The Generalized Method of Wavelet Moments with eXogenous inputs: a fast approach for the analysis of GNSS position time series

The global navigation satellite system (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow to study global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work, we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time-series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogenous variables: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used maximum likelihood estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results (theoretical and obtained in simulations) show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach have important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations (some of them being recorded over several decades) quickly becomes computationally prohibitive. Compared to standard likelihood-based methods, the GMWMX has a considerably reduced algorithmic complexity of order O { log ( n ) n } for a time series of length n. Thus, the GMWMX appears to provide a reduction in processing time of a factor of 10-1000 compared to likelihood-based methods depending on the considered stochastic model, the length of the time series and the amount of missing data. As a consequence, the proposed method allows the estimation of large-scale problems within minutes on a standard computer. We validate the performances of our method via Monte Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power law or Matérn processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.

Transient Deformation in California From Two Decades of GPS Displacements: Implications for a Three-Dimensional Kinematic Reference Frame

Our understanding of plate boundary deformation has been enhanced by transient signals observed against the backdrop of time-independent secular motions. We make use of a new analysis of displacement time series from about 1,000 continuous Global Positioning System (GPS) stations in California from 1999 to 2018 to distinguish tectonic and nontectonic transients from secular motion. A primary objective is to define a high-resolution three-dimensional reference frame (datum) for California that can be rapidly maintained with geodetic data to accommodate both secular and time-dependent motions. To this end, we compare the displacements to those predicted by a horizontal secular fault slip model for the region and construct displacement and strain rate fields. Over the past 19 years, California has experienced 19 geodetically detectable earthquakes and widespread postseismic deformation. We observe postseismic strain rate variations as large as 1,000 nstrain/year with moment releases equivalent up to an Mw6.8 earthquake. We find significant secular differences up to 10 mm/year with the fault slip model, from the Mendocino Triple Junction to the southern Cascadia subduction zone, the northern Basin and Range, and the Santa Barbara channel. Secular vertical uplift is observed across the Transverse Ranges, Coastal Ranges, Sierra Nevada, as well as large-scale postseismic uplift after the 1999 Mw7.1 Hector Mine and 2010 Mw7.2 El Mayor-Cucapah earthquakes. We also identify areas of vertical land motions due to anthropogenic, natural, and magmatic processes. Finally, we demonstrate the utility of the kinematic datum by improving the accuracy of high-spatial-resolution 12-day repeat-cycle Sentinel-1 Interferometric Synthetic Aperture Radar displacement and velocity maps.

Constraining the kinematics of metropolitan Los Angeles faults with a slip-partitioning model

Due to the limited resolution at depth of geodetic and other geophysical data, the geometry and the loading rate of the ramp-décollement faults below the metropolitan Los Angeles are poorly understood. Here we complement these data by assuming conservation of motion across the Big Bend of the San Andreas Fault. Using a Bayesian approach, we constrain the geometry of the ramp-décollement system from the Mojave block to Los Angeles and propose a partitioning of the convergence with 25.5 ± 0.5 mm/yr and 3.1 ± 0.6 mm/yr of strike-slip motion along the San Andreas Fault and the Whittier Fault, with 2.7 ± 0.9 mm/yr and 2.5 ± 1.0 mm/yr of updip movement along the Sierra Madre and the Puente Hills thrusts. Incorporating conservation of motion in geodetic models of strain accumulation reduces the number of free parameters and constitutes a useful methodology to estimate the tectonic loading and seismic potential of buried fault networks.

Physical applications of GPS geodesy: a review

Geodesy, the oldest science, has become an important discipline in the geosciences, in large part by enhancing Global Positioning System (GPS) capabilities over the last 35 years well beyond the satellite constellation's original design. The ability of GPS geodesy to estimate 3D positions with millimeter-level precision with respect to a global terrestrial reference frame has contributed to significant advances in geophysics, seismology, atmospheric science, hydrology, and natural hazard science. Monitoring the changes in the positions or trajectories of GPS instruments on the Earth's land and water surfaces, in the atmosphere, or in space, is important for both theory and applications, from an improved understanding of tectonic and magmatic processes to developing systems for mitigating the impact of natural hazards on society and the environment. Besides accurate positioning, all disturbances in the propagation of the transmitted GPS radio signals from satellite to receiver are mined for information, from troposphere and ionosphere delays for weather, climate, and natural hazard applications, to disturbances in the signals due to multipath reflections from the solid ground, water, and ice for environmental applications. We review the relevant concepts of geodetic theory, data analysis, and physical modeling for a myriad of processes at multiple spatial and temporal scales, and discuss the extensive global infrastructure that has been built to support GPS geodesy consisting of thousands of continuously operating stations. We also discuss the integration of heterogeneous and complementary data sets from geodesy, seismology, and geology, focusing on crustal deformation applications and early warning systems for natural hazards.

Do earthquakes exhibit self-organized criticality?

If earthquakes are phenomena of self-organized criticality (SOC), statistical characteristics of the earthquake time series should be invariant after the sequence of events in an earthquake catalog are randomly rearranged. In this Letter we argue that earthquakes are unlikely phenomena of SOC because our analysis of the Southern California Earthquake Catalog shows that the first-return-time probability PM(T) is apparently changed after the time series is rearranged. This suggests that the SOC theory should not be used to oppose the efforts of earthquake prediction.

Delayed triggering of the 1999 Hector Mine earthquake by viscoelastic stress transfer

Stress changes in the crust due to an earthquake can hasten the failure of neighbouring faults and induce earthquake sequences in some cases. The 1999 Hector Mine earthquake in southern California (magnitude 7.1) occurred only 20 km from, and 7 years after, the 1992 Landers earthquake (magnitude 7.3). This suggests that the Hector Mine earthquake was triggered in some fashion by the earlier event. But uncertainties in the slip distribution and rock friction properties associated with the Landers earthquake have led to widely varying estimates of both the magnitude and sign of the resulting stress change that would be induced at the location of the Hector Mine hypocentre-with estimates varying from -1.4 bar (ref. 6) to +0.5 bar (ref. 7). More importantly, coseismic stress changes alone cannot satisfactorily explain the delay of 7 years between the two events. Here we present the results of a three-dimensional viscoelastic model that simulates stress transfer from the ductile lower crust and upper mantle to the brittle upper crust in the 7 years following the Landers earthquake. Using viscoelastic parameters that can reproduce the observed horizontal surface deformation following the Landers earthquake, our calculations suggest that lower-crustal or upper-mantle flow can lead to postseismic stress increases of up to 1-2 bar at the location of the Hector Mine hypocentre during this time period, contributing to the eventual occurrence of the 1999 Hector Mine earthquake. These results attest to the importance of considering viscoelastic processes in the assessment of seismic hazard.

An elusive blind-thrust fault beneath metropolitan los angeles

Seismic reflection profiles, petroleum wells, and relocated earthquakes reveal the presence of an active blind-thrust fault beneath metropolitan Los Angeles. A segment of this fault likely caused the 1987 Whittier Narrows (magnitude 6.0) earthquake. Mapped sizes of other fault segments suggest that the system is capable of much larger (magnitude 6.5 to 7) and more destructive earthquakes.

Viscoelastic flow in the lower crust after the 1992 landers, california, earthquake

Space geodesy showed that broad-scale postseismic deformation occurred after the 1992 Landers earthquake. Three-dimensional modeling shows that afterslip can only explain one horizontal component of the postseismic deformation, whereas viscoelastic flow can explain the horizontal and near-vertical displacements. The viscosity of a weak, about 10-km-thick layer, in the lower crust beneath the rupture zone that controls the rebound is about 10(18) pascal seconds. The viscoelastic behavior of the lower crust may help to explain the extensional structures observed in the Basin and Range province and it may be used for the analysis of earthquake hazard.

Evidence of shallow fault zone strengthening after the 1992 M7.5 landers, california, earthquake

Repeated seismic surveys of the Landers, California, fault zone that ruptured in the magnitude (M) 7.5 earthquake of 1992 reveal an increase in seismic velocity with time. P, S, and fault zone trapped waves were excited by near-surface explosions in two locations in 1994 and 1996, and were recorded on two linear, three-component seismic arrays deployed across the Johnson Valley fault trace. The travel times of P and S waves for identical shot-receiver pairs decreased by 0.5 to 1.5 percent from 1994 to 1996, with the larger changes at stations located within the fault zone. These observations indicate that the shallow Johnson Valley fault is strengthening after the main shock, most likely because of closure of cracks that were opened by the 1992 earthquake. The increase in velocity is consistent with the prevalence of dry over wet cracks and with a reduction in the apparent crack density near the fault zone by approximately 1.0 percent from 1994 to 1996.