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<p>Focal mechanism data are essential for estimating tectonic stress tensors, but heterogeneous data quality and unequal observation precision can bias inversions when uniform weights are assumed. We introduce a weighted least-squares inversion combined with variance component estimation (VCE; BIQUE in a Gauss–Helmert framework) that infers observation variances directly from residuals and assigns statistically consistent weights. In our implementation, <i>one variance component is estimated per mechanism and applied jointly to its strike, dip, and slip angles</i>, providing a parsimonious and catalog-consistent stochastic model. We validate the method on three datasets: a 40-event synthetic test, the 2008 West Bohemia swarm (167 mechanisms), and Agia Varvara in central Crete (31 mechanisms). Compared with uniform weighting, VCE produces sharper and more stable principal stress orientations, with azimuth and plunge uncertainties reduced by up to an order of magnitude. Variance–trace metrics decrease substantially, by roughly one order of magnitude in the synthetic test and two orders in West Bohemia. In Central Crete, the uncertainties shrink by a factor of 2–3, and the stress–shape ratio converges toward <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R\!\approx \!0.6\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mspace width="-0.166667em" /> <mo>≈</mo> <mspace width="-0.166667em" /> <mn>0.6</mn> </mrow> </math></EquationSource> </InlineEquation>. Shape-ratio distributions become narrower and more tectonically consistent, and Mohr–Coulomb instability analysis shows clearer separation between stable and near-failure planes. These results demonstrate that data-driven stochastic weighting via VCE materially improves focal-mechanism stress tensor inversion and offers a reproducible framework for reliable stress tensor analyses in complex tectonic settings.</p>

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Stress tensor inversion from focal mechanism data: variance component estimation approach for data weighting

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Khosro Moghtased-Azar,
  • Mina Pouragha-Aliabad

摘要

Focal mechanism data are essential for estimating tectonic stress tensors, but heterogeneous data quality and unequal observation precision can bias inversions when uniform weights are assumed. We introduce a weighted least-squares inversion combined with variance component estimation (VCE; BIQUE in a Gauss–Helmert framework) that infers observation variances directly from residuals and assigns statistically consistent weights. In our implementation, one variance component is estimated per mechanism and applied jointly to its strike, dip, and slip angles, providing a parsimonious and catalog-consistent stochastic model. We validate the method on three datasets: a 40-event synthetic test, the 2008 West Bohemia swarm (167 mechanisms), and Agia Varvara in central Crete (31 mechanisms). Compared with uniform weighting, VCE produces sharper and more stable principal stress orientations, with azimuth and plunge uncertainties reduced by up to an order of magnitude. Variance–trace metrics decrease substantially, by roughly one order of magnitude in the synthetic test and two orders in West Bohemia. In Central Crete, the uncertainties shrink by a factor of 2–3, and the stress–shape ratio converges toward \(R\!\approx \!0.6\) R ≈ 0.6 . Shape-ratio distributions become narrower and more tectonically consistent, and Mohr–Coulomb instability analysis shows clearer separation between stable and near-failure planes. These results demonstrate that data-driven stochastic weighting via VCE materially improves focal-mechanism stress tensor inversion and offers a reproducible framework for reliable stress tensor analyses in complex tectonic settings.