Quantum Computing Applications in Seismic Inversion for the Nigerian Petroleum Industry

This study investigates the theoretical foundations and practical potential of quantum computing algorithms for solving seismic inversion problems relevant to the Nigerian petroleum industry, making an original contribution at the frontier of quantum geophysics. Seismic inversion is computationally among the most demanding problems in applied geophysics, particularly full waveform inversion of large 3D datasets where classical computing requires weeks of computation even on high-performance clusters. Quantum algorithms for combinatorial optimisation and linear algebra offer potential for exponential speedup on specific problem formulations, which could transform the economics of seismic inversion for Nigerian petroleum exploration. This study develops quantum algorithm formulations for two core seismic inversion problems: linearised post-stack acoustic inversion (a linear algebra problem suitable for quantum linear systems algorithms) and travel-time tomography (a combinatorial optimisation problem suitable for quantum annealing). Problem formulations are adapted to the specific constraints and signal characteristics of Nigerian Niger Delta seismic data. Implementation uses IBM Qiskit for quantum circuit simulation and IBM quantum hardware access. Classical intractability is demonstrated for full-scale Niger Delta inversion instances. Comparative solution quality between quantum, classical exact, and classical heuristic approaches is assessed on progressively scaled problem instances within quantum hardware capability. Findings demonstrate that the quantum linear systems algorithm provides theoretically valid solutions for the inversion problem with 68 percent fewer logical qubit requirements than naive formulation, but current quantum hardware noise levels prevent advantage demonstration on problems larger than 28 qubits. A 10 to 15 year roadmap for achieving quantum advantage in practical seismic inversion scale is developed. The study contributes the first quantum algorithm formulations for Niger Delta seismic inversion and a quantitative readiness roadmap for the Nigerian petroleum industry.

Keywords: quantum computing, seismic inversion, quantum algorithms, Niger Delta, petroleum geophysics.