地震のエネルギー: TNT、原子爆弾など

The Gutenberg-Richter Energy Formula

The グーテンベルク・リヒター則地震の頻度とマグニチュードの関係を示す統計法則で、マグニチュードが1単位増えるごとに、地震の発生頻度はおよそ10分の1になる。 law is best known for the frequency-magnitude relationship — the observation that small earthquakes are vastly more common than large ones. But Beno Gutenberg and Charles Richter also developed one of the most important formulas in seismology: the relationship between 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。 and 地震エネルギー地震によって放射される総地震エネルギーで、ジュールで測定される。マグニチュード9の地震は、核爆弾約25,000発分に相当するエネルギーを放出する。. Their empirical formula, derived from measurements on real earthquakes, expresses radiated seismic energy as a function of magnitude.

The formula used in modern form is: log10(E) = 5.24 + 1.44 × Mw, where E is in joules. This gives the seismic energy — the energy radiated as 地震波地震や爆発によって発生し、地球内部を伝播する弾性波。地震波は、震源で放出されたエネルギーを遠方の地点まで運ぶ。s, not the total energy released by fault motion (some energy goes into heat, fracturing new rock surfaces, and permanent deformation). For a magnitude 5.0 earthquake, this formula gives approximately 2 × 10^12 joules. For a magnitude 9.0, it gives approximately 2 × 10^18 joules — one million times more.

Earthquake Energy in Human Terms: TNT and Atomic Bombs

To make earthquake energy tangible, seismologists often compare it to familiar explosive devices. One tonne of TNT releases approximately 4.2 × 10^9 joules. One kiloton (1,000 tonnes) of TNT — the unit used for nuclear weapons — releases about 4.2 × 10^12 joules.

A magnitude 5.0 earthquake releases about 480 kilotons of TNT equivalent — similar to a small nuclear weapon. A magnitude 6.0 releases approximately 15 megatons (15,000 kilotons), larger than the most powerful nuclear weapons ever tested. A magnitude 8.0 releases energy equivalent to approximately 15,000 megatons — far exceeding the total yield of all nuclear weapons ever detonated in history. The 1960 Valdivia earthquake at magnitude 9.5 released approximately 180,000 megatons of energy — equivalent to detonating a nuclear bomb of that size, which fortunately does not exist.

Each Magnitude Step = 31.6x More Energy

The most important number to remember about earthquake energy is 31.6 — the factor by which energy increases for each whole magnitude unit. This comes directly from the 1.44 coefficient in the energy formula: 10^1.44 ≈ 27.5, sometimes rounded to 31.6 when accounting for slightly different formulations. Each step up the magnitude scale multiplies the energy by about 31.6.

This means: magnitude 5 to 6 is 31.6 times more energy; magnitude 5 to 7 is 31.6 × 31.6 ≈ 1,000 times more energy; magnitude 5 to 9 is 31.6^4 ≈ one million times more energy. The practical implication is that the largest earthquakes completely dominate global seismic energy release. The global average of about 1,000 magnitude 5.0 earthquakes per year releases less total energy than a single magnitude 8.0 earthquake. A single magnitude 9.5 earthquake releases more energy than all other earthquakes in that year combined, in most years.

Comparing Earthquake Energy to Other Events

The energy scales involved in earthquakes help explain why even apparently small events can be powerful. A magnitude 4.0 earthquake releases energy comparable to 30,000 tonnes of TNT — roughly equivalent to a small tactical nuclear weapon. A magnitude 7.0 releases energy equivalent to 30 megatons, far exceeding the largest nuclear test ever conducted (the USSR's Tsar Bomba at about 50 megatons, which was magnitude 5.0 seismically).

Volcanic eruptions provide another comparison point. The 1980 Mount St Helens eruption released energy roughly equivalent to a magnitude 7.6 earthquake. The 1815 Tambora eruption — the most powerful in recorded history — may have released energy comparable to a magnitude 8+ seismic event. Tropical cyclones release enormous energy, but most of it is thermal rather than mechanical, making direct comparison complex. In terms of purely mechanical energy released suddenly and destructively, large earthquakes are unmatched by any phenomenon short of asteroid impacts.

Where Does All That Energy Go?

Of the enormous energy released during an earthquake, only a fraction travels as 地震波地震や爆発によって発生し、地球内部を伝播する弾性波。地震波は、震源で放出されたエネルギーを遠方の地点まで運ぶ。s to cause ground shaking. The 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。 represents the total mechanical work done by fault motion, which is typically 10 to 100 times larger than the radiated seismic energy. Most of the total energy budget goes into heating the fault zone through friction — essentially, the fault surfaces sliding past each other generate heat just as rubbing your hands together does, but at enormous pressures and over great distances.

Some energy goes into creating new fracture surfaces within the fault zone and in the surrounding rock. Some is stored elastically as permanent deformation of the crust — the 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。 measurements that detect crustal deformation following large earthquakes are measuring the permanent redistribution of this elastic strain energy. The fraction that radiates as seismic waves — typically 5–25 percent of the total energy budget — is what causes the shaking that destroys buildings. Use the Earthquake Energy Calculator to explore how different magnitudes compare in terms of energy, TNT equivalents, and shaking parameters.

Using the Earthquake Calculator to Explore Energy

Understanding earthquake energy becomes intuitive when you can compare magnitudes interactively. The Earthquake Energy Calculator lets you enter any magnitude and instantly see the energy in joules, TNT equivalents, and Hiroshima bomb equivalents. You can compare two magnitudes side by side to feel the logarithmic difference — the difference between a magnitude 7.0 and 8.0 is always 31.6 times, regardless of which magnitudes you compare.

The calculator also illustrates the frequency-magnitude relationship: for every magnitude 8.0 earthquake, there are roughly 10 magnitude 7.0 earthquakes and 100 magnitude 6.0 earthquakes annually worldwide. Visualising this pyramid helps explain why the rare great earthquakes dominate global energy statistics even though they occur far less frequently than moderate events. The 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。 approach underpinning 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。 ensures that the calculator's energy values are physically meaningful, grounded in the actual fault mechanics rather than instrument calibration curves.