Geodetic Time Series Research Articles

A geodetic matched filter search for slow slip with application to the Mexico subduction zone

AbstractSince the discovery of slow slip events, many methods have been successfully applied to model obvious transient events in geodetic time series, such as the widely used network strain filter. Independent seismological observations of tremors or low‐frequency earthquakes and repeating earthquakes provide evidence of low‐amplitude slow deformation but do not always coincide with clear occurrences of transient signals in geodetic time series. Here we aim to extract the signal corresponding to slow slips hidden in the noise of GPS time series, without using information from independent data sets. We first build a library of synthetic slow slip event templates by assembling a source function with Green's functions for a discretized fault. We then correlate the templates with postprocessed GPS time series. Once the events have been detected in time, we estimate their duration T and magnitude Mw by modeling a weighted stack of GPS time series. An analysis of synthetic time series shows that this method is able to resolve the correct timing, location, T, and Mw of events larger than Mw 6 in the context of the Mexico subduction zone. Applied on a real data set of 29 GPS time series in the Guerrero area from 2005 to 2014, this technique allows us to detect 28 transient events from Mw 6.3 to 7.2 with durations that range from 3 to 39 days. These events have a dominant recurrence time of 40 days and are mainly located at the downdip edges of the Mw>7.5 slow slip events.

A Comparison of Geodetic and Geologic Rates Prior to Large Strike‐Slip Earthquakes: A Diversity of Earthquake‐Cycle Behaviors?

AbstractComparison of preevent geodetic and geologic rates in three large‐magnitude (Mw = 7.6–7.9) strike‐slip earthquakes reveals a wide range of behaviors. Specifically, geodetic rates of 26–28 mm/yr for the North Anatolian fault along the 1999 MW = 7.6 Izmit rupture are ∼40% faster than Holocene geologic rates. In contrast, geodetic rates of ∼6–8 mm/yr along the Denali fault prior to the 2002 MW = 7.9 Denali earthquake are only approximately half as fast as the latest Pleistocene‐Holocene geologic rate of ∼12 mm/yr. In the third example where a sufficiently long pre‐earthquake geodetic time series exists, the geodetic and geologic rates along the 2001 MW = 7.8 Kokoxili rupture on the Kunlun fault are approximately equal at ∼11 mm/yr. These results are not readily explicable with extant earthquake‐cycle modeling, suggesting that they may instead be due to some combination of regional kinematic fault interactions, temporal variations in the strength of lithospheric‐scale shear zones, and/or variations in local relative plate motion rate. Whatever the exact causes of these variable behaviors, these observations indicate that either the ratio of geodetic to geologic rates before an earthquake may not be diagnostic of the time to the next earthquake, as predicted by many rheologically based geodynamic models of earthquake‐cycle behavior, or different behaviors characterize different fault systems in a manner that is not yet understood or predictable.

Hydrostatic-season-time model updating using Bayesian model class selection

The aim of this paper is to present a novel attempt for parametric estimation in the hydrostatic-season-time (HST) model. The empirical HST-model has been widely used for the analysis of different measurement data types on dams. The significance of individual parameters or their sub-groups for modelling the influence of the water level, air and water temperature, and irreversible deformations due to the ageing of the dam, depends on the structure itself. The process of finding an accurate HST-model for a given data set, which remains robust to outliers, cannot only be demanding but also time consuming. The Bayesian model class selection approach imposes a penalisation against overly complex model candidates and admits a selection of the most plausible HST-model according to the maximum value of model evidence provided by the data or relative plausibility within a set of model class candidates. The potential of Bayes interference and its efficiency in an HST-model are presented on geodetic time series as a result of a permanent monitoring system on a rock-fill embankment dam. The method offers high potential for engineers in the decision making process, whilst the HST-model can be promptly adapted to new information given by new measurements and can enhance the safety and reliability of dams.

Aseismic transient during the 2010\u20132014 seismic swarm: evidence for longer recurrence of M\u2009\u2265\u20096.5 earthquakes in the Pollino gap (Southern Italy)?

In actively deforming regions, crustal deformation is accommodated by earthquakes and through a variety of transient aseismic phenomena. Here, we study the 2010–2014 Pollino (Southern Italy) swarm sequence (main shock MW 5.1) located within the Pollino seismic gap, by analysing the surface deformation derived from Global Positioning System and Synthetic Aperture Radar data. Inversions of geodetic time series show that a transient slip, with the same mechanism of the main shock, started about 3–4 months before the main shock and lasted almost one year, evolving through time with acceleration phases that correlate with the rate of seismicity. The moment released by the transient slip is equivalent to MW 5.5, significantly larger than the seismic moment release revealing therefore that a significant fraction of the overall deformation is released aseismically. Our findings suggest that crustal deformation in the Pollino gap is accommodated by infrequent “large” earthquakes (MW ≥ 6.5) and by aseismic episodes releasing a significant fraction of the accrued strain. Lower strain rates, relative to the adjacent Southern Apennines, and a mixed seismic/aseismic strain release are in favour of a longer recurrence for large magnitude earthquakes in the Pollino gap.

An approach for estimating time-variable rates from geodetic time series

There has been considerable research in the literature focused on computing and forecasting sea-level changes in terms of constant trends or rates. The Antarctic ice sheet is one of the main contributors to sea-level change with highly uncertain rates of glacial thinning and accumulation. Geodetic observing systems such as the Gravity Recovery and Climate Experiment (GRACE) and the Global Positioning System (GPS) are routinely used to estimate these trends. In an effort to improve the accuracy and reliability of these trends, this study investigates a technique that allows the estimated rates, along with co-estimated seasonal components, to vary in time. For this, state space models are defined and then solved by a Kalman filter (KF). The reliable estimation of noise parameters is one of the main problems encountered when using a KF approach, which is solved by numerically optimizing likelihood. Since the optimization problem is non-convex, it is challenging to find an optimal solution. To address this issue, we limited the parameter search space using classical least-squares adjustment (LSA). In this context, we also tested the usage of inequality constraints by directly verifying whether they are supported by the data. The suggested technique for time-series analysis is expanded to classify and handle time-correlated observational noise within the state space framework. The performance of the method is demonstrated using GRACE and GPS data at the CAS1 station located in East Antarctica and compared to commonly used LSA. The results suggest that the outlined technique allows for more reliable trend estimates, as well as for more physically valuable interpretations, while validating independent observing systems.

Theoretical geodesy

Abstract The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011-2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-Msplit estimation, which allows to estimate a vector of parameter differences and the Shift-Msplit(+) that is a generalisation of Shift-Msplit estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2nd, 3rd and 4th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

AbstractThe current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at today's millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi‐instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.

Detecting transient signals in geodetic time series using sparse estimation techniques

AbstractWe present a new method for automatically detecting transient deformation signals from geodetic time series. We cast the detection problem as a least squares procedure where the design matrix corresponds to a highly overcomplete, nonorthogonal dictionary of displacement functions in time that resemble transient signals of various timescales. The addition of a sparsity‐inducing regularization term to the cost function limits the total number of dictionary elements needed to reconstruct the signal. Sparsity‐inducing regularization enhances interpretability of the resultant time‐dependent model by localizing the dominant timescales and onset times of the transient signals. Transient detection can then be performed using convex optimization software where detection sensitivity is dependent on the strength of the applied sparsity‐inducing regularization. To assess uncertainties associated with estimation of the dictionary coefficients, we compare solutions with those found through a Bayesian inference approach to sample the full model space for each dictionary element. In addition to providing uncertainty bounds on the coefficients and confirming the optimization results, Bayesian sampling reveals trade‐offs between dictionary elements that have nearly equal probability in modeling a transient signal. Thus, we can rigorously assess the probabilities of the occurrence of transient signals and their characteristic temporal evolution. The detection algorithm is applied on several synthetic time series and real observed GPS time series for the Cascadia region. For the latter data set, we incorporate a spatial weighting scheme that self‐adjusts to the local network density and filters for spatially coherent signals. The weighting allows for the automatic detection of repeating slow slip events.

Chapter 14 Continuous and campaign-style gravimetric investigations on Montserrat 2006 to 2009

Abstract Gravimetric time series can provide vital clues about subsurface dynamics associated with active volcanism. Here, we report on continuous and campaign-style gravimetric observations on Montserrat between 2006 and 2009. More than 240 days of continuous gravimetric records enabled us to derive a first local joint solid Earth tides and ocean loading model for Montserrat, and we report the tidal harmonics for 14 major wave groups. Compared to global predictions, the new model (MTY11) achieves an up to one order of magnitude better precision over diurnal and semi-diurnal frequencies. We anticipate that the model will help reduce the effects of tidal perturbations on other geodetic time series recorded on Montserrat. Abrupt variations in gravity accompanied Vulcanian explosions and probably reflect the response of a shallow aquifer to stress changes during pressurization and depressurization of the subvolcanic plumbing system. Campaign data enabled the quantification of mass variations during a cycle of activity including dome formation and repose. Both forward and inverse modelling of the spatio-temporal time series indicates that the source of the recorded gravity variations is situated beneath central Montserrat. Our favourite interpretation of the campaign data is that the gravity variations reflect volcano-tectonic interaction beneath the Centre Hills of Montserrat that are triggered by changes in the active magmatic system of Soufrière Hills Volcano (SHV). We also discuss our findings on subsurface mass variations in relation to annual precipitation records and active dome formation. Both continuous and discrete gravimetric observations indicate coupling between the dominant magmatic sources responsible for the ongoing eruption at SHV and shallow-seated local sources such as aquifers and fluid-saturated fault-damage zones. Our investigations demonstrate the value of including gravimetric observations over a wide frequency range for volcanic system characterization in a volcanic island arc setting. Supplementary material: Details on the inversion routine of the explorative source model GROWTH 2.0 and the resulting images from its application to time-lapse gravity data are available at http://www.geolsoc.org.uk/SUP18701 .

Singular spectrum analysis for modeling seasonal signals from GPS time series

Seasonal signals in GPS time series are of great importance for understanding the evolution of regional mass fluctuations, i.e., ice, hydrology, and ocean mass. Conventionally these signals (quasi-annual and semi-annual signals) are modeled by least-squares fitting harmonic terms with a constant amplitude and phase. In reality, however, such seasonal signals are modulated, i.e., they will have a time-variable amplitude and phase. Recently, Davis et al. (2012) proposed a Kalman filter based approach to capture the stochastic seasonal behavior of geodetic time series. Singular Spectrum Analysis (SSA) is a non-parametric method, which uses time domain data to extract information from short and noisy time series without a priori knowledge of the dynamics affecting the time series. A prominent benefit is that trends obtained in this way are not necessarily linear. Further, true oscillations can be amplitude and phase modulated. In this work, we will assess the value of SSA for extracting time-variable seasonal signals from GPS time series. We compare our SSA-based results to those obtained using (1) least-squares analysis and (2) Kalman filtering. Our results demonstrate that SSA is a viable and complementary tool for extracting modulated oscillations from GPS time series.

Extracting White Noise Statistics in GPS Coordinate Time Series

The noise in GPS coordinate time series is known to follow a power-law noise model with different components (white noise, flicker noise, and random walk). This work proposes an algorithm to estimate the white noise statistics, through the decomposition of the GPS coordinate time series into a sequence of sub time series using the empirical mode decomposition algorithm. The proposed algorithm estimates the Hurst parameter for each sub time series and then selects the sub time series related to the white noise based on the Hurst parameter criterion. Both simulated GPS coordinate time series and real data are employed to test this new method; the results are compared to those of the standard (CATS software) maximum-likelihood (ML) estimator approach. The results demonstrate that this proposed algorithm has very low computational complexity and can be more than 100 times faster than the CATS ML method, at the cost of a moderate increase of the uncertainty (~5%) of the white noise amplitude. Reliable white noise statistics are useful for a range of applications including improving the filtering of GPS time series, checking the validity of estimated coseismic offsets, and estimating unbiased uncertainties of site velocities. The low complexity and computational efficiency of the algorithm can greatly speed up the processing of geodetic time series.

Assessing the importance and expression of the 6 year geomagnetic oscillation

The first time derivative of residual length‐of‐day observations is known to contain a distinctive 6 year periodic oscillation. Here we theorize that through the flow accelerations at the top of the core the same periodicity should arise in the geomagnetic secular acceleration. We use the secular acceleration of the CHAOS‐3 and CM4 geomagnetic field models to recover frequency spectra through both a traditional Fourier analysis and an empirical mode decomposition. We identify the 6 year periodic signal in the geomagnetic secular acceleration and characterize its spatial behavior. This signal seems to be closely related to recent geomagnetic jerks. We also identify a 2.5 year periodic signal in CHAOS‐3 with unknown origin. This signal is strictly axially dipolar and is absent from other magnetic or geodetic time series.

Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series

The detection of discontinuities in geodetic data is an ever more important topic due to both the influence of discontinuities on the results of models and analyses, and to the very meaning of discontinuities in physical phenomena. We consider and describe a mathematical model, originally formulated for the approximation of images by smooth functions, in one dimension (1D). The model had been designed to smooth the data while preserving and detecting its discontinuities following a variational approach. A second and more complex model for the approximation of images by functions with smooth first derivatives is also available. This second model had been designed to smooth the data while preserving and detecting the discontinuities of the data, but also those of the first derivative. Such interesting features suggest the chance to apply this second model to 1D geodetic data, in particular for the detection of discontinuities and velocity changes in position time-series rather than for signal smoothing. The sigseg (signal segmentation) program implements the two variational models in 1D and is presented with applications to geodetic data. The essential mathematical elements are sketched, and some details on the numerical implementation are given.

On seasonal signals in geodetic time series

We explore implications for modeling and noise analysis of stochastic seasonal processes of climatic origin in geodetic time series. Seasonal signals are generally modeled as sinusoids with annual periods (and harmonics thereof), each with constant amplitude and phase. However, environmental noise that underlies the seasonal signal in geodetic time series has a reddened power spectral density (PSD). We investigate the form of the PSD of a time series having a stochastic seasonal component and find that for frequencies greater than the nominal seasonal frequency, the PSD of the time series reflects the PSD of the seasonal amplitudes. For example, if the PSD of the seasonal amplitudes can be expressed as an inverse power law, then the PSD of the time series will behave as an inverse power law for high frequencies. Stochastic seasonal variability will also induce a peak near the nominal seasonal frequency in addition to that of the mean seasonal signal and will be relatively flat below this frequency. It is therefore possible that some of the noise in Global Navigation Satellite Systems (GNSS) time series reported by others may be associated with neglecting the stochastic component of the seasonal signal. We use a GNSS time series from site ZIMM as an example to demonstrate the existence of a variable seasonal signal (without attributing its cause), and we use an example Gravity Recovery and Climate Experiment (GRACE) time series from Alaska to demonstrate that use of a nonstochastic seasonal model can have a significant impact on the value and uncertainty of time‐variable rates estimated from the time series.

Impact of Earth radiation pressure on GPS position estimates

GPS satellite orbits available from the International GNSS Service (IGS) show a consistent radial bias of up to several cm and a particular pattern in the Satellite Laser Ranging (SLR) residuals, which are suggested to be related to radiation pressure mismodeling. In addition, orbit-related frequencies were identified in geodetic time series such as apparent geocenter motion and station displacements derived from GPS tracking data. A potential solution to these discrepancies is the inclusion of Earth radiation pressure (visible and infrared) modeling in the orbit determination process. This is currently not yet considered by all analysis centers contributing to the IGS final orbits. The acceleration, accounting for Earth radiation and satellite models, is introduced in this paper in the computation of a global GPS network (around 200 IGS sites) adopting the analysis strategies from the Center for Orbit Determination in Europe (CODE). Two solutions covering 9 years (2000–2008) with and without Earth radiation pressure were computed and form the basis for this study. In previous studies, it has been shown that Earth radiation pressure has a non-negligible effect on the GPS orbits, mainly in the radial component. In this paper, the effect on the along-track and cross-track components is studied in more detail. Also in this paper, it is shown that Earth radiation pressure leads to a change in the estimates of GPS ground station positions, which is systematic over large regions of the Earth. This observed “deformation” of the Earth is towards North–South and with large scale patterns that repeat six times per GPS draconitic year (350 days), reaching a magnitude of up to 1 mm. The impact of Earth radiation pressure on the geocenter and length of day estimates was also investigated, but the effect is found to be less significant as compared to the orbits and position estimates.

PCAIM joint inversion of InSAR and ground‐based geodetic time series: Application to monitoring magmatic inflation beneath the Long Valley Caldera

This study demonstrates the interest of using a Principal Component Analysis‐based Inversion Method (PCAIM) to analyze jointly InSAR and ground‐based geodetic time series of crustal deformation. A major advantage of this approach is that the InSAR tropospheric biases are naturally filtered out provided they do not introduce correlated or high amplitude noise in the input times series. This approach yields source models which are well‐constrained both in time and space due to the temporal resolution of the ground‐based geodetic data and the spatial resolution of the InSAR data. The technique is computationally inexpensive allowing for the inversion of large datasets. To demonstrate the performance of this approach, we apply it to the 1997–98 magmatic inflation event in the Long Valley Caldera, California.

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.

Inverting geodetic time series with a principal component analysis‐based inversion method

The Global Positioning System (GPS) system now makes it possible to monitor deformation of the Earth's surface along plate boundaries with unprecedented accuracy. In theory, the spatiotemporal evolution of slip on the plate boundary at depth, associated with either seismic or aseismic slip, can be inferred from these measurements through some inversion procedure based on the theory of dislocations in an elastic half‐space. We describe and test a principal component analysis‐based inversion method (PCAIM), an inversion strategy that relies on principal component analysis of the surface displacement time series. We prove that the fault slip history can be recovered from the inversion of each principal component. Because PCAIM does not require externally imposed temporal filtering, it can deal with any kind of time variation of fault slip. We test the approach by applying the technique to synthetic geodetic time series to show that a complicated slip history combining coseismic, postseismic, and nonstationary interseismic slip can be retrieved from this approach. PCAIM produces slip models comparable to those obtained from standard inversion techniques with less computational complexity. We also compare an afterslip model derived from the PCAIM inversion of postseismic displacements following the 2005 8.6 Nias earthquake with another solution obtained from the extended network inversion filter (ENIF). We introduce several extensions of the algorithm to allow statistically rigorous integration of multiple data sources (e.g., both GPS and interferometric synthetic aperture radar time series) over multiple timescales. PCAIM can be generalized to any linear inversion algorithm.

Investigating tropospheric effects and seasonal position variations in GPS and DORIS time-series from the Nepal Himalaya

SUMMARY Geodetic time-series from continuous GPS (cGPS) and 1 DORIS stations across the Himalaya of central Nepal show strong seasonal fluctuations observed on the horizontal and vertical components. Because the fluctuations determined at the different stations have similar phase but different amplitudes, these observations would imply that the secular shortening across the range is modulated by a seasonal strain. Given the geographic and climatic setting, there is however a possibility that the GPS positions be biased by tropospheric effects. We process these data using two different software packages and two different analysis strategies. Our analysis shows evidence for 1-strong seasonal fluctuation of zenithal delays consistent with in situ meteorological data and two strong horizontal tropospheric gradients in particular in the EW direction, that is, parallel to the mountain front at Gumba, also detected in DORIS results. We show that the tropospheric effects cannot however be the source of the observed seasonality of horizontal strain. This study supports the view that the seasonal strain in the Himalaya is real and probably driven by seasonal surface load variations. Our study adds support to the view that seasonal variations of seismicity in the Himalaya reflects seasonal variations of geodetic strain.

Effect of troposphere slant delays on regional double difference GPS processing

Abstract The demand for geodetic time series that are accurate and stable is increasing. One factor limiting their accuracy is troposphere refraction, which is hard to model and compute with sufficient resolution, both in time and space. We have studied the effect of numerical weather model (NWM)-derived troposphere slant delays and the most commonly used mapping functions, Niell and Vienna, on Global Positioning System (GPS) processing. Six months of data were calculated for a regional Finnish network, FinnRef, which consists of 13 stations, using Bernese v. 5.0 in double difference mode. The results showed that when site-specific troposphere zenith delays or gradients are not estimated, the use of NWM-based troposphere delays improved the repeatabilities of all three components of station positions (north, east and up) statistically significantly and up to 60%. The more realistic troposphere model also reduces the baseline length dependence of the solution. When site-specific troposphere delays and the horizontal gradients were estimated, there was no statistically significant improvement between the different solutions.