Stability of Cross-Gradient Joint Inversion under Noisy Conditions: A Systematic Review

Abstract

Cross-gradient joint inversion (CGJI) is a widely applied geophysical method that integrates multiple parameters by enforcing structural similarity through cross-gradient constraints. While its effectiveness has been demonstrated across diverse geological settings, its stability under noisy conditions remains insufficiently characterised. This study presents a systematic literature review (SLR) of 68 publications between 2015 and 2024, following a structured identification, screening, and synthesis protocol based on PRISMA guidelines. The reviewed studies were analysed in terms of applications, methodological developments, and noise stability using a semi-quantitative synthesis approach. The results indicate that CGJI is most commonly applied in geodynamics–tectonics and petroleum exploration, with increasing methodological developments driven by advances in machine learning. Its performance is strongly dependent on the integration of datasets with complementary sensitivities, rather than on any specific geophysical method. Most studies report improved structural delineation and reduced inversion ambiguity compared to single-method approaches, particularly under low-to-moderate noise conditions (≤ 20%). However, a critical gap remains: existing evaluations are predominantly based on synthetic datasets, and noise levels rarely exceed 20%, which may not reflect realistic field conditions. Although metrics such as Root Mean Square (RMS) and Structural Similarity Index Measure (SSIM) are used to assess noise sensitivity, their application remains limited and inconsistent. These findings highlight the need for systematic evaluation of CGJI under higher noise levels and real field conditions to ensure its reliability and practical applicability.

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