Global earthquake alerting feeds provided by organizations like the United States Geological Survey (USGS) or the Euro-Mediterranean Seismological Centre (EMSC) typically stream raw event parameters: moment magnitude ($M_w$), hypocentral coordinates (latitude, longitude), and focal depth. However, they do not provide local seismic intensities on Japan's familiar 10-tier intensity scale (JMA Shindo 1 through 7, including Lower/Upper 5 and Lower/Upper 6).
For disaster response teams and residents in seismically active regions, knowing that a magnitude 6.8 earthquake occurred offshore offers limited actionable insight compared to knowing that downtown Tokyo experienced Shindo 4 while coastal towns experienced Shindo 6-Lower. To bridge this information gap, QuakeViewer3D incorporates an in-browser Ground Motion Prediction Equation (GMPE) attenuation engine capable of instantly calculating Peak Ground Velocity (PGV), Peak Ground Acceleration (PGA in gal), and localized JMA Shindo across any point on Earth.
1. Estimating Bedrock PGV via Si & Midorikawa (1999) Attenuation Relations
As seismic shear waves ($S$-waves) propagate outward from a fault rupture, their amplitude attenuates through geometric spreading and intrinsic anelastic dissipation ($Q^{-1}$). In Japanese earthquake engineering, the empirical GMPE developed by Si & Midorikawa (1999) is recognized as one of the most reliable models. QuakeViewer3D adopts this formulation to evaluate Peak Ground Velocity ($PGV_{600}$, in cm/s) on engineering bedrock ($V_s \approx 400\text{--}600\text{ m/s}$):
// Implementation of Si & Midorikawa (1999) GMPE
// Mw: Moment Magnitude, epicentralDist: km, depth: km
function calculateBedrockPGV(Mw, epicentralDist, depth, quakeType) {
const X = Math.sqrt(epicentralDist * epicentralDist + depth * depth);
let a, b, c, d, k;
if (quakeType === 'interplate') {
// Subduction zone megathrust earthquakes
a = 0.58; b = 0.0038; c = 0.0028; d = 0.50; k = -1.29;
} else if (quakeType === 'intraplate') {
// Deep intraslab earthquakes
a = 0.61; b = 0.0038; c = 0.0028; d = 0.50; k = -1.18;
} else {
// Shallow inland crustal earthquakes
a = 0.58; b = 0.0038; c = 0.0028; d = 0.50; k = -1.41;
}
const logPGV = a * Mw - b * X - Math.log10(X + c * Math.pow(10, d * Mw)) + k;
return Math.pow(10, logPGV);
}This formulation accounts for near-source ground motion saturation (represented by the term $c \cdot 10^{d M_w}$, which prevents peak ground velocity from growing to infinity as hypocentral distance approaches zero) alongside logarithmic distance attenuation in the far field.
2. Correcting for Surface Soil Amplification ($AVS30$)
When high-frequency seismic waves transition from stiff deep bedrock into soft, unconsolidated sediment layers (such as alluvial river valleys, reclaimed waterfronts, and coastal plains), wave velocity decreases sharply, causing wave amplitudes to multiply dramatically. This physical phenomenon explains why adjacent neighborhoods on different soil types often experience vastly different levels of shaking and structural damage.
QuakeViewer3D references $AVS30$ (average shear-wave velocity in the top 30 meters of soil, in m/s) datasets published by Japan's MLIT and NIED, utilizing the empirical soil amplification relationship established by Matsuoka & Midorikawa (1994):
$$ARV = 1.83 \times (AVS30)^{-0.66}$$Surface Peak Ground Velocity: $$PGV_{surface} = PGV_{600} \times ARV$$
While stiff bedrock ridges ($AVS30 > 500\text{ m/s}$) exhibit moderate amplification factors of $ARV \approx 0.8\text{--}1.2$, soft marshlands and river deltas ($AVS30 < 150\text{ m/s}$) can experience amplification factors exceeding $ARV \approx 2.5\text{--}3.2$, amplifying bedrock tremors by up to three times at the surface.
3. Mapping Surface PGV to JMA Instrumental Seismic Intensity
To convert surface Peak Ground Velocity ($PGV_{surface}$) into Japan's continuous Instrumental Seismic Intensity ($I_{jma}$), QuakeViewer3D implements Midorikawa et al.'s (1999) logarithmic correlation formula:
// Convert surface PGV (cm/s) to JMA Instrumental Shindo
function pgvToJmaIntensity(pgv) {
if (pgv <= 0.05) return { raw: 0, text: "Shindo 0", class: "shindo-0" };
// Empirical relation by Midorikawa et al. (1999)
const I = 2.68 + 1.72 * Math.log10(pgv);
if (I < 0.5) return { raw: I, text: "Shindo 0", class: "shindo-0" };
if (I < 1.5) return { raw: I, text: "Shindo 1", class: "shindo-1" };
if (I < 2.5) return { raw: I, text: "Shindo 2", class: "shindo-2" };
if (I < 3.5) return { raw: I, text: "Shindo 3", class: "shindo-3" };
if (I < 4.5) return { raw: I, text: "Shindo 4", class: "shindo-4" };
if (I < 5.0) return { raw: I, text: "Shindo 5-Lower", class: "shindo-5m" };
if (I < 5.5) return { raw: I, text: "Shindo 5-Upper", class: "shindo-5p" };
if (I < 6.0) return { raw: I, text: "Shindo 6-Lower", class: "shindo-6m" };
if (I < 6.5) return { raw: I, text: "Shindo 6-Upper", class: "shindo-6p" };
return { raw: I, text: "Shindo 7", class: "shindo-7" };
}Whenever an incoming earthquake alert is ingested from USGS via WebSocket, this calculation runs in under 5 milliseconds across thousands of pre-indexed municipal centroids, populating localized hazard badges instantly across the 3D globe.
4. Bi-Directional Mapping: JMA Shindo vs. Modified Mercalli Intensity (MMI)
To serve international seismologists and global disaster response agencies, QuakeViewer3D provides seamless bi-directional harmonization between the JMA scale and the global Modified Mercalli Intensity (MMI I through XII) scale:
- JMA Shindo 3 ↔ MMI IV (Light): Felt indoors by many, hanging objects swing slightly.
- JMA Shindo 4 ↔ MMI V–VI (Moderate/Strong): Sleeping individuals awakened, dishes and glassware rattle or shatter.
- JMA Shindo 5-Lower / 5-Upper ↔ MMI VII (Very Strong): Difficult to stand, hairline fractures appear in unreinforced masonry.
- JMA Shindo 6-Lower / 6-Upper ↔ MMI VIII–IX (Severe/Violent): Heavy structural damage, chimneys topple, partial collapse of weak buildings.
- JMA Shindo 7 ↔ MMI X–XII (Extreme): Catastrophic destruction, bridges displaced, widespread ground fissures.
Users can toggle between JMA Shindo and MMI scales dynamically via the top-bar HUD, ensuring culturally intuitive hazard communication worldwide.
5. Conclusion: Bringing Real-Time Seismology to the Browser
Transforming raw seismic telemetry into localized impact simulations empowers users to understand not just where an earthquake struck, but what the tremors felt like on the ground.
Through robust client-side GMPE mathematics and instant WebGL visual overlays, QuakeViewer3D advances the frontier of browser-based geophysical tools, turning abstract seismic bulletins into immediate, life-saving visual insights.