Non‐linear stochastic inversion of gravity data via quantum‐behaved particle swarm optimisation: application to Eurasia–Arabia collision zone (Zagros, Iran)

Abstract

Potential field data such as geoid and gravity anomalies are globally available and offer valuable information about the Earth's lithosphere especially in areas where seismic data coverage is sparse. For instance, non‐linear inversion of Bouguer anomalies could be used to estimate the crustal structures including variations of the crustal density and of the depth of the crust–mantle boundary, that is, Moho. However, due to non‐linearity of this inverse problem, classical inversion methods would fail whenever there is no reliable initial model. Swarm intelligence algorithms, such as particle swarm optimisation, are a promising alternative to classical inversion methods because the quality of their solutions does not depend on the initial model; they do not use the derivatives of the objective function, hence allowing the use of L1 norm; and finally, they are global search methods, meaning, the problem could be non‐convex. In this paper, quantum‐behaved particle swarm, a probabilistic swarm intelligence‐like algorithm, is used to solve the non‐linear gravity inverse problem. The method is first successfully tested on a realistic synthetic crustal model with a linear vertical density gradient and lateral density and depth variations at the base of crust in the presence of white Gaussian noise. Then, it is applied to the EIGEN 6c4, a combined global gravity model, to estimate the depth to the base of the crust and the mean density contrast between the crust and the upper‐mantle lithosphere in the Eurasia–Arabia continental collision zone along a 400 km profile crossing the Zagros Mountains (Iran). The results agree well with previously published works including both seismic and potential field studies.

A Surrogate Assisted Quantum-Behaved Algorithm for Well Placement Optimization

“…Moreover, quantum computation can manage highly nonlinear multimodal optimization problems [51], and PSO also works linearly. In contrast, the probabilistic approach can determine the QPSO's next position [52]. In QBA, researchers use the mean best approach to avoid local optima [53].…”

Quantum-Based Analytical Techniques on the Tackling of Well Placement Optimization

“…Sun et al [44] implemented the principle of quantum mechanics with basic PSO. The QPSO algorithm not only tackles the drawbacks but also preserves the good features of the PSO algorithm [45], and thus the incorporation of improved search capability in addition to fast convergence is possible [46]. Another feature of QPSO is that it has only one parameter that needs to be tuned.…”

“…, Q gD ). Using Monte-Carlo method, the quantum state of the particle's position could be expressed as [45]:…”