An algorithm for solving a 1D seismic data inversion problem on quantum or digital annealers in the presence of a priori information on layer parameters specified by arbitrary functions
Nickolay V Maletin, Anastasiia M Eremenko, Dmitry V Minaev
Abstract This work demonstrates the fundamental possibility of solving quite large-scale problems of seismic data inversion on modern hybrid (quantum-classical) and quantum-inspired annealers using the example of a one-dimensional problem for a horizontally layered model of the medium in the acoustic approximation. The optimization problem for the residual function of observed and model data is decomposed into three problems: the optimization problem for a simpler function of the same dimension, the problem of finding the minimum of a one-dimensional function, and the problem of calculating the terms of a simple recurrent series. Then, the optimization problem for a simpler function is transformed into a quadratic unconstrained binary optimization problem of such a dimension that its solution can be calculated on modern annealers.
Abstract This work demonstrates the fundamental possibility of solving quite large-scale problems of seismic data inversion on modern hybrid (quantum-classical) and quantum-inspired annealers using the example of a one-dimensional problem for a horizontally layered model of the medium in the acoustic approximation. The optimization problem for the residual function of observed and model data is decomposed into three problems: the optimization problem for a simpler function of the same dimension, the problem of finding the minimum of a one-dimensional function, and the problem of calculating the terms of a simple recurrent series. Then, the optimization problem for a simpler function is transformed into a quadratic unconstrained binary optimization problem of such a dimension that its solution can be calculated on modern annealers.
Abstract The paper provides a brief overview of the current state of development of quantum, hybrid and quantum-inspired annealers and the problems that can be solved with their help. We propose a method for reducing high-degree polynomial optimization problems from a large number of continuous variables to quadratic unconstrained binary optimization (QUBO) problems, developed by the authors and not previously encountered in the literature. The QUBO formulation of the 1D problem of synchronous model-based inversion of seismic data, obtained through this method, is presented. Evaluations are carried out that demonstrate a significantly higher efficiency of the introduced technique in comparison with the standard one, as well as the possibility of solving the 1D problem of synchronous model-based inversion of industrial-scale seismic data (containing ∼1000 time steps) on the latest models of the D-Wave hybrid annealer.
Abstract One of the promising areas for the future application of quantum computers is problems that are solved using stochastic modeling methods. One of these problems is the problem of synchronous inversion of seismic data in the presence of multimodal information on the elasticity characteristics of geological rocks. This paper analyzes the possibility of solving this problem using quantum annealing. Its reduction to the QUBO task is demonstrated. An assessment is carried out demonstrating the fundamental possibility of solving industrial-scale 1D problems on the latest models of the D-Wave hybrid quantum-classical annealer. In conclusion, an idea is briefly discussed, which, if successfully implemented, may make it possible to solve many 1D problems at once on such an annealer.
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.
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.
Quantum annealers such as the D-Wave 2X computer are designed to natively solve Quadratic Unconstrained Binary Optimization (QUBO) problems to optimality or near optimality. Most NP-hard problems, which are hard for classical computers, can be naturally described as quadratic binary problems that contain a quadratic binary objective function and one or more constraints. Since a QUBO cannot have constraints, each such constraint has to be added to the objective function as a penalty, in order to solve on D-Wave. For a minimization problem, for instance, such penalty can be a quadratic term that gets a value zero, if the constraint is satisfied, and a large value, if it is not. In many cases, however, the penalty can significantly increase the number of quadratic terms in the resulting QUBO and make it too large to embed into the D-Wave hardware. In this paper, we develop an alternative method for formulating and embedding constraints of the type Σi=1sxi=1, which is much more scalable than the existing ones, and analyze the properties of the resulting embeddings.