Abstract In an era of customized hardware designed to tackle specific geophysical challenges, recent advancements in quantum computing could offer promising solutions to complex global optimization problems using hybrid quantum-classical solvers. We introduce an application of seismic data processing where the stack power of the traces is maximized through quantum annealing for surface-consistent phase and amplitude refraction residual calculations. Refraction residual corrections are a necessary step in the processing workflow to obtain a detailed characterization of the subsurface. The problem of estimating accurate refraction residuals can be solved in a framework where relative time shifts and amplitude distortions of seismic traces are evaluated in multiple common-midpoint-offset bins through computerized cross-correlation operations. The results are then used to build a system of linear equations that is simultaneously inverted for surface-consistent shot and receiver phase and amplitude variations. We rewrote the problem by substituting the cross-correlation operations with global optimization performed by a “black-box” hybrid solver, which uses a physical quantum-annealing machine. With the projected hardware and technology improvements of the near future, the new approach is expected to be more accurate than the current solution because it prevents the phenomenon of the so-called cycle skips in the cross-correlation process. The method has been benchmarked with a classical global optimization algorithm and tested with promising results on synthetics of industrial size and relevance. A first attempt of application on field data has also been carried out. Quantum-annealing-based global optimization can be applied to other disciplines such as material science, logistics, and finance.
Abstract In an era of customized hardware designed to tackle specific geophysical challenges, recent advancements in quantum computing could offer promising solutions to complex global optimization problems using hybrid quantum-classical solvers. We introduce an application of seismic data processing where the stack power of the traces is maximized through quantum annealing for surface-consistent phase and amplitude refraction residual calculations. Refraction residual corrections are a necessary step in the processing workflow to obtain a detailed characterization of the subsurface. The problem of estimating accurate refraction residuals can be solved in a framework where relative time shifts and amplitude distortions of seismic traces are evaluated in multiple common-midpoint-offset bins through computerized cross-correlation operations. The results are then used to build a system of linear equations that is simultaneously inverted for surface-consistent shot and receiver phase and amplitude variations. We rewrote the problem by substituting the cross-correlation operations with global optimization performed by a “black-box” hybrid solver, which uses a physical quantum-annealing machine. With the projected hardware and technology improvements of the near future, the new approach is expected to be more accurate than the current solution because it prevents the phenomenon of the so-called cycle skips in the cross-correlation process. The method has been benchmarked with a classical global optimization algorithm and tested with promising results on synthetics of industrial size and relevance. A first attempt of application on field data has also been carried out. Quantum-annealing-based global optimization can be applied to other disciplines such as material science, logistics, and finance.
ABSTRACT Much of recent progress in geophysics can be attributed to the adaptation of heterogeneous high-performance computing architectures. It is projected that the next major leap in many areas of science, and hence hopefully in geophysics too, will be due to the emergence of quantum computers. Finding a right combination of hardware, algorithms, and a use case, however, proves to be a very challenging task — especially when looking for a relevant application that scales efficiently on a quantum computer and is difficult to solve using classical means. We find that maximizing stack power for residual statics correction, an NP-hard combinatorial optimization problem, appears to naturally fit a particular type of quantum computing known as quantum annealing. We express the underlying objective function as a quadratic unconstrained binary optimization, which is a quantum-native formulation of the problem. We choose some solution space and define a proper encoding to translate the problem variables into qubit states. We find that these choices can have a significant impact on the maximum problem size that can fit on the quantum annealer and on the fidelity of the final result. To improve the latter, we embed the quantum optimization step in a hybrid classical-quantum workflow, which aims to increase the frequency of finding the global, rather than some local, optimum of the objective function. Finally, we find that a generic, black-box, hybrid classical-quantum solver also could be used to solve stack-power maximization problems proximal to industrial relevance and capable of surpassing deterministic solvers prone to cycle skipping. A custom-built workflow capable of solving larger problems with an even higher robustness and greater control of the user appears to be within reach in the very near future.
Summary Recent progress in geophysics can be attributed to developments in heterogeneous HPC architectures, with one of the next major leaps being forecasted to be due to quantum computers. It is, however, very difficult to find the right combination of hardware, algorithms and a use-case. This is especially true for applications which have to be simultaneously: relevant and operating at scales where problems become difficult to solve using classical means. Maximizing stack-power for improved near surface characterization and velocity model building, an NP-hard combinatorial optimization problem, appears to naturally fit a particular type of quantum computing known as quantum annealing. We present the quantum-native formulation of this problem. Furthermore, in order to improve the probability of success we embed it in a hybrid classical-quantum workflow. We present the results on controlled experiments run using a 5000-qubit machine and discuss the impact of different classical to quantum problem re-formulations.
Summary Quantum annealing emerged as a very promising tool for solving combinatorial optimization problems. In particular, residual refraction statics estimation has been identified to be the first potential industrial use case of quantum annealing in geoscience. The currently available quantum annealers have still too small computing capabilities to effectively and independently estimate residual statics on problems of industrial scale. On the other hand, a quantum annealer-assisted hybrid solver, combining classical and quantum information processing could already be a viable tool for this purpose. Here we show the application of such a hybrid solver to the residual refraction statics estimation through stack-power maximization on a significant subset of the SEAM Arid model dataset, comprising of over two thousand gathers. We benchmark our approach against a dedicated deterministic classical solver, showing that in a fixed amount of time per gather, the quantum annealer-assisted solution can in many instances outperform the standard approach.
Abstract ABSTRACT Quantum computing harnesses the principles of quantum mechanics to solve problems that are intractable for classical computers. Quantum annealing, a specialized approach within quantum computing, is particularly effective for optimization tasks, as it leverages quantum tunneling to escape local minima and efficiently explore complex energy landscapes. In geosciences, many problems are framed as high-dimensional optimization problems, including seismic inversion, which aims to estimate subsurface impedances from seismic data for accurate geological interpretation and resource exploration. A novel application of quantum computing for seismic inversion is presented, marking the first instance of inverting seismic data to estimate both P-wave and S-wave impedances using a quantum annealer. Building upon the prior work, which demonstrated the estimation of acoustic impedances from post-stack data using a two-step framework, we propose an enhanced workflow capable of inverting both post-stack and pre-stack seismic data in a single step. This advancement significantly reduces the number of qubits per model parameter (from 20 to 5) while improving computational speed (from 20 seconds to 6.3 seconds). The seismic inversion is implemented using the D-Wave Leap hybrid solver, achieving impedance estimation within 4-9 seconds, with the quantum processing unit (QPU) contributing just 0.043-0.085 seconds. Comparative analysis with simulated annealing reveals that quantum annealing produces impedance models closely matching true values in a single epoch, whereas simulated annealing requires 10 epochs for improved accuracy. These findings underscore the transformative potential of quantum computing for real-time, high-precision seismic inversion, marking a crucial step toward fully quantum-driven geophysical solutions.
Quantum computing is increasingly recognized as a transformative technology in geophysics, offering the potential to significantly enhance computational power and efficiency. This advancement holds promise for the simulation and processing of complex geological data at unprecedented speeds. Recent studies have begun exploring the application of quantum computing methods to simplified versions of seismic inversion problems, underscoring the technology’s capability to address real-world inverse problems. The primary aim of this study is to tackle a realistic, scalable, and business-relevant problem by estimating acoustic impedances from seismic trace data using a quantum computer. To the best of our knowledge, this is the first instance of seismic impedances being predicted from seismic data through quantum computing, with a discussion on the advantages of solving the inverse problem on quantum processing units (QPUs). In this paper, we leverage the D-Wave quantum annealer to tackle the poststack seismic inversion problem, employing a novel two-step workflow. In the first step, we utilize the quantum annealer to estimate reflectivities from seismic data. Subsequently, these estimated normal-incidence reflectivities serve as the basis for predicting acoustic impedances with the same quantum technology. To validate the effectiveness of our approach, we present five examples, juxtaposing the impedance predictions from the D-Wave quantum annealer against those obtained through Simulated Annealing—a stochastic global optimizer traditionally employed for seismic inversion. Remarkably, the impedances derived from the quantum annealer matched closely with the true values in just a single epoch, whereas simulated annealing required 10 epochs to achieve a similar accuracy. Furthermore, the QPUs within our hybrid solver took only about 0.08 seconds to estimate these seismic impedances. This is remarkably efficient when compared to the time needed by both the classical component of the hybrid solver and simulated annealing, which each took over 10 seconds. This highlights the potential of QPUs to entirely resolve the seismic inverse problem in under a second, underscoring the transformative impact that quantum computing can have in the field of geophysics.
This study demonstrates the application of quantum computing based quantum annealing to seismic traveltime inversion, a critical approach for inverting highly accurate velocity models. The seismic inversion problem is first converted into a Quadratic Unconstrained Binary Optimization problem, which the quantum annealer is specifically designed to solve. We then solve the problem via quantum annealing method. The inversion is applied on a synthetic velocity model, presenting a carbon storage scenario at depths of 1000-1300 m. As an application example, we also show the capacity of quantum computing to handle complex, noisy data environments. This work highlights the emerging potential of quantum computing in geophysical applications, providing a foundation for future developments in high-precision seismic imaging.