12.1 Principles of seismic tomography

Seismic tomography unveils Earth's hidden structures by analyzing seismic wave data. This technique creates 3D images of the planet's interior, revealing crucial information about temperature, composition, and density variations within the crust, mantle, and core.

Travel time analysis and ray path tracing are key components of seismic tomography. By comparing observed and predicted wave arrival times, scientists can develop detailed velocity models that describe how seismic waves move through Earth's layers.

Seismic Tomography Fundamentals

Imaging Earth's Interior

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  SE - 3-D seismic travel-time tomography validation of a detailed subsurface model: a case study ... View original

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• Seismic tomography creates 3D images of Earth's interior using seismic wave data
• Analyzes variations in seismic wave velocities to infer subsurface structures and properties
• Utilizes data from earthquakes and controlled seismic sources (explosions, air guns)
• Produces detailed maps of Earth's crust, mantle, and core structures
• Reveals information about temperature, composition, and density variations within the Earth

Travel Time Analysis and Ray Paths

• Travel time inversion reconstructs subsurface velocity structure from seismic wave arrival times
• Compares observed travel times with predicted times based on theoretical models
• Iteratively adjusts velocity model to minimize differences between observed and predicted times
• Ray path represents the trajectory of seismic waves through Earth's interior
• Bends and refracts based on velocity contrasts between different layers and structures
• Follows Snell's law, describing the relationship between angles of incidence and refraction
• Crucial for accurately interpreting seismic data and constructing velocity models

Velocity Model Development

• Velocity model describes the distribution of seismic wave speeds within Earth's interior
• Incorporates known geological information and initial assumptions about Earth structure
• Includes both P-wave (primary) and S-wave (secondary) velocities
• Accounts for variations in velocity due to changes in temperature, pressure, and composition
• Updated iteratively during the tomographic inversion process
• Serves as a foundation for interpreting seismic data and understanding Earth's internal structure

Inverse Problem Techniques

Fundamentals of Inverse Problems

• Inverse problem involves determining unknown causes from observed effects
• In seismic tomography, reconstructs Earth's internal structure from seismic wave observations
• Challenges include non-uniqueness of solutions and sensitivity to noise in the data
• Requires careful consideration of data quality, model parameterization, and inversion algorithms
• Often ill-posed, meaning small changes in input data can lead to large changes in the solution
• Utilizes mathematical techniques to find the most probable solution given the available data

Resolution and Model Quality

• Resolution measures the ability to distinguish between closely spaced features in the model
• Depends on the distribution of seismic sources and receivers, as well as the frequency content of the data
• Higher resolution allows for more detailed imaging of Earth's interior structures
• Trade-off exists between resolution and model stability
• Evaluated using resolution matrices, checkerboard tests, and synthetic data experiments
• Helps identify areas of the model that are well-constrained versus poorly-constrained

Regularization Techniques

• Damping stabilizes the inversion process by limiting the magnitude of model perturbations
• Prevents unrealistic oscillations in the solution caused by noise or data inconsistencies
• Implemented by adding a damping term to the objective function being minimized
• Smoothing enforces spatial continuity in the velocity model
• Reduces artifacts and improves the overall stability of the solution
• Applied through spatial averaging or by including smoothness constraints in the inversion
• Both damping and smoothing require careful parameter selection to balance stability and resolution

Computational Methods

Iterative Inversion Algorithms

• Iterative methods solve large-scale tomographic problems through repeated refinement
• Include techniques such as conjugate gradient, LSQR, and simultaneous iterative reconstruction technique (SIRT)
• Gradually improve the velocity model by minimizing the misfit between observed and predicted data
• Computationally efficient for handling large datasets and complex model parameterizations
• Allow for incorporation of non-linear effects and adaptive model updates
• Convergence criteria determine when to stop the iteration process (misfit reduction, model change threshold)
• Require careful initialization and parameter tuning to ensure stable and accurate results

Parallel Computing and Optimization

• Parallel computing distributes tomographic calculations across multiple processors or computers
• Significantly reduces computation time for large-scale problems
• Utilizes domain decomposition techniques to divide the model space or data among processors
• Optimization strategies improve the efficiency and accuracy of tomographic inversions
• Include techniques such as multi-grid methods, adaptive mesh refinement, and wavelet-based approaches
• Focuses computational resources on areas of the model with higher complexity or data coverage
• Balances the trade-off between computational cost and model resolution