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Results of the first North American comparison of absolute gravimeters, NACAG-2010

The first North American Comparison of absolute gravimeters (NACAG-2010) was hosted by the National Oceanic and Atmospheric Administration at its newly renovated Table Mountain Geophysical Observatory (TMGO) north of Boulder, Colorado, in October 2010. NACAG-2010 and the renovation of TMGO are part of NGS’s GRAV-D project (Gravity for the Redefinition of the American Vertical Datum). Nine absolute gravimeters from three countries participated in the comparison. Before the comparison, the gravimeter operators agreed to a protocol describing the strategy to measure, calculate, and present the results. Nine sites were used to measure the free-fall acceleration of g. Each gravimeter measured the value of g at a subset of three of the sites, for a total set of 27 g-values for the comparison. The absolute gravimeters agree with one another with a standard deviation of 1.6 µGal (1 Gal = 1 cm s-2). The minimum and maximum offsets are -2.8 and 2.7 µGal. This is an excellent agreement and can be attributed to multiple factors, including gravimeters that were in good working order, good operators, a quiet observatory, and a short duration time for the experiment. These results can be used to standardize gravity surveys internationally.

Journal of Geodesy

Estimating rate uncertainty with maximum likelihood: differences between power-law and flicker–random-walk models

Recent studies have documented that global positioning system (GPS) time series of position estimates have temporal correlations which have been modeled as a combination of power-law and white noise processes. When estimating quantities such as a constant rate from GPS time series data, the estimated uncertainties on these quantities are more realistic when using a noise model that includes temporal correlations than simply assuming temporally uncorrelated noise. However, the choice of the specific representation of correlated noise can affect the estimate of uncertainty. For many GPS time series, the background noise can be represented by either: (1) a sum of flicker and random-walk noise or, (2) as a power-law noise model that represents an average of the flicker and random-walk noise. For instance, if the underlying noise model is a combination of flicker and random-walk noise, then incorrectly choosing the power-law model could underestimate the rate uncertainty by a factor of two. Distinguishing between the two alternate noise models is difficult since the flicker component can dominate the assessment of the noise properties because it is spread over a significant portion of the measurable frequency band. But, although not necessarily detectable, the random-walk component can be a major constituent of the estimated rate uncertainty. None the less, it is possible to determine the upper bound on the random-walk noise.

Journal of Geodesy

Measurement of slow-moving along-track displacement from an efficient multiple-aperture SAR interferometry (MAI) stacking

Multiple-aperture SAR interferometry (MAI) has demonstrated outstanding measurement accuracy of along-track displacement when compared to pixel-offset-tracking methods; however, measuring slow-moving (cm/year) surface displacement remains a challenge. Stacking of multi-temporal observations is a potential approach to reducing noise and increasing measurement accuracy, but it is difficult to achieve a significant improvement by applying traditional stacking methods to multi-temporal MAI interferograms. This paper proposes an efficient MAI stacking method, where multi-temporal forward- and backward-looking residual interferograms are individually stacked before the MAI interferogram is generated. We tested the performance of this method using ENVISAT data from Kīlauea Volcano, Hawai‘i, where displacement on the order of several centimeters per year is common. By comparing results from the proposed stacking methods with displacements from GPS data, we documented measurement accuracies of about 1.03 and 1.07 cm/year for the descending and ascending tracks, respectively—an improvement of about a factor of two when compared with that from the conventional stacking approach. Three-dimensional surface-displacement maps can be constructed by combining stacked InSAR and MAI observations, which will contribute to a better understanding of a variety of geological phenomena.

Hawaii

Improved efficiency of maximum likelihood analysis of time series with temporally correlated errors

Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, 1 / f α "> 1 / f α 1/fα with frequency, f . With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013 . doi: 10.1007/s00190-012-0605-0 ) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.

Journal of Geodesy

Special issue: The changing shapes of active volcanoes: Recent results and advances in volcano geodesy

The 18 papers herein report on new geodetic data that offer valuable insights into eruptive activity and magma transport; they present new models and modeling strategies that have the potential to greatly increase understanding of magmatic, hydrothermal, and volcano-tectonic processes; and they describe innovative techniques for collecting geodetic measurements from remote, poorly accessible, or hazardous volcanoes. To provide a proper context for these studies, we offer a short review of the evolution of volcano geodesy, as well as a case study that highlights recent advances in the field by comparing the geodetic response to recent eruptive episodes at Mount St. Helens. Finally, we point out a few areas that continue to challenge the volcano geodesy community, some of which are addressed by the papers that follow and which undoubtedly will be the focus of future research for years to come.

Journal of Volcanology and Geothermal Research

Volcano Geodesy: Recent developments and future challenges

Ascent of magma through Earth's crust is normally associated with, among other effects, ground deformation and gravity changes. Geodesy is thus a valuable tool for monitoring and hazards assessment during volcanic unrest, and it provides valuable data for exploring the geometry and volume of magma plumbing systems. Recent decades have seen an explosion in the quality and quantity of volcano geodetic data. New datasets (some made possible by regional and global scientific initiatives), as well as new analysis methods and modeling practices, have resulted in important changes to our understanding of the geodetic characteristics of active volcanism and magmatic processes, from the scale of individual eruptive vents to global compilations of volcano deformation. Here, we describe some of the recent developments in volcano geodesy, both in terms of data and interpretive tools, and discuss the role of international initiatives in meeting future challenges for the field.

Journal of Volcanology and Geothermal Research

The changing shapes of active volcanoes: History, evolution, and future challenges for volcano geodesy

At the very heart of volcanology lies the search for the 'plumbing systems' that form the inner workings of Earth’s active volcanoes. By their very nature, however, the magmatic reservoirs and conduits that underlie these active volcanic systems are elusive; mostly they are observable only through circumstantial evidence, using indirect, and often ambiguous, surficial measurements. Of course, we can infer much about these systems from geologic investigation of materials brought to the surface by eruptions and of the exposed roots of ancient volcanoes. But how can we study the magmatic processes that are occurring beneath Earth’s active volcanoes? What are the geometry, scale, physical, and chemical characteristics of magma reservoirs? Can we infer the dynamics of magma transport? Can we use this information to better forecast the future behavior of volcanoes? These questions comprise some of the most fundamental, recurring themes of modern research in volcanology. The field of volcano geodesy is uniquely situated to provide critical observational constraints on these problems. For the past decade, armed with a new array of technological innovations, equipped with powerful computers, and prepared with new analytical tools, volcano geodesists have been poised to make significant advances in our fundamental understanding of the behavior of active volcanic systems. The purpose of this volume is to highlight some of these recent advances, particularly in the collection and interpretation of geodetic data from actively deforming volcanoes. The 18 papers that follow report on new geodetic data that offer valuable insights into eruptive activity and magma transport; they present new models and modeling strategies that have the potential to greatly increase understanding of magmatic, hydrothermal, and volcano-tectonic processes; and they describe innovative techniques for collecting geodetic measurements from remote, poorly accessible, or hazardous volcanoes. To provide a proper context for these studies, we offer a short review of the evolution of volcano geodesy, as well as a case study that highlights recent advances in the field by comparing the geodetic response to recent eruptive episodes at Mount St. Helens. Finally, we point out a few areas that continue to challenge the volcano geodesy community, some of which are addressed by the papers that follow and which undoubtedly will be the focus of future research for years to come.

Journal of Volcanology and Geothermal Research

The value of geophysical methods in ground‐water studies

Two meanings are unfortunately given to the term geophysics. In the broad sense, based on the etymology of the term, geophysics means the physics of the Earth. This is its significance in the names “Geophysical Laboratory of the Carnegie Institution of Washington,” “International Union of Geodesy and Geophysics,” and “American Geophysical Union.” In this sense the sciences of geology and hydrology are largely geophysics, although in part they are geochemistry or biology. Geologists and hydraulic engineers who are elected to membership in the American Geophysical Union are, however, often surprised to find that they are regarded as “geophysicists.” I hope that when the Union establisnes a journal, its name will include the expression “Earth physics” or “Physics of the Earth,” in order that there will be no misunderstanding as to its scope.

Eos, Transactions, American Geophysical Union

Volcanic tremor masks its seismogenic source: Results from a study of noneruptive tremor recorded at Mount St. Helens, Washington

On 2 October 2004, a significant noneruptive tremor episode occurred during the buildup to the 2004–2008 eruption of Mount St. Helens (Washington). This episode was remarkable both because no explosion followed, and because seismicity abruptly stopped following the episode. This sequence motivated us to consider a model for volcanic tremor that does not involve energetic gas release from magma but does involve movement of conduit magma through extension on its way toward the surface. We found that the tremor signal was composed entirely of Love and Rayleigh waves and that its spectral bandwidth increased and decreased with signal amplitude, with broader bandwidth signals containing both higher and lower frequencies. Our modeling results demonstrate that the forces giving rise to this tremor were largely normal to conduit walls, generating hybrid head waves along conduit walls that are coupled to internally reflected waves. Together these form a crucial part of conduit resonance, giving tremor wavefields that are largely a function of waveguide geometry and velocity. We find that the mechanism of tremor generation fundamentally masks the nature of the seismogenic source giving rise to resonance. Thus multiple models can be invoked to explain volcanic tremor, requiring that information from other sources (such as visual observations, geodesy, geology, and gas geochemistry) be used to constrain source models. With concurrent GPS and field data supporting rapid rise of magma, we infer that tremor resulted from drag of nearly solid magma along rough conduit walls as magma was forced toward the surface.

Washington

Imaging the next Cascadia earthquake: Optimal design for a seafloor GNSS- A network

The Cascadia subduction zone in the Pacific Northwest of the United States of America capable of producing magnitude ∼9 earthquakes, likely often accompanied by tsunamis. An outstanding question in this region is the degree and spatial extent of interseismic strain accumulation on the subduction megathrust. Seafloor geodetic methods combining GNSS and underwater acoustic ranging (GNSS-A) are capable of imaging this strain accumulation on the offshore portion of the subduction zone and therefore anticipating the potential size and rupture pattern of a future earthquake. However, the high cost of seafloor geodesy means that only a limited number of stations may be deployed and monitored. To facilitate expansion of current geodetic networks offshore, we develop a quantitative recommendation of optimal locations for future seafloor geodetic observations, based on the amount of new information provided by that observation. The optimal network depends on the problem that one is trying to solve with those observations (mapping subduction locking rates, coupling rates, constraining total moment rate, etc.), and on a number of modelling and data uncertainty assumptions. In particular, data uncertainty assumptions will change over time, as more position observations reduce velocity uncertainties. We find that near-trench observations on the megathrust hangingwall, distributed along-strike, consistently provide significant reduction in differential entropy over a large suite of assumptions, and that a well-placed seafloor observation can provide up to ∼30 times the information gain of the most optimal onshore observation.

British Columbia, California, Oregon, Washington

How to handle glacier area change in geodetic mass balance

Innovations in geodesy enable widespread analysis of glacier surface elevation change and geodetic mass balance. However, coincident glacier area data are less widely available, causing inconsistent handling of glacier area change. Here we quantify the bias introduced into meters water equivalent (m w.e.) specific geodetic mass balance results when using a fixed, maximum glacier area, and illustrate the bias for five North American glaciers. Sites span latitudes from the northern U.S. Rocky Mountains (48°N) to the Central Alaska Range (63°N) between 1948 and 2021. Results show that fixed (maximum) area treatment subdues the m w.e. mass change signal, underestimating mass balance by up to 19% in our test cases. This bias scales with relative glacier area change and the mass balance magnitude. Thus, the bias for specific geodetic mass balances will be most pronounced across rapidly deglaciating regions. Our analysis underscores the need for temporally resolved glacier area in geodetic mass balance studies.

Journal of Glaciology

Accuracy of finite fault slip estimates in subduction zone regions with topographic Green's functions and seafloor geodesy

Until recently, the lack of seafloor geodetic instrumentation and the use of unrealistically simple, half-space based forward models have resulted in poor resolution of near-trench slip in subduction zone settings. Here, we use a synthetic framework to investigate the impact of topography and geodetic data distribution on coseismic slip estimates in various subduction zone settings. We calculate surface displacements in two synthetic topographic domains that have topography similar to that of Chile and Japan, respectively. We then attempt to image target slip distributions by using a Bayesian approach to solve for slip with two sets of Green's functions—one that accounts for topography and one that does not—and five sets of 50 or more observation points selected from the synthetic surface displacements. Three of these sets of observation points are entirely onland, and two include 5–10 seafloor geodetic sites. We find that the use of topographic Green's functions always improves inferred slip models, and with seafloor geodetic data, it enables an almost perfect recovery of a target slip model, even in the near-trench region. Critically, our results demonstrate that it would be impossible for non-topographic Green's functions to properly recover the true slip distribution, particularly in the near-trench region. We also perform a parameter study with approximately 4,000 slip models estimated using a least-square approach, and find that topographic Green's functions yield significantly more accurate slip models in cases where good data (well distributed and reasonably dense) are available, even in the absence of seafloor geodetic sites.

Journal of Geophysical Research: Solid Earth

Displacement fields from point cloud data: Application of particle imaging velocimetry to landslide geodesy

Acquiring spatially continuous ground-surface displacement fields from Terrestrial Laser Scanners (TLS) will allow better understanding of the physical processes governing landslide motion at detailed spatial and temporal scales. Problems arise, however, when estimating continuous displacement fields from TLS point-clouds because reflecting points from sequential scans of moving ground are not defined uniquely, thus repeat TLS surveys typically do not track individual reflectors. Here, we implemented the cross-correlation-based Particle Image Velocimetry (PIV) method to derive a surface deformation field using TLS point-cloud data. We estimated associated errors using the shape of the cross-correlation function and tested the method's performance with synthetic displacements applied to a TLS point cloud. We applied the method to the toe of the episodically active Cleveland Corral Landslide in northern California using TLS data acquired in June 2005–January 2007 and January–May 2010. Estimated displacements ranged from decimeters to several meters and they agreed well with independent measurements at better than 9% root mean squared (RMS) error. For each of the time periods, the method provided a smooth, nearly continuous displacement field that coincides with independently mapped boundaries of the slide and permits further kinematic and mechanical inference. For the 2010 data set, for instance, the PIV-derived displacement field identified a diffuse zone of displacement that preceded by over a month the development of a new lateral shear zone. Additionally, the upslope and downslope displacement gradients delineated by the dense PIV field elucidated the non-rigid behavior of the slide.

California

Differential uplift and incision of the Yakima River terraces, central Washington State

The fault-related Yakima folds deform Miocene basalts and younger deposits of the Columbia Plateau in central Washington State. Geodesy implies ~2 mm/yr of NNE directed shortening across the folds, but until now the distribution and rates of Quaternary deformation among individual structures has been unclear. South of Ellensburg, Washington, the Yakima River cuts a ~600 m deep canyon across several Yakima folds, preserving gravel-mantled strath terraces that record progressive bedrock incision and related rock uplift. Here we integrate cosmogenic isochron burial dating of the strath terrace gravels with lidar analysis and field mapping to quantify rates of Quaternary differential incision and rock uplift across two folds transected by the Yakima River: Manastash and Umtanum Ridge. Isochron burial ages from in situ produced 26 Al and 10 Be at seven sites across the folds date episodes of strath terrace formation over the past ~2.9 Ma. Average bedrock incision rates across the Manastash (~88 m/Myr) and Umtanum Ridge (~46 m/Myr) anticlines are roughly 4 to 8 times higher than rates in the intervening syncline (~14 m/Myr) and outside the canyon (~10 m/Myr). These contrasting rates demonstrate differential bedrock incision driven by ongoing Quaternary rock uplift across the folds at rates corresponding to ~0.13 and ~0.06 mm/yr shortening across postulated master faults dipping 30 ± 10°S beneath the Manastash and Umtanum Ridge anticlines, respectively. The reported Quaternary shortening across the anticlines accounts for ~10% of the ~2 mm/yr geodetic budget, suggesting that other Yakima structures actively accommodate the remaining contemporary deformation.

Washington

Degradation of 100‐m‐scale rocky ejecta craters at the InSight Landing Site on Mars and implications for surface processes and erosion rates in the hesperian and amazonian

Rocky ejecta craters (RECs) at the Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) landing site on Elysium Planitia, Mars, provide constraints on crater modification and rates for the Hesperian and Amazonian. The RECs are between 10 m and 1.2 km in diameter and exhibit five classes of preservation. Class 1 represents pristine craters with sharp rims and abundant ejected rocks. From Classes 2 to 5, rims become more subdued, craters are infilled, and the ejecta become discontinuously distributed. High‐Resolution Imaging Science Experiment digital elevation models indicate a maximum depth to diameter ratio of ~0.15, which is lower than pristine models for craters of similar size. The low ratio is related to the presence of a loosely consolidated regolith and early‐stage eolian infill. Rim heights have an average height to diameter ratio of ~0.03 for the most pristine class. The size‐frequency distribution of RECs, plotted using cumulative and differential methods, indicates that crater classes within the diameter range of 200 m to 1.2 km are separated by ~100 to 200 Myr. Smaller craters degrade faster, with classes separated by <100 Myr. Rim erosion can be entirely modeled by nonlinear diffusional processes using the calculated timescales and a constant diffusivity of 8 × 10 −7 m 2 /year for craters 200 to 500 m in diameter. Diffusion models only partly capture depth‐related degradation, which requires eolian infill. Depth degradation and rim erosion rates are 10 −2 to 10 −3 m/Myr, respectively. The rates are consistent with relatively slow modification that is typical of the last two epochs of Martian history.

Journal of Geophysical Research - Planets

Elucidating the magma plumbing system of Ol Doinyo Lengai (Natron Rift, Tanzania) Using satellite geodesy and numerical modeling

Ol Doinyo Lengai, located in the southern Eastern Branch of the East African Rift had several eruptive episodes with ash falls and lava flows (VEI 3) that caused damage to the nearby communities between 2007 and 2010. The volcano is remote and access is difficult. Although this volcano has been studied for decades, its plumbing system is still poorly understood, in part, because of the lack of precise observations of surface deformation during periods of quiet and unrest. This study investigates the volcanic plumbing system of Ol Doinyo Lengai and its surroundings using data from the network of permanent Global Navigation Satellite System (GNSS) sites monitoring the volcano (the TZVOLCANO network) around the flanks of the volcano and Interferometric Synthetic Aperture Radar (InSAR) observations. We constrain surface motions using 6 GNSS sites distributed around Ol Doinyo Lengai, operating between 2016 and 2021, and InSAR data covering nearly the same time period. Because of the complex local tectonics, the interpretation of the deformation pattern is not straightforward. We first invert the GNSS deformation and InSAR observations independently to infer potential deformation sources. Then we perform a joint inversion of both GNSS and InSAR datasets to verify our findings. We compare the results from the joint inversion with the results from inverting each dataset independently. The GNSS, InSAR, and joint inversion results point to a deflating source, located east of Ol Doinyo Lengai and southwest of the dormant volcano Gelai at a depth of 3.49 ± 0.03 km (GNSS inversion), 5.2 ± 1.2 km (InSAR inversion) and 3.49 ± 0.06 km (joint inversion) relative to the summit (vent) and with a volume change ∆V of −0.04 ± 0.05 × 10 6 m 3 (GNSS inversion), −0.39 ± 0.29 × 10 6 m 3 (InSAR inversion), and − 0.04 ± 0.01 × 10 6 m 3 (joint inversion). Although this is non-unique modeling of geodetic datasets with small signals, the inversion results suggest that Ol Doinyo Lengai could be fed by an offset multi-reservoir system that includes a shallow magma reservoir (<5 km) east of Ol Doinyo Lengai, possibly connected to a deeper magma reservoir.

Natron Rift, Ol Doinyo Lengai