Reflection seismology aims to estimate the Earth's subsurface elastic parameters for further investigation by geologists and engineers. This involves generating elastic waves using seismic sources and recording the Earth's response with receivers. The subsurface model is typically considered a combination of a background model and a short-wavelength reflectivity model. There are two main paths to estimate these parameters: non-linear waveform inversion to directly compute the elastic parameters or depth migration to estimate a structural image or reflectivity of the subsurface.
Reverse-Time Migration (RTM) is a common depth migration technique that migrates recorded wavefields from the space-time domain to the space-depth domain. It utilizes the Born approximation and the adjoint of the Born operator to produce an RTM image. However, RTM can suffer from errors, such as noise, temporal and spatial limitations, and multiple reflections.
Least-Squares Reverse-Time Migration (LSRTM) is used to overcome some of these errors. LSRTM involves resolving the reflectivity model by least-squares inversion, which is computationally expensive. Gradient-based optimization algorithms are often employed to reduce the computational burden, but they still require solving the wave equation and its adjoint for a large model in multiple iterations. One way to reduce the computational cost is by limiting the computational domain to a target region of interest.
Target-oriented LSRTM, known as TOLSRTM, focuses on the wavefield just above the target by bypassing the overburden. This approach proves beneficial when the overburden generates strong internal multiple reflections that obscure the reflections from the target area. However, a redatuming method is required to predict all orders of multiples. Marchenko redatuming is a data-driven technique that predicts the Green's functions at the boundary of the target region, incorporating all orders of internal multiples. It allows for double-sided redatuming, considering both the source and receiver perspectives. By combining the LSRTM algorithm and Marchenko double-focusing, a target-oriented LSRTM algorithm is devised that can predict interactions between the target and overburden and remove the effects of the overburden in the image. Predicting these interactions results in an artifact-free image, a better convergence rate, and a high-resolution image of the target.
Target-oriented migration algorithms typically consider only the upper horizontal boundary of the region of interest (ROI), neglecting wavefields entering the ROI from the medium beneath the lower boundary. To address this, a target-enclosed LSRTM algorithm is proposed, including both the ROI's upper and lower boundaries. Including the lower boundary provides transmission information and can improve inversion convergence. In addition, this algorithm is adopted for virtual receivers created by Marchenko redatuming. In the case of physical receivers at the boundaries of the target zone, the target-enclosed algorithm can incorporate the transmission information emanating from the lower boundary to the upper one. Consequently, when the initial model is far from the actual model, the resulting image partly recovers the long wavelength part of the model in agreement with the Born approximation criteria. Moreover, when an initial model closer to the actual model is used, the algorithm can partially recover the vertical interfaces of the perturbation. In the case of virtual receivers at the boundaries of the target zone, since the Marchenko redatuming is performed in the initial background model, the redatumed wavefields at the lower boundary suffer from kinematic errors. Therefore, the algorithm can not recover the long wavelength part of the model.
The thesis concludes with a discussion of the results obtained from applying the algorithms to marine datasets. The images resulting from the Marchenko double-focusing based target-oriented LSRTM algorithm show improvements in both resolution and artifact reduction by suppressing the overburden generated internal multiple effects. Moreover, the double-focusing enables the user to reduce the computational costs of the LSRTM algorithm and choose finer spatial sampling for the image.
An appendix proposes a formulation for integrating the target-oriented algorithms with non-linear inversion like Full Waveform Inversion (FWI). The results of this proposed algorithm show its effectiveness by reducing the internal multiple related artifacts and increasing resolution and faster convergence.
Dr. ir. J.R. van der Neut of Delft University of Technology has contributed greatly to the preparation of this dissertation. This work has received funding from the European Union’s Horizon 2020 research and innovation programme: European Research Coun-cil (grant agreement 742703).
- Marchenko method
- Least-squares migration
- Seismic imaging