly with Mw or Mw, and generally implied with use of a single M for magnitude) is a measure of an earthquake's magnitude ('size' or strength) based on its seismic moment (a measure of the 'work' done by the earthquake), expressed in terms of the familiar magnitudes of the original 'Richter' magnitude scale. Moment magnitude (Mw) is considered the authoritative magnitude scale for ranking earthquakes by size because it is more directly related to the energy of an earthquake, and does not saturate. (That is, it does not underestimate magnitudes like other scales do in certain conditions.) It has become the standard scale used by seismological authorities (such as the U.S. Geological Survey), replacing (when available, typically for M > 4) use of the ML (Local magnitude) and Ms (surface-wave magnitude) scales. Subtypes of the moment magnitude scale (Mww , etc.) reflect different ways of estimating the seismic moment. At the beginning of the twentieth century, very little was known about how earthquakes happen, how seismic waves are generated and propagate through the earth's crust, and what they can tell us about the earthquake rupture process; the first magnitude scales were therefore empirical. The initial step in determining earthquake magnitudes empirically came in 1931 when the Japanese seismologist Kiyoo Wadati showed that the maximum amplitude of an earthquake's seismic waves diminished with distance at a certain rate. Charles F. Richter then worked out how to adjust for epicentral distance (and some other factors) so that the logarithm of the amplitude of the seismograph trace could be used as a measure of 'magnitude' that was internally consistent and corresponded roughly with estimates of an earthquake's energy. He established a reference point and the now familiar ten-fold (exponential) scaling of each degree of magnitude, and in 1935 published his 'magnitude' scale, now called the Local magnitude scale, labeled ML . The Local magnitude scale was developed on the basis of shallow (~15 km (9 mi) deep), moderate-sized earthquakes at a distance of approximately 100 to 600 km (62 to 373 mi), conditions where the surface waves are predominant. At greater depths, distances, or magnitudes the surface waves are greatly reduced, and the Local magnitude scale underestimates the magnitude, a problem called saturation. Additional scales were developed – a surface-wave magnitude scale (Ms) by Beno Gutenberg in 1945, a body-wave magnitude scale (mB) by Gutenberg and Richter in 1956, and a number of variants – to overcome the deficiencies of the ML  scale, but all are subject to saturation. A particular problem was that the Ms  scale (which in the 1970s was the preferred magnitude scale) saturates around Ms   8.0, and therefore underestimates the energy release of 'great' earthquakes such as the 1960 Chilean and 1964 Alaskan earthquakes. These had Ms  magnitudes of 8.5 and 8.4 respectively but were notably more powerful than other M 8 earthquakes; their moment magnitudes were closer to 9.6 and 9.3. The study of earthquakes is challenging as the source events cannot be observed directly, and it took many years to develop the mathematics for understanding what the seismic waves from an earthquake can tell us about the source event. An early step was to determine how different systems of forces might generate seismic waves equivalent to those observed from earthquakes. The simplest force system is a single force acting on an object. If it has sufficient strength to overcome any resistance it will cause the object to move ('translate'). A pair of forces, acting on the same 'line of action' but in opposite directions, will cancel; if they cancel (balance) exactly there will be no net translation, though the object will experience stress, either tension or compression. If the pair of forces are offset, acting along parallel but separate lines of action, the object experiences a rotational force, or torque. In mechanics (the branch of physics concerned with the interactions of forces) this model is called a couple, also simple couple or single couple. If a second couple of equal and opposite magnitude is applied their torques cancel; this is called a double couple. A double couple can be viewed as 'equivalent to a pressure and tension acting simultaneously at right angles'. The single couple and double couple models are important in seismology because each can be used to derive how the seismic waves generated by an earthquake event should appear in the 'far field' (that is, at distance). Once that relation is understood it can be inverted to use the earthquake's observed seismic waves to determine its other characteristics, including fault geometry and seismic moment. In 1923 Hiroshi Nakano showed that certain aspects of seismic waves could be explained in terms of a double couple model. This led to a three-decade long controversy over the best way to model the seismic source: as a single couple, or a double couple? While Japanese seismologists favored the double couple, most seismologists favored the single couple. Although the single couple model had some short-comings, it seemed more intuitive, and there was a belief – mistaken, as it turned out – that the elastic rebound theory for explaining why earthquakes happen required a single couple model. In principle these models could be distinguished by differences in the radiation patterns of their S-waves, but the quality of the observational data was inadequate for that. The debate ended when Maruyama (1963), Haskell (1964), and Burridge & Knopoff (1964) showed that if earthquake ruptures are modeled as dislocations the pattern of seismic radiation can always be matched with an equivalent pattern derived from a double couple, but not from a single couple. This was confirmed as better and more plentiful data coming from the World-Wide Standard Seismograph Network (WWSSN) permitted closer analysis of seismic waves. Notably, in 1966 Keiiti Aki showed that the seismic moment of the 1964 Niigata earthquake as calculated from the seismic waves on the basis of a double couple was in reasonable agreement with the seismic moment calculated from the observed physical dislocation.