モーメント・マグニチュード・スケールの理解

What Seismic Moment Tells Us About Earthquakes

To understand the モーメントマグニチュード断層面積・平均すべり量・岩石の剛性の積である地震モーメントに基づく、地震規模を測定する現代の標準的な尺度（Mw）。あらゆる規模の地震に対して精度が高い。 scale, you must first understand seismic moment — the physical quantity it measures. Seismic moment (M0) is the most fundamental description of earthquake size, rooted directly in the mechanics of fault rupture rather than in any instrumental quirk. It captures three essential physical properties of an earthquake: how large an area of the fault ruptured, how far the two sides of the fault slipped past each other, and how rigid the rock surrounding the fault is.

The intuition is straightforward. Imagine tearing a piece of paper. The larger the tear, the further the paper has separated, and the stiffer the paper, the more energy was released. 地震モーメント断層面積・平均変位量・岩石のせん断弾性率の積として算出される、地震が放出した総エネルギーの尺度。モーメントマグニチュードの算出基盤となる。 works exactly the same way. A great earthquake like the 2011 Tohoku event ruptured a fault area roughly 500 kilometres long and 200 kilometres wide, with average slip of perhaps 20 metres, in very rigid oceanic crust — yielding a seismic moment so enormous it dwarfs nearly all other recorded earthquakes.

The Formula: Fault Area x Slip x Rock Rigidity

The seismic moment is defined as M0 = μ × A × d, where μ (mu) is the rigidity of the rock (typically around 30 GPa for crustal rock), A is the area of the 断層破壊地震時に断層に沿って岩盤が破断し、蓄積された弾性エネルギーが地震波として放出される現象。破壊の長さは、小規模地震では数メートル、大地震では1,000km以上に及ぶこともある。 surface, and d is the average displacement (slip) across that surface. All three quantities must be measured or estimated from seismological data, geodetic measurements, or field observations.

The モーメントマグニチュード断層面積・平均すべり量・岩石の剛性の積である地震モーメントに基づく、地震規模を測定する現代の標準的な尺度（Mw）。あらゆる規模の地震に対して精度が高い。 (Mw) is then derived from seismic moment using a formula established by Hanks and Kanamori (1979): Mw = (2/3) × log10(M0) − 10.7, where M0 is in dyne-centimetres. This formula is deliberately scaled so that Mw values align closely with the リヒタースケール1935年にチャールズ・リヒターが考案した、局地地震のマグニチュードを測定するための最初の対数マグニチュード尺度。現在はモーメントマグニチュードに大きく置き換えられているが、報道では今も広く使われている。 for moderate earthquakes, providing continuity with the historical record. The logarithm compresses the enormous range of seismic moments — spanning more than 20 orders of magnitude from micro-earthquakes to mega-quakes — into the familiar 0–10+ マグニチュード地震が放出した総エネルギー量を表す単一の数値。整数値が1増えるごとに、放出エネルギーはおよそ31.6倍になる。 range.

Advantages Over Richter Scale and Other Scales

The primary advantage of Mw over the リヒタースケール1935年にチャールズ・リヒターが考案した、局地地震のマグニチュードを測定するための最初の対数マグニチュード尺度。現在はモーメントマグニチュードに大きく置き換えられているが、報道では今も広く使われている。 and other earlier scales is that it does not saturate. Earlier scales were based on specific wave types or frequency ranges that become insensitive at large earthquake sizes. The original Richter local magnitude saturates around M 6.5–7.0; surface wave magnitude saturates around 8.0–8.5. Moment magnitude, anchored in the true physical size of the earthquake, keeps growing for the largest events ever recorded.

Mw is also physically meaningful in a way earlier scales were not. Because it is derived from seismic moment, it can be independently verified by multiple methods: long-period seismogram analysis, field measurements of fault slip, 干渉SAR（InSAR）地震前後に撮影されたレーダー画像を比較することで、センチメートル単位の精度で地表変動を測定する衛星レーダー技術。断層のすべりパターンを明らかにする。 satellite geodesy measurements of ground deformation, and GPS geodesy (GPS測地学全地球測位システムの受信機を用いて、プレートの動きや地殻変動をミリメートル単位の精度で測定する手法。地震と地震の間に断層に歪みがどのように蓄積するかを明らかにする。) that tracks how the ground moves before and after the event. The convergence of these independent estimates gives scientists high confidence in Mw values for well-studied earthquakes.

Another practical advantage: Mw is defined globally and does not depend on local calibration curves. The リヒタースケール1935年にチャールズ・リヒターが考案した、局地地震のマグニチュードを測定するための最初の対数マグニチュード尺度。現在はモーメントマグニチュードに大きく置き換えられているが、報道では今も広く使われている。 was calibrated specifically for Southern California. When seismologists tried to apply it elsewhere, they needed correction factors. Mw requires only the seismic moment, which can be estimated from any well-calibrated global 地震観測網地震活動を継続的に監視する、連携した地震観測点の集合。世界地震観測網（GSN）は150以上の観測点から構成され、世界規模の観測範囲を提供する。.

How Seismologists Calculate Mw in Real Time

Modern seismological agencies estimate moment magnitude by analysing the long-period content of seismograms recorded on 広帯域地震計0.001〜50Hzという広い周波数帯域にわたって地震波を記録できる地震計。現代の世界的な地震観測網における主要な観測機器。 networks around the world. When a significant earthquake occurs, automated systems at アメリカ地質調査所（USGS）地震の監視、National Earthquake Information Centerの運用、世界の地震データのリアルタイム公開を担う、アメリカ政府の主要機関。 and national agencies like Japan's JMA ingest data from dozens or hundreds of stations simultaneously.

The key step is determining the seismic moment tensor — a mathematical representation of the earthquake's focal mechanism that encodes the orientation of the fault, the direction of slip, and the seismic moment. Automated algorithms can produce an initial moment tensor solution and a preliminary Mw estimate within minutes of a major event, good enough for tsunami warning systems and initial response decisions. A more precise solution is refined over hours to days as more data are processed.

For very recent earthquakes, the first reports may cite a slightly different value than the final Mw. This is normal and reflects the iterative nature of the process. Initial estimates from body-wave analysis may differ slightly from the final centroid moment tensor solution, but for earthquakes above about magnitude 5.0 the differences are usually small.

Notable Earthquakes on the Moment Magnitude Scale

The moment magnitude scale's ability to handle extreme events is best illustrated by the largest earthquakes ever recorded. The 1960 Valdivia, Chile earthquake holds the record at Mw 9.5 — a rupture that broke approximately 1,000 kilometres of the subduction zone boundary between the Nazca and South American plates. The seismic moment of this single event was so large that it represents a substantial fraction of all the energy released by earthquakes worldwide in the entire 20th century.

The 1964 Alaska Good Friday earthquake (Mw 9.2) remains the second-largest in the instrumental record, followed by the 2004 Indian Ocean earthquake (Mw 9.1–9.3) and the 2011 Tohoku, Japan earthquake (Mw 9.0–9.1). At the other end of the scale, modern high-sensitivity networks can detect earthquakes with negative magnitudes — tiny events releasing less energy than a firecracker. The Mw scale thus spans an enormous dynamic range with a single consistent formula, a feat that no earlier magnitude scale could match.