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.@en

Reflection waveform inversion (RWI) is a technique that uses pure reflection data to estimate subsurface background velocity, relying on evolving seismic images. Conventional RWI operates in a cyclic workflow, with two key components in each cycle—migration and reflection tomography. Conventional RWI may result in suboptimal background velocity estimation, partly due to limited or unresolved resolution within each component in each cycle. While gradient pre-conditioning with the reciprocal of Hessian information helps resolve this issue in both components of RWI, it becomes impractical for a large number of model parameters. One-way reflection waveform inversion (ORWI) is a reflection waveform inversion technique in which the forward modelling scheme operates in one direction (downward and then upward) via virtual parallel depth levels within the medium. Leveraging the ORWI framework, we decompose and reduce the linear Hessian operator (also known as the approximate Hessian or Gauss–Newton Hessian) into multiple smaller suboperators. In particular, the diagonal blocks of the monofrequency approximate Hessian operators, each corresponding to a single depth level within the medium, are extracted and inverted to pre-condition the corresponding monofrequency gradients in both the migration and reflection tomography components of ORWI. This depth-dependent gradient pre-conditioning transforms standard ORWI into a high-resolution, yet computationally feasible version aimed at addressing suboptimal velocity estimation, referred to as high-resolution ORWI. The effectiveness of the proposed approach is demonstrated through successful applications to synthetic data examples.

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Enhanced pre-stack depth migration, characterized by improved resolution and amplitudes, ensures a more accurate representation of the subsurface, proving essential for reducing the likelihood of geological misinterpretations and facilitating informed decision-making in seismic exploration. However, obtaining high-resolution images with preserved amplitudes through standard depth migration could face several hurdles known as migration artifacts. Iterative least-squares migration (LSM) was developed to address these migration artifacts. However, the convergence rate of LSM using a gradient descent approach tends to be slow. Several researchers have attempted to achieve computational efficiency in linearized LSM through gradient preconditioning. In the context of iterative least-squares wave-equation migration, this extended abstract compares three minimization approaches that differ in error functions and gradient preconditioning—including the depth-dependent Hessian approximation inverse—through two numerical examples, one with an inverse-crime scenario and the other with a non-inverse-crime scenario.@en

Since seismic imaging creates an image of the subsurface structure based on information received from the measured wavefield, it is essential to fully utilize the reflected waves. Full Wavefield Modeling (FWMod) was developed with recursive and iterative up-and-down wavefield propagation, using one-way wave propagation, to model both primary and multiple reflections. Using FWMod as the modeling engine, Full Wavefield Migration (FWM) has been introduced to directly image data including internal multiples, where internal multiple crosstalk is suppressed automatically via an inversion-based data-fitting process. This avoids the need for applying internal multiple removal, which is often challenging. Conventional one-way wave propagators calculated in the wavenumber domain, like the phase shift (PS) operator, have limitations when applied to strongly inhomogeneous media. Even when computing a new operator at each lateral grid point, they still suffer difficulties because the medium is assumed to be locally homogeneous. In the past, matrix eigendecomposition has been proposed as a way to create accurate, local velocity-based one-way propagation operators. In this article, an accurate propagator based on eigendecomposition is incorporated into FWMod and FWM. In the numerical examples, four models with strong lateral velocity variations were used to test the propagator. With a comparison of the conventional FWM based on the PS operator with input data including FWMod and a finite-difference (FD) approach, the numerical examples demonstrated that the proposed method has the potential to significantly enhance image reflectivity, suppress internal multiples, and maintain convergence speed during the least-squares inversion.

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Since the appearance of wave-equation migration, many have tried to improve the resolution and effectiveness of this technology. Least-squares wave-equation migration is one of those attempts that tries to fill the gap between the migration assumptions and reality in an iterative manner. However, these iterations do not come cheap. A proven solution to limit the number of least-squares iterations is to correct the gradient direction within each iteration via the action of a preconditioner that approximates the Hessian inverse. However, the Hessian computation, or even the Hessian approximation computation, in large-scale seismic imaging problems involves an expensive computational bottleneck, making it unfeasible. Therefore, we propose an efficient computation of the Hessian approximation operator, in the context of one-way wave-equation migration (WEM) in the space-frequency domain. We build the Hessian approximation operator depth by depth, considerably reducing the operator size each time it is calculated. We prove the validity of our proposed method with two numerical examples. We then extend our proposal to the framework of full-wavefield migration, which is based on WEM principles but includes interbed multiples. Finally, this efficient preconditioned least-squares full-wavefield migration is successfully applied to a dataset with strong interbed multiple scattering.

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Seismic imaging is crucial for subsurface exploration and monitoring, with a focus on deep and complex structures. Seismic wave migration solves the wave equation, and an accurate propagator is essential. Full Wavefield Modeling (FWMod) was developed based on recursive and iterative up/down wavefield propagation, modeling both primaries and multiples. Embedded within Full Wavefield Migration (FWM) it can be used to image data including multiples, resulting in better illumination in case primary illumination is not sufficient. FWM can be efficient and effective, but conventional one-way wave operators, such as Phase Shift Plus Interpolation Migration, have limitations in strongly inhomogeneous media. Local velocity-based one-way operator based on eigen decomposition was proposed and integrated within FWMod and FWM in this study, improving image amplitudes and fidelity and improving converage speed in the least-squares inversion process.@en

Reflection waveform inversion (RWI) is a method that relies on primary pure reflection data to recover the subsurface background velocity based on the associated evolving seismic images. Background velocity updates estimated by conventional RWI are nonoptimal, which is partly attributed to low-resolution tomographic wavepaths and migration isochrones. Preconditioning RWI sensitivity kernels using Hessian information solves this problem but is not practical for a large number of model parameters. One-way reflection waveform inversion (ORWI) is a reflection waveform tomography technique in which the forward modeling scheme operates in one direction (downward and then upward) via virtual parallel data levels in the medium. The ORWI framework allows us to break down the Hessian matrix into smaller operators, which makes the preconditioning operation more efficient and less computationally expensive. This extended abstract turns conventional ORWI into a high-resolution but computationally feasible ORWI (Gauss-Newton ORWI) to improve the nonoptimal background velocity updates.@en

Since the appearance of wave-equation migration, many have tried to push this technology to the limits of its capacity. Least-squares wave-equation migration is one of those attempts that tries to fill the gap between the migration assumptions and reality in an iterative manner. However, these iterations do not come cheap. A proven solution to limit the number of iterations is to correct the update direction in every iteration via a proper but cheap preconditioner that approximates the second-order partial derivatives, known as Hessian, of the data-error functional employed in the least-squares formulation. In this study, we will address this issue, namely the cheap computation of the Hessian inverse in the context of our one-way wave-equation-based migration method, cited as full wavefield migration. To do so, we will build and apply the Hessian inverse matrix depth by depth, reducing the Hessian matrix size considerably each time it is calculated. We prove the validity of our proposed method by two numerical examples.@en

Conventional full waveform inversion has proven ineffective in recovering background velocity models for the targets out of the reach of refracted and diving waves. Therefore, different reflection waveform inversion (RWI) tools have been presented so far, one of which is joint migration inversion (JMI). JMI, unlike most similar tools, is parameterized by two classes of parameters, reflectivity and velocity, and equipped with decoupled imaging and tomographic sensitivity kernels. The fundamental characteristic shared by JMI or any RWI technique is the arrival-time consistency between the anchor parts of the modeled and observed data. This characteristic helps and keeps any reflection waveform tomography tool robust against cycle-skipping in near-offset data. In this paper, through examining the tomographic gradient of JMI, we show that conventional JMI suffers from cycle skipping in near-offset traces, which degenerates the fidelity of the tomographic gradient of JMI. Next, we demonstrate how the degeneracy can be lifted from two different perspectives, either by muting the misguiding tomographic wavepaths or migration isochrones built by near-offset residuals. Coupled with this, we show how excluding the cycle-skipped far-offset data significantly improves the validity of the tomographic gradient of JMI.

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Considering the steadily declining prices in the oil and gas industry, nowadays, the requirement for geophysical information becomes more important in order to get the most out of available reservoirs. Electromagnetic measurements could complement seismic data where it lacks information. The EM response to fluid fill complements the resolving power of seismic data. In the current study, we use a probabilistic method to estimate reservoir parameters individually and jointly through two simplistic, synthetic, 2D reservoir models which can be considered as the geometrical limits of water-oil-contacts in oil and gas fields. We demonstrate a constructive contribution of the measurements with different physical natures in the estimation of reservoir parameters.@en

In this paper we compared time-domain FWI problem vs. frequency-domain in terms of the behavior of cost function and model misfit error on a synthetic model with transmission geometry. Synthetic data was generated by solution of 2D acoustic wave equation and optimization was performed using L-BFGS algorithm for both approaches in time and frequency-domain. Although FWI problem has a better expression in frequency-domain but inversion of selected frequency components is drawback of this approach despite its lower computational costs in term of memory. This paper shows the difference of full band data inversion in the time-domain with sequential inversion of some selected frequency components in the frequency-domain numerically. According to the results timedomain FWI leads to better results due to its full band characteristics when computational resources permits us to use it.@en