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QuakeFYI

Calculadora de Energia Sísmica

Convert earthquake magnitude to energy equivalent in joules, TNT tons, and atomic bombs.

Calculation

Entendendo a Energia e Magnitude dos Terremotos

A magnitude de um terremoto é medida em uma escala logarítmica, o que significa que cada aumento de número inteiro representa um aumento de dez vezes na amplitude medida e aproximadamente 31,6 vezes mais energia liberada. Esta relação exponencial é descrita pela fórmula energia-magnitude de Gutenberg-Richter: log₁₀(E) = 1,5M + 4,8, onde E é a energia em joules e M é a magnitude de momento. Um terremoto de magnitude 7,0 libera cerca de 1.000 vezes mais energia do que um de magnitude 5,0 — aproximadamente equivalente a detonar 500.000 toneladas de TNT.

A escala de magnitude de momento (Mw), que substituiu a escala Richter original para a maioria dos fins, é baseada no momento sísmico — uma medida da energia total liberada pelo deslizamento da falha. Diferentemente da magnitude local de Richter (ML), a magnitude de momento não satura em valores altos, tornando-a a escala preferida para grandes terremotos. O momento sísmico depende de três fatores: a rigidez da rocha, a área da falha que rompeu e o deslocamento médio ao longo da falha.

A Ciência por Trás do Cálculo

  • A escala Richter foi desenvolvida em 1935 por Charles Richter para terremotos do sul da Califórnia; a escala de magnitude de momento a substituiu na década de 1970 para uso global.
  • Apenas cerca de 1-10% da energia total do terremoto é irradiada como ondas sísmicas; o restante é consumido pela fratura de rocha e geração de calor ao longo da falha.
  • A equivalência de TNT fornece uma comparação intuitiva: o terremoto M9,1 de Tōhoku de 2011 liberou energia equivalente a aproximadamente 600 milhões de toneladas de TNT.
  • Terremotos pequenos (M2-3) liberam energia comparável a alguns quilogramas de explosivos, enquanto grandes terremotos (M8+) rivalizam com arsenais nucleares.

Usos Comuns

  • Comparar a potência relativa de terremotos históricos para entender seu potencial destrutivo.
  • Ensinar alunos sobre escalas logarítmicas e relações exponenciais de energia em cursos de ciências da terra.
  • Colocar magnitudes de terremotos em perspectiva usando equivalentes de energia do cotidiano como TNT ou raios.

How to Use

  1. 1
    Enter the Earthquake Magnitude

    Input the moment magnitude (Mw) of the earthquake. Mw is the standard scale used by seismological agencies since the 1970s and is the most accurate measure across all magnitude ranges.

  2. 2
    Select Your Energy Units

    Choose whether to see energy equivalents in joules, kilotons of TNT, or Hiroshima atomic bomb equivalents. The calculator applies the USGS energy-magnitude relation: log E = 5.24 + 1.44 Mw.

  3. 3
    Compare Across Magnitudes

    Add a second magnitude to see the energy ratio between the two events. Because the scale is logarithmic, each unit increase in Mw corresponds to about 31.6 times more released energy.

About

Earthquake energy and magnitude are connected through one of science's most consequential logarithmic scales. Charles Richter introduced the local magnitude (ML) scale in 1935, calibrated to a specific seismograph at a specific distance in Southern California. While the name 'Richter scale' persists in popular usage, seismologists now use moment magnitude (Mw), developed by Hiroo Kanamori and Thomas Hanks in 1979, which remains consistent across the full spectrum from microearthquakes to the largest megathrust events and does not saturate at high magnitudes as earlier scales did.

The physical quantity underlying Mw is the seismic moment (M0), calculated as M0 = μ × A × d, where μ is the shear modulus of the rock (typically 3 × 10^10 Pa for the crust), A is the ruptured fault area, and d is the average displacement across the fault. Mw is then derived as Mw = (2/3) × log10(M0) − 6.07. This formulation means that fault geometry directly determines magnitude: a rupture covering a 200 × 100 km fault plane with 5 m of average slip yields a specific, calculable M0 and hence a well-defined Mw.

Energy equivalents help communicate earthquake power to non-specialist audiences. The most commonly cited comparison is the atomic bomb: the Hiroshima bomb released approximately 63 terajoules. A magnitude 6.0 earthquake releases energy comparable to about 1 Hiroshima bomb, while a magnitude 8.0 releases energy comparable to about 1,000. These comparisons, while vivid, can mislead: earthquake energy is released over a fault plane tens to hundreds of kilometers long over tens of seconds, and only a fraction couples into the seismic waves that cause damage at the surface. The depth, focal mechanism, and local site response all shape the destruction as much as the raw energy figure.

FAQ

Qual é a diferença entre magnitude e intensidade?
Magnitude is an objective, instrumentally measured quantity describing the total energy released at the earthquake source, reported as a single number regardless of where it is measured. The moment magnitude scale (Mw) is now universal and calculated from the seismic moment—the product of the fault area, average slip, and rock rigidity. Intensity, by contrast, is a subjective measure of ground shaking severity at a specific location, described by the Modified Mercalli Intensity (MMI) scale from I (not felt) to XII (total destruction). Intensity decreases with distance from the epicenter and varies with local geology, so the same earthquake can produce MMI V in one city and MMI VIII in another.
How much energy does a magnitude 7 earthquake release?
Using the USGS energy-magnitude relation (log E = 5.24 + 1.44 Mw), a magnitude 7.0 earthquake releases approximately 2 × 10^15 joules, equivalent to roughly 475 kilotons of TNT or about 32 Hiroshima-sized atomic bombs. For comparison, a magnitude 8.0 releases about 31.6 times more energy than a 7.0, and a magnitude 9.0 releases about 1,000 times more. The 2011 Tohoku M9.1 earthquake released energy equivalent to approximately 600 million tons of TNT, or about 40,000 Hiroshima bombs. It is worth noting that seismic energy represents only a fraction (roughly 5–10%) of the total strain energy released; the rest is converted to heat at the fault surface.
Why does each magnitude unit feel so much stronger?
The moment magnitude scale is logarithmic in seismic moment but the energy-magnitude relationship has a steeper exponent. A one-unit increase in Mw corresponds to a factor of 10^1.5 ≈ 31.6 in energy release. Peak ground acceleration (the shaking you actually feel) scales differently: a one-unit increase in Mw roughly doubles the felt shaking amplitude as measured by instruments, though local site conditions, depth, and distance complicate this relationship. This is why the jump from M6.0 to M7.0 is so consequential for structural damage—the energy released increases by a factor of roughly 32, but the duration of strong shaking also increases substantially, compounding structural fatigue.
What is the largest earthquake ever recorded?
The 1960 Valdivia earthquake in southern Chile holds the record at M9.5, occurring along the Nazca–South American subduction zone. It ruptured approximately 1,000 km of fault surface, generated a transoceanic tsunami that killed people as far away as Hawaii and Japan, and triggered volcanic activity in the Andes. The seismic moment released was approximately 1.8 × 10^23 newton-meters. In comparison, the 2004 Sumatra–Andaman earthquake (M9.1–9.3) and the 2011 Tohoku earthquake (M9.1) are the next largest recorded events. All occurred at subduction zone megathrusts, the only tectonic setting capable of producing such extreme events.
Is a magnitude 10 earthquake possible?
A magnitude 10.0 earthquake is considered physically implausible given the geometry of Earth's plate boundaries. The magnitude is determined by fault dimensions and average slip: a M10.0 would require a fault rupture of roughly 4,000–5,000 km in length, more than the entire length of the longest subduction zone on Earth (the Chile-Peru trench). While cascading multi-segment ruptures are possible—the 1964 Alaska earthquake ruptured about 800 km—no tectonic configuration exists that could sustain a single coherent rupture at M10 scale. The theoretical upper bound for subduction zone earthquakes is generally placed around M9.5–9.6.