Surface Displacement Time Series Research Articles

Separation of Water Level Change From Atmospheric Artifacts Through Application of Independent Component Analysis to InSAR Time Series

AbstractIn recent years, synthetic aperture radar (SAR) interferometry (InSAR) has emerged as a valuable tool for measuring water level change (WLC) to study hydrodynamic processes in coastal wetlands. However, the highly dynamic wet atmosphere conditions common in these areas have a significant impact on InSAR observations, producing errors in the derived values. Standard methods for estimating atmospheric noise in InSAR time series lack the spatial or temporal resolution needed to adequately correct for wet tropospheric delays. In this study, we utilize the Independent Component Analysis (ICA) signal decomposition technique to identify the likely WLC signal and eliminate atmospheric noise in a time series derived from rapid repeat measurements made with the L‐band uninhabited aerial vehicle synthetic aperture radar airborne instrument. The method compares in‐situ water level measurements with the independent components (IC) to identify the ICA components corresponding to WLC. The signal‐to‐noise ratio between the WLC after the ICA‐based filtering and in situ water level gauges used for validation reaches 16 dB compared to an average of 2.6 dB before filtering. The excluded IC are used to generate maps showing a time series of likely atmospheric features. The identified features in the maps generally correspond to atmospheric features identifiable in Next Generation Weather Radar (NEXRAD) S‐band ground weather radar reflectivity maps collected during the SAR acquisitions. The method is sufficiently general to be applied to any InSAR‐derived surface displacement time series.

Dynamic deformation monitoring and scenario simulation of the Xiaomojiu landslide in the Jinsha River Basin, China

The Xiaomojiu landslide is a typical high-elevation, long-runout landslide located in the Jinsha River Corridor. In this study, sequential InSAR time-series estimation was used to calculate the line of sight (LOS) surface displacements with descending and ascending Sentinel-1 images, and it turned out that the cumulative LOS surface displacement of the landslide was up to −78.4 mm during the period from October 2017 to April 2021 with the maximum LOS surface displacement rate of −38.5 mm/year. The landslide body could be divided into five zones (A, B1, B2, B3, and C) according to its topographical characteristics together with the LOS surface displacement time series. Combining engineering geological characteristics, LOS cumulative surface displacements with site investigation suggest that the Xiaomojiu landslide is likely to be a precipitation-triggered ancient traction rock landslide at the accelerated deformation stage. A dynamic simulation of the Xiaomojiu landslide with the PFC3D software shows that it could take approximately 65 s for the Xiaomojiu landslide from start-up to acceleration to deceleration to build-up of a barrier lake, followed by a simulation from the barrier lake to outburst floods with the HEC-RAS software indicating that the maximum depth of the outburst floods could be 13.5 m (15%), 24.6 m (25%), 42.1 m (50%), and 50.3 m (75%) along Qinghai-Tibet Plateau Transportation Corridor (QTPTC). It is believed that the results of this study provide a reference for landslide prevention along the QTPTC and the Jinsha River.

A Procedure for the Quantitative Comparison of Rainfall and DInSAR-Based Surface Displacement Time Series in Slow-Moving Landslides: A Case Study in Southern Italy

Earth observation data are useful to analyze the impact of climate-related variables on geomorphological processes. This work aims at evaluating the impact of rainfall on slow-moving landslides, by means of a quantitative procedure for identifying satellite-based displacement clusters, comparing them with rainfall series, and applying statistical tests to evaluate their relationships at the regional scale. The chosen study area is the Basento catchment in the Basilicata region (southern Italy). Rainfall series are gathered from rain gauges and are analyzed to evaluate the presence of temporal trends. Ground displacements are obtained by applying the P-SBAS (Parallel Small BAseline Subset) to three datasets of Sentinel-1 images: T146 ascending orbit, and T51 and T124 descending orbits, for the period 2015–2020. The displacement series of the pixels located in areas mapped as landslides by the Italian Landslide Inventory and sited within rain gauge influence regions (defined as 10 km circular buffers) are studied. Those displacement series are analyzed and compared to the rainfall series to search for correlations, by employing statistical and non-parametric tests. In particular, two landslides are selected and investigated in detail. Significant results were obtained for the T124 descending orbit for both landslides, for a 3-day cumulative rainfall and a 7-day delay of the slope response. Challenges in the whole procedure are highlighted and possible solutions to overcome the raised problems are proposed. Given the replicability of the proposed quantitative procedure it might be applied to any study area.

Nonlinear dynamic pressure beneath waves in water of intermediate depth: Theory and experiment

The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different approximations for modulated potential gravity waves. Regular and irregular wave sequences in intermediate depths are considered. The efficiency of different models for reconstruction the pressure field from the known surface displacement time series (the direct problem) is investigated. A new two-component theory for weakly modulated weakly nonlinear waves is proposed showing the best performance among all applied models. Peculiarities of the vertical mode of the pressure second harmonic are discussed.

Insights on fault reactivation during the 2019 November 11, Mw 4.9 Le Teil earthquake in southeastern France, from a joint 3-D geological model and InSAR time-series analysis

SUMMARY The 2019, Mw 4.9 Le Teil earthquake occurred in southeastern France, causing substantial damage in this slow deforming region. Field observations, remote sensing and seismological studies following the event revealed that coseismic slip concentrates at shallow depth along a ∼5 km long rupture associated with surface breaks and a thrusting mechanism. We further investigate this earthquake by combining geological field mapping, 3-D geology, InSAR time-series analysis and a coseismic slip inversion. From structural, stratigraphic and geological data collected around the epicentre, we first produce a 3-D geological model of the region surrounding the rupture using the GeoModeller software. Our model includes the geometry of the geological layers and the main faults, including the La Rouvière Fault, (LRF) the Oligocene normal fault that ruptured during the earthquake. We generate a time-series of surface displacement from Sentinel-1 SAR data ranging from early 2019 January to late 2020 January using the NSBAS processing chain. The spatio-temporal patterns of surface displacement for this time span show neither a clear pre-seismic signal nor significant post-seismic transient deformation. We extract the coseismic displacement pattern from the InSAR time-series, highlighting along-strike variations of coseismic surface slip. The maximum relative displacement along the line of sight is up to ∼16 cm and is located in the southwestern part of the rupture. We invert for the slip distribution on the fault from the InSAR coseismic surface displacement field. Constraining our fault geometry from the geological model, acceptable fault dip ranges between 55° and 60°. Our model confirms the reactivation of LRF, with reverse slip at very shallow depth and two main slip patches reaching, respectively, 30 and 24 cm of slip, both around 500 m depth. We finally discuss how the 3-D fault geometry and geological structure may have impacted the slip distribution and propagation during the earthquake. This study is a step to reassess the seismic hazard of the many faults similar to the La Rouvière one along the Cévennes fault system, in a densely populated area hosting several sensitive nuclear sites.

Long-lived shallow slow-slip events on the Sunda megathrust

During most of the time between large earthquakes at tectonic plate boundaries, surface displacement time series are generally observed to be linear. This linear trend is interpreted as a result of steady stress accumulation at frictionally locked asperities on the fault interface. However, due to the short geodetic record, it is still unknown whether all interseismic periods show similar rates, and whether frictionally locked asperities remain stationary. Here we show that two consecutive interseismic periods at Simeulue Island, Indonesia experienced significantly different displacement rates, which cannot be explained by a sudden reorganization of locked and unlocked regions. Rather, these observations necessitate the occurrence of a 32-year slow-slip event on a shallow, frictionally stable area of the megathrust. We develop a self-consistent numerical model of such events driven by pore-fluid migration during the earthquake cycle. The resulting slow-slip events appear as abrupt velocity changes in geodetic time series. Due to their long-lived nature, we may be missing or mis-modelling these transient phenomena in a number of settings globally; we highlight one such ongoing example at Enggano Island, Indonesia. We provide a method for detecting these slow-slip events that will enable a substantial revision to the earthquake and tsunami hazard and risk for populations living close to these faults. A 32-year-long slow-slip event occurred on a shallow part of the Sunda megathrust, perhaps because of stress accumulation after fluid expulsion, according to an analysis of the deformation history of the area and physics-based simulations.

Impact of Forest Disturbance on InSAR Surface Displacement Time Series

As interferometric synthetic aperture radar (InSAR) data improve in their global coverage and temporal sampling, studies of ground deformation using InSAR are becoming feasible even in heavily vegetated regions such as the American Pacific Northwest (PNW) and Sumatra. However, ongoing forest disturbance due to logging, wildfires, or disease can introduce time-variable signals which could be misinterpreted as ground displacements. This study constrains the error introduced into InSAR time series in the presence of time-variable forest disturbance using synthetic data. For satellite platforms with randomly distributed orbital positions in time (e.g., Sentinel-1), mid-time series forest disturbance results in random error on the order of 0.2 and 10 cm/year for 1-year secular and time-variable velocities, respectively. If the orbital positions are not randomly distributed in time (e.g., ALOS-1), a biased error on the order of 10 cm/year is introduced to the inferred secular velocity. A time series using real ALOS-1 data near Eugene, OR, USA, shows agreement with the bias estimated by synthetic models. Mitigation of time-variable land cover change effects can be achieved if their timing is known, either through independent observations of surface properties (e.g., Landsat/Sentinel-2) or through the use of more computationally expensive, nonlinear inversions with additional terms for the timing of height changes. Inclusion of these additional terms reduces the potential for misinterpretation of InSAR signals associated with land surface change as ground deformation.

The Multiple Aperture SAR Interferometry (MAI) Technique for the Detection of Large Ground Displacement Dynamics: An Overview

This work presents an overview of the multiple aperture synthetic aperture radar interferometric (MAI) technique, which is primarily used to measure the along-track components of the Earth’s surface deformation, by investigating its capabilities and potential applications. Such a method is widely used to monitor the time evolution of ground surface changes in areas with large deformations (e.g., due to glaciers movements or seismic episodes), permitting one to discriminate the three-dimensional (up–down, east–west, north–south) components of the Earth’s surface displacements. The MAI technique relies on the spectral diversity (SD) method, which consists of splitting the azimuth (range) Synthetic Aperture RADAR (SAR) signal spectrum into separate sub-bands to get an estimate of the surface displacement along the azimuth (sensor line-of-sight (LOS)) direction. Moreover, the SD techniques are also used to correct the atmospheric phase screen (APS) artefacts (e.g., the ionospheric and water vapor phase distortion effects) that corrupt surface displacement time-series obtained by currently available multi-temporal InSAR (MT-InSAR) tools. More recently, the SD methods have also been exploited for the fine co-registration of SAR data acquired with the Terrain Observation with Progressive Scans (TOPS) mode. This work is primarily devoted to illustrating the underlying rationale and effectiveness of the MAI and SD techniques as well as their applications. In addition, we present an innovative method to combine complementary information of the ground deformation collected from multi-orbit/multi-track satellite observations. In particular, the presented technique complements the recently developed Minimum Acceleration combination (MinA) method with MAI-driven azimuthal ground deformation measurements to obtain the time-series of the 3-D components of the deformation in areas affected by large deformation episodes. Experimental results encompass several case studies. The validity and relevance of the presented approaches are clearly demonstrated in the context of geospatial analyses.

Classification of slope processes based on multitemporal DInSAR analyses in the Himalaya of NW Bhutan

Slope deformation in mountainous terrain can be driven by different processes, the nature of which is either gravitational and irreversible or seasonal and reversible, the latter induced by permafrost variations or by hydromechanical or thermomechanical effects. The importance of identifying such deformations is not only related to the hazard they can pose, but also to the understanding of changes that permafrost or local hydrological conditions undergo. Here, we carry out a multi-temporal InSAR analysis over a mountainous area 8000 km2 large, straddling north-western Bhutan and southern Tibet. We propose a methodology to separate locally deforming areas from the effects of long-wavelength signals through the analysis of the spatio-temporal behaviour of 4-years long time series of surface displacements. We present the mapping of hundreds of small-scale features that appear to be actively deforming, as well as several examples of reversible deformation rarely detected at this scale in such a challenging and vast region. The analysis of the multi-annual trend of ground deformation shows a relatively small number of irreversible gravitational movements clearly related to rock slides which attests a low level of recent activity of large rock slope instabilities in the region. In the southernmost, lower elevation parts of the study area, we quantify reversible surface displacements with amplitudes ranging between 5 and 17 mm, and showing maximum displacements towards the satellite in summer months, thus compatible with hydro-mechanical effects related to groundwater table variations. In addition, the ground movement induced by the active layer's response to thawing and freezing over the gentler slopes and high-elevation permafrost regions of Bhutan and southern Tibet is on average around 10 mm, with maxima up to 28 mm. The localised displacements appear to be largely associated to braided stream plains, glacier outwash plains or low angle, fine sediment covered slopes.

Tropospheric corrections for InSAR: Statistical assessments and applications to the Central United States and Mexico

The rapid expansion of SAR data availability and advancements in InSAR processing methods has enabled the formation of ground displacement time series for many parts of the world where such research was previously hindered by decorrelation due to sparse temporal sampling and SAR operating frequency. In particular, free and open data access from the European Sentinel-1 constellation and the future NASA-ISRO SAR (NISAR) mission is encouraging the global community to move towards automated, cloud-based processing that can accommodate these rapidly growing data volumes and facilitate the use of a suite of corrections to the data. A key challenge is related to path delays introduced when the radar signal propagates through the troposphere. Tropospheric corrections estimated from empirical, phase-based methods and those using independent data from weather models, GPS, and radiometers have been included in open-source packages such as TRAIN, PyAPS and GACOS. Users within the InSAR community have reported varying degrees of success using these methods in a range of areas around the world. However, the various statistical metrics used to evaluate the reliability of tropospheric corrections are not consistently applied and often depend on the area and the spatial scale over which they are evaluated. Examination of a simple metric such as the overall reduction in phase variability within an interferogram does not allow the user to determine whether the improvement was at large or short length scales. We present a review of existing tropospheric correction methods and statistical performance metrics, providing guidelines for global assessment and verification of the efficacy of tropospheric correction methods. We summarize the assumptions and limitations for each correction method as well as each statistical performance metric. We examine two regions with different atmospheric characteristics - one Sentinel-1 swath covering the central United States and one swath covering south central Mexico, including part of the Pacific coast. As the SAR community moves towards reliance on global and automated InSAR processing platforms that incorporate tropospheric corrections, approaches such as those examined here can aid researchers in their efforts to evaluate such corrections and include their uncertainties in derived products such as surface displacement time series, coseismic offsets, processes that correlate with topography, and signals with smaller magnitude or larger spatial scales such as those associated with small earthquakes, aseismic creep and slow slip events. We found that the GACOS products (leveraging the operational high resolution ECMWF weather model) outperform the other correction methods explored here on average, but this result is highly dependent on location, acquisition time, and data availability. We found spatial structure functions to be most useful for performance assessment because of their ability to convey information about performance at discrete spatial scales.

Theory and Statistical Description of the Enhanced Multi-Temporal InSAR (E-MTInSAR) Noise-Filtering Algorithm

In this work, the statistical fundaments of the recently proposed enhanced, multi-temporal interferometric synthetic aperture radar (InSAR) noise-filtering (E-MTInSAR) technique is addressed. The adopted noise-filtering algorithm is incorporated into the improved extended Minimum Cost Flow (EMCF) Small Baseline Subset (SBAS) differential interferometric SAR (InSAR) processing chain, which has extensively been used for the generation of Earth’s surface displacement time-series in several different contexts. Originally, the input of the InSAR EMCF-SBAS processing toolbox consisted of a sequence of multi-looked, small baseline interferograms, which were unwrapped using the space-time EMCF phase unwrapping algorithm. Subsequently, the unwrapped interferograms were inverted through the SBAS algorithm to retrieve the expected InSAR deformation products. The improved processing chain has complemented the original codes with two additional steps. In particular, a new multi-temporal noise-filtering algorithm for sequences of time-redundant multi-looked DInSAR interferograms, followed by a proper interferogram selection step, has been proposed. This research study is aimed at primarily assessing the performance of the E-MTInSAR noise-filtering algorithm from a theoretical perspective. To this aim, the principles of directional statistics and errors propagation are exploited. Experimental results, carried out by applying the E-MTInSAR algorithm to a sequence of SAR data collected over the Los Angeles bay area, have been used to corroborate the academic outcome of this research.

Hazard Implications of the 2016 Mw 5.0 Cushing, OK Earthquake from a Joint Analysis of Damage and InSAR Data

The Cushing Hub in Oklahoma, one of the largest oil storage facilities in the world, is federally designated as critical national infrastructure. In 2014, the formerly aseismic city of Cushing experienced a Mw 4.0 and 4.3 induced earthquake sequence due to wastewater injection. Since then, an M4+ earthquake sequence has occurred annually (October 2014, September 2015, November 2016). Thus far, damage to critical infrastructure has been minimal; however, a larger earthquake could pose significant risk to the Cushing Hub. In addition to inducing earthquakes, wastewater injection also threatens the Cushing Hub through gradual surface uplift. To characterize the impact of wastewater injection on critical infrastructure, we use Differential Interferometric Synthetic Aperture Radar (DInSAR), a satellite radar technique, to observe ground surface displacement in Cushing before and during the induced Mw 5.0 event. Here, we process interferograms of Single Look Complex (SLC) radar data from the European Space Agency (ESA) Sentinel-1A satellite. The preearthquake interferograms are used to create a time series of cumulative surface displacement, while the coseismic interferograms are used to invert for earthquake source characteristics. The time series of surface displacement reveals 4–5.5 cm of uplift across Cushing over 17 months. The coseismic interferogram inversion suggests that the 2016 Mw 5.0 earthquake is shallower than estimated from seismic inversions alone. This shallower source depth should be taken into account in future hazard assessments for regional infrastructure. In addition, monitoring of surface deformation near wastewater injection wells can be used to characterize the subsurface dynamics and implement measures to mitigate damage to critical installations.

Influence of environmental parameters on the seismic velocity changes in a clayey mudflow (Pont-Bourquin Landslide, Switzerland)

An earthflow/mudflow of a few thousand cubic metres occurred at the toe of the Pont-Bourquin Landslide (PBL, Swiss Alps) in late August 2010. This event was preceded by a drop of about 6% in surface wave velocity (dV/V) determined from ambient vibration records. A seismic monitoring system made of three pairs of sensors was re-installed across the transportation and accumulation zones of the landslide in October 2011, allowing daily relative changes in seismic velocity to be measured for a period of 4.5 years. No similar drop in dV/V was observed during this period, consistently with the lack of significant landslide acceleration or earthflow/mudflow events. However, the three dV/V time series showed periodic and reversible variations in a range − 2% to 2%, suggesting a probable influence of seasonal parameters. They were cross-correlated to daily environmental (temperature and rainfall) and surface displacement time series. In the long term (yearly scale), dV/V variations are mainly driven by the temperature with short delays (30 to 50 days) indicating that the shallow layer (first 2 m) controls the dV/V variations. In the short term, the landslide response to precipitations exhibits a small decrease in dV/V with a delay of 2 to 5 days, in contrast with the displacement rate that almost instantaneously responds to the rainfall. The continuous seismic monitoring of PBL using ambient vibrations has proved to be a robust method for getting information at depth, with no data gap even during winters. The seasonal reversible seismic velocity variations turned out to be in a range lower than the drop observed before the August 2010 earthflow/mudflow, highlighting the interest of incorporating the dV/V technique in monitoring systems.

Relocation of River Storage From Global Hydrological Models to Georeferenced River Channels for Improved Load‐Induced Surface Displacements

AbstractVariations in terrestrial surface water storage cause elastic crustal displacements of several millimeters in the vertical direction on daily to seasonal time scales. Locally, strong signals with exceptionally high amplitudes can be observed along the major river channels. As the horizontal resolution of global hydrological models is typically limited to 0.5° × 0.5°, the generalized model drainage network leads to simulated river mass distributions that are not necessarily collocated with the real courses of the rivers. Moreover, the spreading of locally concentrated surface water on the coarse model grids leads to substantially underestimated amplitudes of simulated hydrologically induced surface displacements. We therefore develop a relocation procedure to improve such hydrological loading estimates, especially at locations near the river banks. We separate the water masses stored in the modeled river network from the total water storage and relocate them on a georeferenced river map with higher resolution. Applying the relocated river masses, simulated hydrological loading amplitudes increase by 0.2–5 mm for the vertical load‐induced surface displacement along the major rivers, at the Amazon even up to additional 15 mm. The amplitudes for the horizontal load‐induced surface displacements are slightly increased, up to maximum 3 mm. Besides changes in the distance to the mass loads, the horizontal displacement fields is also heavily affected by significant changes in the directions to the relocated river mass load. The comparison of modeled hydrologically induced surface displacement time series with Global Positioning System observations shows a significantly improved fit for stations in close proximity to larger rivers when applying the relocation procedure.

Variations in the long-term uplift rate due to the Altiplano–Puna magma body observed with Sentinel-1 interferometry

We present new Interferometric Synthetic Aperture Radar (InSAR) observations of surface deformation in the Altiplano–Puna region (South America) where previous studies documented a broad uplift at an average rate of ∼10 mm/yr. We use data from the Sentinel-1 satellite mission to produce high-resolution velocity maps and time series of surface displacements between years 2014–2017. The data reveal that the uplift has slowed down substantially compared to the 1992–2010 epoch and is characterized by short-term fluctuations on time scales of months to years. The observed variations in uplift rate may indicate a non-steady supply of melt and/or volatiles from the partially molten Altiplano–Puna Magma Body (APMB) into an incipient diapir forming in the roof of the APMB.

A Cloud Computing Solution for the Efficient Implementation of the P-SBAS DInSAR Approach

We present an efficient Cloud Computing (CC) implementation of the Parallel Small BAseline Subset (P-SBAS) algorithm, which is an advanced Differential Interferometric Synthetic Aperture Radar (DInSAR) technique for the generation of Earth surface displacement time series through distributed computing infrastructures. The rationale of our approach consists in properly distributing the large data volumes and the processing tasks involved in the P-SBAS chain among the available (virtual and/or physical) computing nodes of the CC infrastructure, so that each one of these elements can concurrently work on data that are physically stored on its own local volume. To do this, both an ad hoc management of the data flow and an appropriate scheduling of the parallel jobs have been also implemented to properly handle the high complexity of the P-SBAS workflow. The proposed solution allows minimizing the overall data transfer and network load, thus improving the P-SBAS efficiency and scalability within the exploited CC environments. The presented P-SBAS implementation has been extensively validated through two experimental analyses, which have been carried out by exploiting the Amazon Web Services (AWS) Elastic Cloud Compute (EC2) resources. The former analysis involves the processing of a large (128 SAR images) COSMO-SkyMed dataset, which has been performed by exploiting up to 64 computing nodes, and is aimed at demonstrating the P-SBAS scalable performances. The latter allows us to show the P-SBAS capability to generate DInSAR results at a regional scale (150 000 km2 in Southern California) in a very short time (about 9 h), by simultaneously processing 18 ENVISAT frames that correspond to a total of 741 SAR images, exploiting in parallel 144 AWS computing nodes. The presented results confirm the effectiveness of the proposed P-SBAS CC solution, which may contribute to further extend the frontiers of the DInSAR investigation at a very large scale.

A Minimum Acceleration Approach for the Retrieval of Multiplatform InSAR Deformation Time Series

We present in this paper a technique for the generation of 3-D (2-D) displacement time series of the earth's surface, based on the combination of multiplatform SAR data. The algorithm assumes the availability of two (or more) archives of SAR images acquired from complementary (i.e., ascending/descending) tracks over the same area on the ground. SAR data are preprocessed through one of the currently available multitemporal differential interferometry synthetic aperture radar (DInSAR) toolboxes in order to recover, in correspondence to a set of very coherent points, the line-of-sight (LOS) displacement time series. The latter are then geocoded to a common grid and jointly inverted (pixel-by-pixel) to estimate the (unknown) time series of the 3-D (East-West, North-South, Up-Down) displacement components. To this aim, an underdetermined system of linear equations has to be solved. Previous works have proposed to solve similar ill-posed problems by applying the (truncated) singular-value-decomposition method and/or by regularizing the germane system of linear equations by adding further constraints, which impose conditions on the minimum-norm velocity of the solution. On the contrary, in this study, we adopt a different strategy, which is based on imposing that the 3-D deformation time series have minimum acceleration. The developed combination technique is a postprocessing tool that can be easily implemented. Indeed, it does not require the simultaneous processing of very large sequences of DInSAR interferograms. As a matter of fact, the retrieval of preliminary LOS-projected DInSAR time series can be independently carried out by using one (or more) of the currently available multitemporal DInSAR toolboxes, with no restrictions at all on the class to which they belong (small-baseline- and/or permanent-scatterers-oriented). Experiments carried out on simulated and real data prove the validity of the proposed combination algorithm in retrieving 2-D (East-West, Up-Down) surface displacement time series with subcentimeter accuracy, and the North-South components with an accuracy of some centimeters.

Using short‐term postseismic displacements to infer the ambient deformation conditions of the upper mantle

To interpret short‐term postseismic surface displacements in the context of key ambient conditions (e.g., temperature, pressure, background strain rate, water content, creep mechanism), we combined steady state and transient flow into a single constitutive relation that can explain the response of a viscoelastic material to a change in stress. The flow law is then used to investigate mantle deformation beneath the Eastern California Shear Zone following the 1999 M7.1 Hector Mine earthquake. The flow law parameters are determined using finite element models of relaxation processes, constrained by surface displacement time series recorded by 55 continuous GPS stations for 7 years following the earthquake. Results suggest that postseismic flow following the Hector Mine earthquake occurs below a depth of ∼50 km and is controlled by dislocation creep of wet olivine. Diffusion creep models can also explain the data, but require a grain size (3.5 mm) that is smaller than the inferred grain size (10–20 mm) based on the mantle conditions at these depths. In addition, laboratory flow laws predict dislocation creep would dominate at the stress/grain size conditions that provide the best fit to diffusion creep models. Model results suggest a transient creep phase that lasts ∼1 year and has a viscosity ∼10 times lower than subsequent steady state flow, in general agreement with laboratory observations. The postseismic response is best explained as occurring within a relatively hot upper mantle (e.g., 1200–1300°C at 50 km depth) with a long‐term background mantle strain rate of 0.1–0.2μstrain/yr, consistent with the observed surface strain rate. Long‐term background shear stresses at the top of the mantle are ∼4 MPa, then decrease with depth to a minimum of 0.1–0.2 MPa at 70 km depth before increasing slowly with depth due to the pressure dependence of viscosity. These conditions correspond to a background viscosity of 1021 Pa s within a thin mantle lid that decreases to ∼5 × 1019 Pa s within the underlying asthenosphere. This study shows the utility of using short‐term postseismic observations to infer long‐term mantle conditions that are not readily observable by other means.

Analysis of capillary-gravity waves using the discrete periodic inverse scattering transform

Abstract An online measurement technique based on capacitance measurements has been used to study surface water waves induced by harmonic forcing propagating in a laboratory flow cell with dimensions of the order of a few centimeters. It has been postulated theoretically that such nonlinear dispersive waves propagating on an interface of length just a few multiples of the fluid depth satisfy an evolution equation with steeper nonlinearity than the conventional Korteweg–de Vries (KdV) equation for shallow water theory. In this paper a nonlinear Fourier analysis is performed on time-series of surface displacement made at two locations downstream of an oscillating membrane. Results from a discrete periodic inverse scattering transform based on the KdV equation, which decomposes a signal into soliton, cnoidal and sinusoidal components, indicate that whilst the amplitudes of linear modes are conserved as the disturbance propagates between the two sensors, the amplitudes of the nonlinear modes increase. This suggests that the nonlinearity of such surface waves is indeed stronger than that predicted by the KdV equation.

Spatiotemporal evolution of surface creep in the Parkfield region of the San Andreas Fault (1993–2004) from synthetic aperture radar

The Parkfield section of the San Andreas Fault (SAF) is defined as a transitional portion of the fault between slip-release behavior types in the creeping section of the SAF to the northwest and the apparently locked section to the southeast. The Parkfield section is characterized by complex frictional fault behavior because it represents a transition zone from aseismic creep to stick-slip regime. At least six historic earthquakes of M w ~ 6 have occurred in this area in 1881, 1901, 1922, 1934, 1966, and 2004. It was observed in the 2004 M w 6.0 Parkfield earthquake that ~ 70% of the total (coseismic and postseismic) moment release occurred aseismically. To understand the SAF behavior in this area, it is of particular interest to measure and analyze, not only the spatial evolution of the surface displacement in this area, but also its evolution over time. Using radar data acquired by the European Space Agency's European Remote Sensing (ERS1-2) satellites, we constructed descending interferograms and retrieved time series of surface displacements along the central SAF for the decade preceding the 2004 Parkfield earthquake. We focus on characterizing the space and time evolution of surface creep in the Parkfield and Cholame sections. The spatial pattern of the interseismic displacement rate indicates that tectonic strain was not uniformly distributed along the strike of the fault between 1993 and 2004. Our data indicate not only a decrease in the creep rate from the Parkfield section to south of Highway-46 from 1.4 ± 0.3 cm/yr to 0.6 ± 0.3 cm/yr, but also a small but significant creep-rate increase in the Cholame section to 0.2 ± 0.1 cm/yr. The evidence for episodic creep in the Cholame section of the SAF south-east of Parkfield is in contrast with previously published interpretations of GPS and trilateration data. The Cholame section of the SAF merits close monitoring because it was likely the nucleation site of the 1857 Fort Tejón earthquake and because it has shown recent evidence of deep slow slip as revealed by deep tremors.