Subsurface Simulation & Illumination Engineering

Ray Tracing & Elastic Wave Equation Modelling

A deep-dive technical overview analyzing the differences between high-frequency asymptotic ray approximation and full discrete elastic grid wavefield propagation.

1. Kinematic Ray Tracing (Asymptotic Approximation)

**Ray Tracing** is a high-frequency computational approximation based on optical physics. Instead of simulating an entire complex continuous wavefront, it models seismic energy traveling as discrete, localized directional trajectories called "rays." This method tracks travel times and reflection pathways by applying Snell’s Law across distinct boundaries where velocity shifts.

In survey design, engineers run **Illumination Workflows** using ray tracing. By shooting thousands of mathematical rays from planned surface locations down into a complex geological model (like a salt dome or fault block), designers map precisely where energy bounces back successfully and where shadows form. This helps identify blind spots where surface equipment must be adjusted to capture missing data.

Source Velocity Interface (Snell's Law) Reflected Ray Downward Ray
Figure 1: High-Frequency Specular Ray Tracing Path & Reflection Geometry Simulation

2. Full Elastic Wave Equation Modelling

While ray tracing simplifies paths into thin lines, **Elastic Wave Equation Modelling** makes no approximations. It uses numerical frameworks (such as Finite-Difference time-domain methods) to solve the fundamental partial differential equations of continuum mechanics across a dense grid.

Unlike simpler acoustic assumptions that only track pressure variants in fluids, the elastic wave approach models a complex solid earth matrix. This allows the system to accurately handle both compressional energy (**P-waves**) and shear energy (**S-waves**).

This simulation style computes complex wave behaviors, including ground roll, diffractions around fault edges, head waves, conversions between wave modes ($P \rightarrow S$), and amplitude changes across varying angles. This delivers a highly realistic, full-waveform synthetic record.

Primary P-Wavefront Converted S-Wave Fault Edge Diffraction
Figure 2: Finite-Difference Grid Solving Complex Elastic Wavefield Vectors (P-wave, S-wave, and Diffractions)

3. Comparative Integration in 3D Survey Workflows

Both modeling styles play distinct, complementary roles when evaluating survey design variables like bin sizes, target folds, or geometry offsets:

Analysis Metric Ray Tracing Method Elastic Wave Modelling
Computational Expense Extremely Low (Runs in minutes on standard laptops) Extremely High (Requires High-Performance Cluster Compute nodes)
Geological Target Focus Macro-illumination, geometric shadows, and structural path checks Fine stratigraphy, amplitude validation (AVO), and sub-salt scattering
Wave Phenomena Handled Primary reflections, transmissions, basic multi-pathing Full wavefields: Ground roll, diffractions, phase shifts, shear conversions