Tomographic Waveform Inversion SEP‑197 (2025)

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Júlio Oliva Frigério Thesis

Table of contents

• Chapter 1. Introduction
  • 1.1 The Scientific Problem
  • 1.2 Thesis Overview
• Chapter 2. Fundamental Concepts
  • 2.1 Acronyms
  • 2.2 Notations
  • 2.3 Dot-product and inner-product
  • 2.4 Asymptotic solutions and the method of stationary phase
  • 2.5 Asymptotic solutions in this dissertation
  • 2.6 Wave propagation
  • 2.7 Relations with Green's functions in the frequency-domain
  • 2.8 Born scattering
  • 2.9 Born modeling operator and its adjoint
  • 2.10 The adjoint of modeling is imaging
  • 2.11 Extended Born modeling and imaging
  • 2.12 Derivatives of wavefields and Born operators
• Chapter 3. Kinematics of extended Born imaging
  • 3.1 Moveouts
  • 3.2 Point of stationary-phase contribution
  • 3.3 Space-lag moveouts of reflection events
  • 3.4 Time-lag moveouts of reflection events
  • 3.5 Exact space-lag moveouts of reflection events
  • 3.6 Exact time-lag moveouts of reflection events
  • 3.7 Consequences in the angle-domain
  • 3.8 Space-lag moveouts of transmission events
  • 3.9 Time-lag moveouts of transmission events
• Chapter 4. Properties of extended Born imaging-modeling
  • 4.1 Space-lag EBIM
  • 4.2 Time-lag EBIM
  • 4.3 Kinematic Invariance and Orthogonality
  • 4.4 Space-lag EBIM with shot-stack extended images
  • 4.5 Time-lag EBIM with shot-stack extended images
  • 4.6 Practical examples
  • 4.7 Discussion
• Chapter 5. Kinematic Misfit Operator (KMO)
  • 5.1 KMO for reflection events
  • 5.2 Kinematic effects of KMO on EBIM of relection events
  • 5.3 KMO for transmission events
  • 5.4 KMO for space-lags and dipping reflectors
• Chapter 6. Inverse Problem Formulation and Solution
  • 6.1 TWI as a constrained optimization problem
  • 6.2 Shape and convexity of TWI's objective function
  • 6.3 TWI's gradient computation
  • 6.4 Inverse problem solution
  • 6.5 Physical meaning of data residuals
• Chapter 7. Synthetic Examples
  • 7.1 Basic examples of TWI optimization
  • 7.2 Models with local velocity anomaly
  • 7.3 Horizontally Layered Models
  • 7.4 Acoustic Marmousi2 Model
  • 7.5 Chevron 2014 Benchmark Model
  • 7.6 Basic examples of TWI optimization
  • 7.7 Models with local velocity anomaly
• Chapter 8. Marimbá OBC
  • 8.1 Geology, data, and model
  • 8.2 TWI application process
  • 8.3 Analysis of results
• Chapter 9. Tiber WATS
  • 9.1 Introduction and motivation
  • 9.2 Problem context: geology, data, and imaging
  • 9.3 TWI application: model update and imaging improvement
  • 9.4 TWI application: details of the inversion procedure

Abstract

Seismic imaging and inversion of the Earth's subsurface in regions with a high degree of geological complexity is a challenging problem. To date, there is no methodology that solves this problem entirely. In some cases, the combined use of several distinct methods can successfully provide accurate, high-resolution models. However, many cases of significant interest remain for which such success cannot be achieved, even when combining multiple technologies currently available.

Tomographic Waveform Inversion (TWI) is proposed in this PhD thesis as a method that complements the traditional Full Waveform Inversion (FWI), filling in many of the relevant gaps that exist in FWI and other techniques presently available. TWI is able to recover the lower-wavenumber components of the velocity model from refraction and/or reflection events, because it successfully employs all tomographic kernels. The method performs well in complex geological settings, is virtually immune to convergence to local minima (cycle skipping), and can achieve a correct solution even when the starting model is very inaccurate. The algorithm is also attractive because its overall computational cost is equal to or smaller than that of FWI. One iteration of TWI is about three times the cost of one FWI iteration; however, it requires significantly fewer iterations than FWI to converge to a satisfactory solution. Other important advantages of the method are: it does not require accurate physical modeling of data amplitudes (such as elastic or viscoelastic modeling); it relies solely on kinematic information, which reduces the risk of inversion cross-talk by naturally decoupling parameters such as Vp, Vs, and density.

At the root of the method lies a robust theoretical framework, strongly supported by experimental results from applications to several meaningful cases spanning a broad range of complexity, from 2D synthetic models to 3D field data. These examples demonstrate the ability of TWI to fulfill its objectives and highlight its great potential as a technology for large industrial projects as well as basic geophysical research.

Reproducibility and source codes

Download Codes with reproducible experiments of results shown in the thesis.

Defense

Júlio Oliva Frigério Defense PPT