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We present an improved neotectonic numerical model of the complex NW Africa-SW Eurasia plate boundary segment that runs from west to east along the Gloria Fault up to the northern Algerian margin. We model the surface velocity field and the ongoing lithospheric deformation using the most recent version of the thin-shell code SHELLS and updated lithospheric model and fault map of the region. To check the presence versus the absence of an independently driven Alboran domain, we develop two alternative plate models: one does not include an Alboran plate; another includes it and determines the basal shear tractions necessary to drive it with known velocities. We also compare two alternative sets of Africa-Eurasia velocity boundary conditions, corresponding to geodetic and geological-scale averages of plate motion. Finally, we perform an extensive parametric study of fault friction coefficient, trench resistance, and velocities imposed in Alboran nodes. The final run comprises 5240 experiments, each scored to geodetic velocities (estimated for 250 stations and here provided), stress direction data, and seismic strain rates. The model with the least discrepancy to the data includes the Alboran plate driven by a basal WSW directed shear traction, slightly oblique to the westward direction of Alboran motion. We provide estimates of long-term strain rates and slip rates for the modeled faults, which can be useful for further hazard studies. Our results support that a mechanism additional to the Africa-Eurasia convergence is required to drive the Alboran domain, which can be related to subduction processes occurring within the mantle.

It has been generally accepted that the noise in continuous GPS observations can be well described by a power-law plus white noise model. Using maximum likelihood estimation (MLE) the numerical values of the noise model can be estimated. Current methods require calculating the data covariance matrix and inverting it, which is a significant computational burden. Analysing 10 years of daily GPS solutions of a single station can take around 2 h on a regular computer such as a PC with an AMD AthlonTM 64 X2 dual core processor. When one analyses large networks with hundreds of stations or when one analyses hourly instead of daily solutions, the long computation times becomes a problem. In case the signal only contains power-law noise, the MLE computations can be simplified to a process where N is the number of observations. For the general case of power-law plus white noise, we present a modification of the MLE equations that allows us to reduce the number of computations within the algorithm from a cubic to a quadratic function of the number of observations when there are no data gaps. For time-series of three and eight years, this means in practise a reduction factor of around 35 and 84 in computation time without loss of accuracy. In addition, this modification removes the implicit assumption that there is no environment noise before the first observation. Finally, we present an analytical expression for the uncertainty of the estimated trend if the data only contains power-law noise