What Is the Snell's Law Seismic Ray Parameter Calculator?
The ray parameter p represents the invariant horizontal phase slowness along a seismic ray.
It links the surface epicentral distance and traveltime derivative (dT/dDelta).
How Does the Snell's Law Seismic Ray Parameter Calculator Work?
Evaluates ray parameter p from initial surface velocity and takeoff angle.
Computes horizontal phase velocity and turning point velocity.
Evaluates ray angle of incidence at deeper structural velocity horizons.
Snell's Law Seismic Ray Parameter Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Conservation of horizontal slowness along a seismic acoustic ray trajectory.
How to Use the Snell's Law Seismic Ray Parameter Calculator
- Enter the surface seismic wave velocity in km/s.
- Specify the initial takeoff angle in degrees from vertical.
- Enter the seismic velocity at the depth of interest.
Step-by-Step Example Calculation
Crust-to-Mantle P-Wave Refraction
Input Values:
Understanding Your Result
Ray parameter p stays constant along the ray.
The turning velocity V_turn is the velocity where the ray becomes purely horizontal (i = 90 deg) and turns back toward the surface.
Factors That Affect the Result
- Velocity gradients: Positive velocity gradients cause rays to curve concavely upwards.
- Low velocity zones: Regions with decreasing velocity trap rays and cause shadow zones.
When Should You Use This Calculator?
- Global seismic tomography and traveltime curve modeling.
- Determining turning depths for teleseismic P and S body wave phases.
Assumptions & Limitations
- Assumes flat, isotropic, vertically varying 1D Earth model.
- Does not incorporate spherical Earth Earth-flattening transformations.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Snell refraction invariance is exact in geometric ray theory.