Sains Malaysiana 55(6)(2026): 959-973

http://doi.org/10.17576/jsm-2026-5506-02

 

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

(Kestabilan Penyongsangan Bersama Kecerunan Silang di bawah Keadaan Hingar: Satu Kajian Sistematik)

 

MUHAMMAD FAWZY ISMULLAH MASSINAI^1,2, MUHAMMAD TAQIUDDIN ZAKARIA^1,*, MOHD HARIRI ARIFIN¹, NURUL ASIKIN MOHD ARAHA¹ & NUR IRDINA INSYIRAAH MOHD SALWIRA¹

 

¹Geology Programme, Department of Earth Sciences and Environment, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

²Department of Geophysics, Faculty of Mathematics and Natural Science, Hasanuddin University, Makassar 90245, Indonesia

 

Diserahkan: 15 Disember 2025/Diterima: 20 Mei 2026

 

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.

Keywords: Cross gradient joint inversion; geophysical applications; methodological development; noise stability; systematic literature review

 

Abstrak

Penyongsangan bersama kecerunan silang (CGJI) ialah kaedah geofizik yang digunakan secara meluas yang mengintegrasikan pelbagai parameter dengan menguatkuasakan keserupaan struktur melalui kekangan kecerunan silang. Walaupun keberkesanannya telah ditunjukkan merentasi pelbagai persekitaran geologi, kestabilannya di bawah keadaan hingar masih belum dicirikan dengan mencukupi. Penyelidikan ini membentangkan satu tinjauan kepustakaan sistematik (SLR) terhadap 68 penerbitan antara tahun 2015 hingga 2024, mengikut protokol pengenalpastian, penapisan dan sintesis yang berstruktur berdasarkan garis panduan PRISMA. Kajian yang dikaji dianalisis dari segi aplikasi, perkembangan metodologi dan kestabilan hingar menggunakan pendekatan sintesis separa kuantitatif. Keputusan menunjukkan bahawa CGJI paling kerap digunakan dalam geodinamik-tektonik dan penerokaan petroleum dengan peningkatan perkembangan metodologi didorong oleh kemajuan dalam pembelajaran mesin. Prestasinya sangat bergantung pada penyepaduan set data dengan kepekaan pelengkap dan bukannya pada mana-mana kaedah geofizik tertentu. Kebanyakan kajian melaporkan peningkatan dalam penentuan struktur dan pengurangan ketaksaan penyongsangan berbanding pendekatan kaedah tunggal, terutamanya di bawah keadaan hingar rendah hingga sederhana (≤ 20%). Walau bagaimanapun, terdapat jurang kritikal masih wujud, penilaian sedia ada kebanyakannya berdasarkan data sintetik dan tahap hingar jarang melebihi 20% yang mungkin tidak mencerminkan keadaan lapangan sebenar. Walaupun metriks seperti ralat Punca Purata Kuasa Dua (RMS) dan Ukuran Indeks Kesamaan (SSIM) digunakan untuk menilai kepekaan hingar, penggunaannya masih terhad dan tidak tekal. Keputusan ini menekankan keperluan untuk penilaian sistematik terhada CGJI di bawah tahap hingar yang lebih tinggi dan keadaan lapangan sebenar bagi memastikan kebolehpercayaan dan kebolehgunaan praktikalnya.

Kata kunci: Aplikasi geofizik; kestabilan hingar; penyongsangan bersama kecerunan silang; perkembangan metodologi; tinjauan kepustakaan sistematik

 

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*Pengarang untuk surat-menyurat; email: taqiuddin@ukm.edu.my