Ray Tracers

The calculation of seismic travel times is a cornerstone for the migration and stacking approach. Qseek supports different ray tracers for travel time calculation, which can be adapted for different geological settings.

Constant Velocity

The constant velocity models is trivial and follows:

\[ t_{P} = \frac{d}{v_P} \]

This module is used for simple use cases and cross-referencing testing.

ConstantVelocityTracer Module

Travel time tracer with a constant velocity.

Config ConstantVelocityTracerJSON

phase: constant:P: Name of the phase.
velocity: 5000.0: Constant velocity of the phase in m/s.

JSON for ConstantVelocityTracer

{
  "tracer": "ConstantVelocityTracer",
  "phase": "constant:P",
  "velocity": 5000.0
}

1D Layered Velocity Model

Travel times for 1D layered velocity models can be calculated by two different modules.

FastMarchingTracer Module

Travel time calculation for layered 1D velocity models.

Calculation is based on fast marching method to solve the Eikonal solution. This the more perfomant than the Pyrocko Cake ray tracer, especially for large number of stations and nodes.

Config FastMarchingTracerJSON

velocity_model: Velocity model for the ray tracer.
interpolation_method: nearest | linear | cubic: Interpolation method for travel times in the volume. Choose from nearest, linear or cubic.
nthreads: 0: Number of threads to use for travel time. If set to 0, cpu_count*2 will be used.
implementation: pyrocko | scikit-fmm: Implementation of the Fast Marching Method. Pyrocko only supports first-order FMM for now.
phases: Phases to calculate.

JSON for FastMarchingTracer

{
  "tracer": "FastMarching",
  "velocity_model": {
    "filename": "/home/runner/.cache/qseek/velocity_models/default.nd",
    "format": "nd",
    "crust2_profile": "",
    "raw_file_data": null
  },
  "interpolation_method": "linear",
  "nthreads": 0,
  "implementation": "scikit-fmm",
  "phases": [
    "fm:P",
    "fm:S"
  ]
}

Calculation of travel times in 1D layered media is based on the Pyrocko Cake ray tracer.

CakeTracer Module

Travel time calculation for 1D layered velocity models.

Calculation is based on Pyrocko Cake ray tracer.

Config CakeTracerJSON

phases: Dictionary of phases and timings to calculate.
earthmodel: Earth model to calculate travel times for.

JSON for CakeTracer

{
  "tracer": "CakeTracer",
  "phases": {
    "cake:P": {
      "definition": "P,p"
    },
    "cake:S": {
      "definition": "S,s"
    }
  },
  "earthmodel": {
    "filename": "/home/runner/.cache/qseek/velocity_models/default.nd",
    "format": "nd",
    "crust2_profile": ""
  }
}

3D Velocity Model 🚀

We implement the fast marching method for calculating first arrivals of waves in 3D volumes. Currently three different 3D velocity models are supported:

Import NonLinLoc 3D velocity model
1D layered model 🥞
Constant velocity, mainly for testing purposes 🥼

Fast Marhing Concept — Conceptual 2D visualisation for seismic traveltimes calculation in heterogenous media using the fast-marching method for the Eikonal solution is presented. Traveltimes from the receiving station at the surface (indicated by a yellow triangle) towards the subsurface grid are calculated, resulting in station-specifig traveltimes for all potential source locations simultaneously.

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/markdown_exec/_internal/formatters/python.py", line 71, in _run_python
    exec_python(code, code_block_id, exec_globals)
  File "/opt/hostedtoolcache/Python/3.11.13/x64/lib/python3.11/site-packages/markdown_exec/_internal/formatters/_exec_python.py", line 8, in exec_python
    exec(compiled, exec_globals)  # noqa: S102
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "<code block: n10>", line 2, in <module>
    from qseek.insights.tracers.fast_marching_3d import FastMarching3DTracer
ModuleNotFoundError: No module named 'qseek.insights'

Visualizing 3D Models

For quality check, all 3D velocity models are exported to vtk/ folder as .vti files. Use ParaView to inspect and explore the velocity models.

Velocity model FORGE Seismic velocity model of the Utah FORGE testbed site, visualized in ParaView.