Visualization
P-wave
S-wave
Calculating hypocenter location...
Data Matrix (G·m = d)
Jacobian matrix for the last iteration:
Mathematical Framework
1. Travel Time Equation
Ti = t0 + ∫ray path (1/v(s)) ds
For layered model:
Ti = t0 + Σk (Δsk/vk)
For layered model:
Ti = t0 + Σk (Δsk/vk)
2. Geiger's Method (Linearization)
ΔTi = (∂T/∂x)Δx + (∂T/∂y)Δy + (∂T/∂z)Δz + Δt0
Matrix form: Gm = d
Where G = Jacobian matrix, m = model parameters, d = data
Matrix form: Gm = d
Where G = Jacobian matrix, m = model parameters, d = data
3. Least Squares Solution
m = (GTG)-1GTd
RMS = √(Σ(Tobs - Tcalc)2 / N)
RMS = √(Σ(Tobs - Tcalc)2 / N)
4. Ray Parameter (Snell's Law)
p = sin(θi)/vi = constant along ray path
For flat layers: X = Σi hitan(θi)
For flat layers: X = Σi hitan(θi)
Velocity Model (km/s)
Layer 1 (0-10 km):
Vp = Vs =
Layer 2 (10-30 km):
Vp = Vs =
Layer 3 (>30 km):
Vp = Vs =
Seismic Stations
This visualization demonstrates the iterative process of locating an earthquake hypocenter using: • Multiple seismic stations recording P and S wave arrivals • A layered Earth velocity model • Geiger's iterative least-squares method • Ray tracing through velocity layers