Abstract
<jats:p>Detectability of pre-rupture crustal deformation depends on sensor precision, node density, array aperture, spatial covariance, deformation footprint, and causal filtering. We derive a covariance-propagation framework for targeted dense arrays of low-cost dual-band global navigation satellite system (GNSS) sensors. Regional offset and planar fields are fitted as nuisance modes, while independent receiver noise and residual locally correlated noise enter an explicit covariance matrix. For a prescribed spatial template, minimum-variance weighting estimates the same localized amplitude used in the performance figures. The exponential covariance is retained only as a transparent benchmark; other positive-definite kernels can be inserted through their covariance matrix or integrated correlation area. Because the proposed hardware has not been field-calibrated, we use favorable, reference, and conservative design scenarios rather than a universal noise value. For a $20\times20$~km domain and a radial $R_c=3$~km footprint, the reference scenario gives spatial-search-adjusted thresholds of approximately 2.03, 1.63, 1.41, and 1.19~cm for $N=900$, 1,600, 2,500, and 4,900 nodes, respectively; persistent local correlation creates a several-centimeter floor even at larger $N$. Independent PSGA and IQQE records from the 2014 Iquique sequence provide filtered amplitudes of 1.54 and 1.02~cm without rescaling. In a counterfactual $N=4,096$ benchmark, PSGA crosses the favorable and reference thresholds, whereas IQQE crosses only the favorable threshold; this is not a retrospective dense-array detection. Direct matrix inversion, a finite-grid matrix-free solution, and 5,000 Monte Carlo realizations agree at the sub-percent level. The framework identifies the density, covariance, footprint, and cost conditions for mechanically grounded pre-rupture monitoring, together with the field-calibration and false-alarm tests required before operational use.</jats:p>