One-Way Reflection Waveform Inversion

Abstract

The introduction and adoption of seismic full waveform inversion (FWI) revolutionized Earth's subsurface imaging practices. FWI uses all the information in the seismic data (amplitudes and phases) to reconstruct a detailed Earth's subsurface model. However, it does come with limitations. Beyond the reach of refractions and diving waves, FWI cannot effectively reconstruct subsurface layers. This led to the development of reflection waveform inversion (RWI), which exclusively uses the pair of transmission-after-reflection wavepaths to sample deeper compared to FWI. RWI reconstructs the background velocity model of the subsurface by alternating between a migration loop and a tomography loop.

Despite the theoretical appeal, RWI has its own share of limitations. This dissertation investigates the barriers limiting the optimal performance of reflection waveform inversion in the context of one-way RWI (ORWI), a variation of reflection waveform inversion that adopts one-way wavefield propagators to forward model seismic reflection data. After exploring the barriers, the dissertation offers solutions to improve the reliability, accuracy, and convergence of ORWI.

The dissertation acknowledges several barriers that limit the optimal performance of conventional/standard ORWI. First, ORWI relies on accurate subsurface images. However, limited-resolution images with unpreserved amplitudes, resulting from the migration loop, lead to suboptimal background velocity updates. This issue also extends to the tomography loop, where limited-resolution tomographic wavepaths impede optimal background velocity updates. Second, ORWI overlooks the immediate impact that updating the velocity model has on the reflectivity model, as the reflectors' positions in depth remain fixed while the background velocity is updated. This oversight leads to inconsistent reflectivity and velocity models in ORWI, introducing full-wave inconsistencies in the short-offset residual waveforms for tomography. Third, similar to other seismic waveform inversion techniques, ORWI suffers from the detrimental effect of including cycle-skipped data from long offsets.

To mitigate the barriers, the dissertation proposes a range of solutions. Initially, the dissertation introduces a computationally efficient high-resolution migration algorithm called preconditioned least-squares wave-equation migration (PLS-WEM) through depth-dependent gradient preconditioning. PLS-WEM reconstructs high-resolution, amplitude-preserved seismic images in fewer iterations.

Following that, by incorporating PLS-WEM into standard ORWI, the dissertation enhances ORWI, achieving improved reflectivity imaging and thereby reconstructing tomograms that are more representative of the true subsurface layers. The dissertation also proposes the following data solutions: (a) Muting short-offset residual waveforms in the tomography data to reduce the adverse imprint of inconsistencies between the reflectivity and velocity models on the tomographic gradient of ORWI. (b) Building on (a), extending the migration offset to the maximum effective migration offset (MEMO) to enhance both the signal-to-noise ratio and the illumination of the reflectivity model. (c) Introducing a data selection algorithm to minimize the impact of cycle-skipped long-offset data.

The dissertation then presents high-resolution ORWI (HR-ORWI) technology, which leverages depth-dependent gradient preconditioning in both migration and tomography loops to reconstruct optimal tomograms in fewer cycles.

The dissertation next evaluates three approaches to depth-dependent gradient preconditioning: conventional, source-interference-free, and source-interference-inclusive. Numerical results show the superiority of the source-interference-inclusive approach, offering enhanced resolution, reduced computational demands, and resilience to source interference.

Lastly, the dissertation develops a mathematical framework that integrates early-arrival waveform inversion with ORWI through the subspace gradient method, combining the strengths of transmission and transmission-after-reflection wavepaths to enhance tomogram reconstruction.

In conclusion, this dissertation offers a comprehensive set of solutions to overcome the limitations of ORWI, facilitating its broader adoption and application in seismic exploration and velocity model building.