This paper presents a system identification (SID) study of the UC San Diego Geisel Library using acceleration data from six low-intensity earthquakes. Five SID methods, input-output and output-only, were used to cross-validate results, enhance noise robustness, increase the reliability and number of identified modes, and assess potential soil-structure interaction (SSI) effects, considering both 3-DOF and 6-DOF rigid-base seismic excitation. The identified modal parameters (natural frequencies, damping ratios, and mode shapes) were compared with those obtained from ambient vibration data in a previous study and with predictions from an uncalibrated detailed linear FE model. Modal decomposition of the seismic response was also performed using the identified linear state-space models.A total of thirteen vibration modes were identified across the five SID methods and six earthquake events. Results indicate slight decreases in natural frequencies and increases in damping ratios with increasing response amplitude, particularly between ambient and seismic responses. No clear evidence of significant SSI effects was found. The influence of rotational seismic base excitation is noticeable but small, with no consistent trends. Potential sources of discrepancies among the various comparative results are discussed in detail.This study provides a rare opportunity to investigate linear SID of a large, complex building under low-intensity seismic excitation and establishes a high-quality experimental-numerical baseline for Bayesian FE model updating and future structural health monitoring of the Geisel Library.

Rapid and accurate estimation of earthquake moment magnitude is crucial for early warning systems, for alerting coastal populations vulnerable to tsunamigenic hazards. Most seismic-based estimation approaches introduce time delays that limit applicability near the source, while geodetic approaches have been limited to empirical scaling relationships. We extend a physics-based approach for seismogeodetic moment magnitude (M wg) estimation initially developed for thrust earthquakes to also include strike-slip and normal fault mechanisms by examining 17 M w 7.0 to 9.1 earthquakes. We find that considering S-wave propagation is critical for accurately estimating the magnitude of strike-slip events. Radiation pattern (RP) corrections offer substantial benefits for normal fault events but are difficult to compute in real-time. However, RP corrections can be neglected for strike-slip events, while thrust and normal earthquakes are more reliably handled using the previously established seismogeodetic approach, allowing accurate M wg estimates within about 2-3 min of earthquake initiation in early warning scenarios. We further broaden the seismogeodetic approach by interpolating coseismic windows from collocated GNSS and/or accelerometer stations to stand-alone GNSS stations, thereby increasing the size and geometry of the available network. We present an integrated workflow for rapid M wg estimation that leverages tectonic information from subduction-zone geometry to inform focal mechanism selection, rather than relying on uncertain hypocentral depths. Our extended approach provides rapid earthquake magnitudes (similar to 2-3 min after earthquake initiation) for moderate to large events (M w >= 7) with an M wg accuracy of 0.2 magnitude units. Our approach is useful for operational environments where timely magnitude estimates are essential.

Through a parametric fit to daily vertical displacement time series from European Permanent GNSS stations, we conducted a statistical sensitivity analysis focusing on Vertical Land Motion (VLM) – specifically, station velocity (linear trend). We compared two independent corrections to raw observed displacements: non-tidal atmospheric, oceanic, and hydrological loading displacements, as well as a correction for common mode errors (CME). Our methodology involved selecting the most realistic stochastic models based on information criteria, analyzing GNSS-observed displacements and identifying discrepancies with loading model predictions. We also employed restricted maximum likelihood estimation (RMLE) to mitigate low-frequency noise biases, enhancing the reliability of velocity uncertainty estimates. Our results demonstrate that 1) an autoregressive, power-law, and white noise model combination is preferred for uncorrected GNSS VLM data, 2) when compared to the corrected cases, this model choice yields lower improvement rates in trend sensitivity than previously reported, and 3) RMLE reveals that for many stations, noise is optimally modeled by a combination of random-walk, flicker-noise, and white noise. We report median trend sensitivity and detection rates of about 0.5 mm/year (with best results for the CME-corrected case), approaching the GGOS goal of a 0.1 mm/year precision, crucial for sea level studies and other applications.

We perform a statistical sensitivity analysis on a parametric fit to vertical daily displacement time series of 244 European Permanent GNSS stations, with a focus on linear vertical land motion (VLM), i.e., station velocity. We compare two independent corrections to the raw (uncorrected) observed displacements. The first correction is physical and accounts for non-tidal atmospheric, non-tidal oceanic and hydrological loading displacements, while the second approach is an empirical correction for the common-mode errors. For the uncorrected case, we show that combining power-law and white noise stochastic models with autoregressive models yields adequate noise approximations. With this as a realistic baseline, we report improvement rates of about 14% to 24% in station velocity sensitivity, after corrections are applied. We analyze the choice of the stochastic models in detail and outline potential discrepancies between the GNSS-observed displacements and those predicted by the loading models. Furthermore, we apply restricted maximum likelihood estimation (RMLE), to remove low-frequency noise biases, which yields more reliable velocity uncertainty estimates. RMLE reveals that for a number of stations noise is best modeled by a combination of random walk, flicker noise, and white noise. The sensitivity analysis yields minimum detectable VLM parameters (linear velocities, seasonal periodic motions, and offsets), which are of interest for geophysical applications of GNSS, such as tectonic or hydrological studies.

We present an interferometric method of analyzing GPS phase observations to determine relative position coordinates of stations in a geodetic network. Relative positions are best determined from between-stations difference observations, in which common-mode errors (propagation-medium, satellite clocks and orbits) are cancelled. A second difference may be taken, between satellites, to cancel station-associated errors. The errors remaining in differenced observations are greater, the greater the distance between the stations. In view of this distance dependence, we consider relative weighting of observations, optimal differencing algorithms, and problems related to the analysis of dual-band observations, integer-bias fixing, and automatic cycle-slip detection. The methods developed are also applicable to orbit improvement.

With the advent of GPS interferometry it is now possible to determine very accurate ellipsoidal height differences. This information can now be used in combination with gravimetric and geoid undulation differences to determine orthometric height differences, or in combination with precise orthometric height differences to determine a very accurate relative geoid. The method was used in the Eifel test network south of Bonn. In this network ellipsoidal height differences were determined by GPS to an accuracy of ±1.6 cm for baselines whose average length was 10 km. To test the method, geoid undulation differences between 14 stations of well known orthometric heights have been determined, using a modified Stokes integration procedure. For these computations a set of potential coefficients to degree 180, and 6’x10’ free air gravity anomalies in a 2° cap were used. The rms discrepancy between the GPS undulation differences and the gravimetric undulation differences was ±3.3 cm for lines whose average length was 13 km. Comparisons at 6 stations whose orthometric heights were determined using trigonometric techniques were considerably poorer (±15 cm) indicating that improvement of the orthometric heights was possible. A small adjustment was carried out to convert the GPS and gravity data to final optimum estimates for the orthometric elevations of the trigonometric stations. The adjusted elevations of these stations had an accuracy of ±1.3 cm. These computations clearly support the accuracy estimates of both GPS and the gravity methods. They also point out the possibility of GPS interferometry to provide, in combination with gravity data, orthometric height information at the accuracy level of 1–2 cm.

Following Y. Bock (1983), Y. Bock/B. Schaffrin (1986), and B. Schaffrin (1985 - 1989) we introduce a robust alternative for deformation analyses where, e.g., crustal deformation is to be derived from geodetic data such as repeated baseline measurements. Since this is a highly ill-conditioned problem we developed methods of type “robust collocation” in order to integrate a vague geophysical model as so-called “weak datum”. Beside the pure prediction of the displacement vector on the basis of some stochastic prior information, we also present less-sensitive test statistics being robust against errors in the geophysical model, but exploiting the full content of geodetic information. The behavior of both, the robust predictors and the less-sensitive tests, will be demonstrated in a forthcoming paper; the extension to the continuous case is also underway.

Seismic moment accumulation rate is a fundamental parameter for assessing seismic hazard. It can be estimated geodetically from either fault-based modeling, or strain rate-based calculations, where fault-based models largely depend on the rheological layering and the number of faults. The strain-rate method depends on an unknown (Kostrov) thickness used to convert strain rate into moment rate. In Part 1 of this study, we use three published fault-based models from southern California to establish the value of the Kostrov thickness such that the total moment from the strain-rate approach, calculated from the fault model-predicted strain rate, matches the fault-based approach. Constrained thickness estimates of 7.3, 9.7, and 11.5 km (6.4-13.0 km, including uncertainties) suggest that the 11 km value used in previous studies may be too large and a lower value may be more accurate. In Part 2 we use calibrated values of Kostrov thickness, along with the latest compilation of GNSS velocity data, to partition moment rate into on-fault and off-fault moment rate, where off-fault varies from 32%-43% of the total moment rate. The largest uncertainty is related to the method used to interpolate sparse GNSS data. Lastly, we compare our estimates of total moment rate (mean: 2.13 +/- 0.42 x 1019 Nm/yr) with the historical seismic catalog. Results suggest that including uncertainties in Kostrov thickness brings fault-based geodetic moment rate closer to the seismic moment release (particularly when aseismic afterslip is accounted for), while the (uncertain) values of off-fault moment rate push geodetic moment rates to be larger than seismic moment rates. One commonly-used method of evaluating the future earthquake potential of a known fault is to estimate the moment rate accumulating along that fault. In other words, one can estimate how much earthquake energy is accumulating over time, caused by the forces that propel plate boundary motion along fault systems. Two ways to do this are: (a) using detailed fault models of plate boundary motion, which are constrained by satellite-based measurements of surface motion or (b) using those satellite-based measurements directly through the estimation of regional strain rate. Here, we investigate the uncertainties present in the latter method by comparing previously published estimates of fault-based moment rate, with their equivalent strain rate-based versions. We estimate uncertainties related to the strain-rate based method, which can lead to an over- or under-estimation of earthquake potential on a given fault system. In addition, we explore the off-fault moment rate accumulation in southern California which can help identify areas of enhanced moment accumulation and thus increased seismic hazard. Previously published fault-based models can constrain a Kostrov thickness range of 6.4-13.0 km, including uncertainties Differences between strain rate moment estimates and fault-based estimates suggest 32%-43% off-fault moment rate in southern California The largest uncertainty in estimating moment rate from strain rate is the degree of smoothing used to estimate strain from geodetic data

This paper focuses on system identification (SID) of the UC San Diego Geisel Library building using ambient vibration (AV) data, assuming that the building’s behavior can be fully described by linear models in terms of material, geometry, damping, etc. Three state-space-based, output-only time domain SID methods are applied and fully automated to identify the library’s modal properties using AV data from both a 15-day and a 486-day monitoring period. The modes identified from the AV data are higher-order coupled torsional-flexural modes. The identified modal properties are influenced by the atmospheric conditions, and the amplitude of the building’s ambient vibration. The time-varying identified modal properties show a cyclical 1-day pattern due to human activity, earth tremors, and short-term changes in atmospheric conditions such as wind speed and temperature. One of the output-only SID methods was used to estimate modal properties from ambient vibration data recorded continuously over a 486-day period, including three low-intensity earthquakes. No permanent changes in the identified modal properties were observed due to the three low-intensity earthquakes that occurred during that period. Renovations of the Geisel Library involving only non-structural components (e.g., non-load-bearing partition walls, changes in space allocations, and inertial/live loads) caused some discontinuities in the identification of the modes of interest in this study. The influence of the data window length on system identification results, in terms of identification success rate and estimation uncertainty, was investigated. The identified state-space models are also used to assess the relative contribution of the ambient base excitation to the building’s total ambient vibrational response. This research offered a unique opportunity to study linear SID of a large and complex real-world structure under ambient excitations, and the effects of changing environmental conditions on the identified modal properties. It provided insight into some of the causes of the observed temporal variation in the identified modal properties. The SID results presented in this study also provide a baseline for future structural health monitoring studies of the Geisel Library building.

Time series produced through processing large Synthetic Aperture Radar (SAR) datasets have begun to revolutionize our understanding of crustal signals at spatial scales smaller than can be observed by GNSS arrays. Here, we present insights from our processing of nine tracks of ascending/descending Sentinel-1 InSAR time series data, processed between November 2014 (2014.8500) and January 2022 (2022.0000), spanning the San Andreas Fault plate boundary in California using published methods [1] [2] . To correct for long-wavelength atmospheric effects and to apply an underlying ITRF 2014 reference frame, we integrate this InSAR time series with continuous GNSS coordinate time series datasets from the NASA MEaSUREs ESESES project [3] . The ascending and descending integrated time series are provided at a 6 – 12-day temporal sampling and a 500 m wavelength filter leading to a pixel resolution of 125 m ( https://topex.ucsd.edu/gmtsar/insargen/ ).

This paper focuses on the linear system identification (SID) of the UC San Diego Geisel Library building using recorded seismic data. This study assumes that the structure is linear viscously damped and has a rigid base. Five state-of-the-art state-space-based time domain system identification methods, including two input-output and three output-only, are used to identify the modal properties of the structure by using the seismic vibration data recorded during a small earthquake. Results show that the first three modes are the global torsional and first flexural/lateral modes, while the remaining identified modes are coupled flexural/lateral-torsional modes. The identified state-space model was also used to predict the total acceleration response of the structure to the considered earthquake. This research provides a unique opportunity to study linear system identification of a large and complex real-world operational structure under seismic excitation.

We estimate a seismogeodetic earthquake moment magnitude using unclipped, broadband velocity and displacement waveforms from collocated Global Navigation Satellite Systems and seismic stations located within 800 km epicentral distance for nine 7.2 < M-w < 9.1 earthquakes. We consider the vertical component of seismogeodetic displacement as an approximate source time function and integrate the associated time series to obtain the seismic moment. By continuing to integrate vertical displacement beyond the initial P-waves, we obtain rapid estimates of M-w that are within 0.2 magnitude units for 8 thrust faulting events and within 0.3 units for the single normal faulting event. Because our estimates of the seismic moment are based on the maximum value of integrated displacement, no regression against other source parameters, or distance, is necessary. Our new method shows promise for integration into earthquake and local tsunami early warning systems, including tsunami earthquakes characterized by relatively slow moment release over a longer rupture time, and earthquakes with complex source time functions.

The 2019 Ridgecrest conjugate Mw6.4 and Mw7.1 events resulted in several meters of strike‐slip and dip‐slip along an intricate rupture, extending from the surface down to 15 km. Now with >2 years of post‐rupture observations, we utilize these results to better understand vertical postseismic deformation from the Ridgecrest sequence and illuminate the emerging significance of vertical earthquake cycle deformation data. We determine the cumulative vertical displacement observed by the continuous GNSS network since Ridgecrest, which requires additional time series analyses to adequately resolve vertical deformation compared to the horizontal. Using a Maxwell‐type viscoelastic relaxation model, with a best fit time‐averaged asthenosphere viscosity of 4e17 Pa·s and a laterally heterogeneous lithosphere, we find that viscoelastic relaxation accounts for a majority of the cumulative vertical deformation at Ridgecrest and strongly controls far‐field observations in all north‐east‐up components. The viscoelastic model alone generally underpredicts deformation from GNSS and the remaining nonviscoelastic displacement is most prominent in the horizontal near‐field (−16 to 19 mm), revealing a deformation pattern matching the coseismic observations. This suggests that multiple deformation mechanisms are contributing to Ridgecrest's postseismic displacement, where afterslip likely dominates the near‐field while viscoelastic relaxation controls the far‐field. Similar deformation at individual GNSS stations has been observed for past earthquakes and additionally reveals long‐term transient viscosity over several years. Moreover, the greater temporal and spatial resolution of the GNSS array for Ridgecrest will help resolve the evolution of deformation for the entire network of observations as regional postseismic deformation persists for the next several years.

SUMMARYInSAR displacement time-series are emerging as a valuable product to study a number of Earth processes. One challenge to current time-series processing methods, however, is that when large earthquakes occur, they can leave sharp coseismic steps in the time-series. These discontinuities can cause current atmospheric correction and noise smoothing algorithms to break down, as these algorithms commonly assume that deformation is steady through time. Here, we aim to remedy this by exploring two methods for correcting earthquake offsets in InSAR time-series: a simple difference offset estimate (SDOE) process and a multiparameter offset estimate (MPOE) parametric time-series inversion technique. We apply these methods to a 2-yr time-series of Sentinel-1 interferograms spanning the 2019 Ridgecrest, CA earthquake sequence. Descending track results indicate that the SDOE method precisely corrects for only 20 per cent of the coseismic offsets at 62 study locations included in our scene and only partially corrects or sometimes overcorrects for the rest of our study sites. On the other hand, the MPOE estimate method successfully corrects the coseismic offset for the majority of sites in our analysis. This MPOE method allows us to produce InSAR time-series and data-derived estimates of deformation during each phase of the earthquake cycle. In order to better isolate and estimate the signal of post-seismic lithospheric deformation in the InSAR time-series, we apply a GNSS-based correction to our interferograms. This correction ties the interferograms to median-filtered weekly GNSS displacements and removes additional atmospheric artefacts. We present InSAR-based estimates of post-seismic deformation for the area around the Ridgecrest rupture, as well as a 2-yr coseismic-corrected, GNSS-corrected InSAR time-series data set. This GNSS-corrected InSAR time-series will enable future modelling of post-seismic processes such as afterslip in the near field of the rupture, poroelastic deformation at intermediate distances and viscoelastic deformation at longer timescales in the far field.

Earth's crustal deformation cycle is traditionally divided into coseismic, postseismic, and interseismic phases upon which transient motions from various sources may be superimposed. Here we present a new seismogeodetic methodology to define and identify the transition from the coseismic to the early postseismic phase. While this early period of postseismic deformation has not been well observed, it plays an important role in better understanding fault processes and crustal rheology because it is where the fastest evolution of fault slip occurs. Current methods often choose to rely on geodetic displacements with several hour to daily resolution to estimate static coseismic offsets. The choice of data span is often arbitrary and introduces some fraction of postseismic motion. Instead, we apply a more physics‐based approach that is applicable to interleaved regional networks of high‐rate Global Navigation Satellite System (GNSS) and seismic sensors. The start time of the coseismic phase is based on P wave arrivals and its end time on the total release of energy derived from seismic velocities integrated from strong‐motion accelerations. In the absence of physical collocations, we interpolate the coseismic time window to the GNSS stations and estimate the static offsets from the high‐rate displacements. We demonstrate our methodology by applying it to 10 earthquakes over a range of magnitudes and fault mechanisms. We observe that the presence of early postseismic motions within the widely used estimates of daily coseismic offsets can lead to an overprediction of coseismic moment and fault slip, up to several meters depending on the magnitude and mechanism of the event.

Measuring crustal strain and seismic moment accumulation, is crucial for understanding the growth and distribution of seismic hazards along major fault systems. Here, we develop a methodology to integrate 4.5 years (2015–2019.5) of Sentinel‐1 Interferometric Synthetic Aperture Radar (InSAR) and continuous Global Navigation Satellite System (GNSS) time series to achieve 6 to 12‐day sampling of surface displacements at ∼500 m spatial resolution over the entire San Andreas fault system. Numerous interesting deformation signals are identified with this product (video link: https://www.youtube.com/watch?v=SxNLQKmHWpY). We decompose the line‐of‐sight InSAR displacements into three dimensions by combining the deformation azimuth from a GNSS‐derived interseismic fault model. We then construct strain rate maps using a smoothing interpolator with constraints from elasticity. The resulting deformation field reveals a wide array of crustal deformation processes including, on‐ and off‐fault secular and transient tectonic deformation, creep rates on all the major faults, and vertical signals associated with hydrological processes. The strain rate maps show significant off‐fault components that were not captured by GNSS‐only models. These results are important in assessing the seismic hazard in the region.

Large earthquakes often lead to transient deformation and enhanced seismic activity, with their fastest evolution occurring at the early, ephemeral post-rupture period. Here, we investigate this elusive phase using geophysical observations from the 2004 moment magnitude 6.0 Parkfield, California, earthquake. We image continuously evolving afterslip, along with aftershocks, on the San Andreas fault over a minutes-to-days postseismic time span. Our results reveal a multistage scenario, including immediate onset of afterslip following tens-of-seconds-long coseismic shaking, short-lived slip reversals within minutes, expanding afterslip within hours, and slip migration between subparallel fault strands within days. The early afterslip and associated stress changes appear synchronized with local aftershock rates, with increasing afterslip often preceding larger aftershocks, suggesting the control of afterslip on fine-scale aftershock behavior. We interpret complex shallow processes as dynamic signatures of a three-dimensional fault-zone structure. These findings highlight important roles of aseismic source processes and structural factors in seismicity evolution, offering potential prospects for improving aftershock forecasts.

AbstractIce shelves play a critical role in modulating dynamic loss of ice from the grounded portion of the Antarctic Ice Sheet and its contribution to sea-level rise. Measurements of ice-shelf motion provide insights into processes modifying buttressing. Here we investigate the effect of seasonal variability of basal melting on ice flow of Ross Ice Shelf. Velocities were measured from November 2015 to December 2016 at 12 GPS stations deployed from the ice front to 430 km upstream. The flow-parallel velocity anomaly at each station, relative to the annual mean, was small during early austral summer (November–January), negative during February–April, and positive during austral winter (May–September). The maximum velocity anomaly reached several metres per year at most stations. We used a 2-D ice-sheet model of the RIS and its grounded tributaries to explore the seasonal response of the ice sheet to time-varying basal melt rates. We find that melt-rate response to changes in summer upper-ocean heating near the ice front will affect the future flow of RIS and its tributary glaciers. However, modelled seasonal flow variations from increased summer basal melting near the ice front are much smaller than observed, suggesting that other as-yet-unidentified seasonal processes are currently dominant.