Paleoseismological data for the Wasatch and San Andreas fault zones have led to the formulation of the characteristic earthquake model, which postulates that individual faults and fault segments tend to generate essentially same size or characteristic earthquakes having a relatively narrow range of magnitudes near the maximum. Analysis of scarp-derived colluvium in trench exposures across the Wasatch fault provides estimates of the timing and displacement associated with individual surface faulting earthquakes. At all of the sites studied, the displacement per event has been consistently large; measured values range from 1.6 to 2.6 m, and the average is about 2 m. On the basis of variability in the timing of individual events as well as changes in scarp morphology and fault geometry, six major segments are recognized along the Wasatch fault. On the basis of the most likely number of surface faulting events (18) that have occurred on segments of the Wasatch fault zone during the past 8000 years, an average recurrence interval of 400–666 years with a preferred average of 444 years is calculated for the entire zone. Geologic data on the distribution of slip associated with prehistoric earthquakes and slip rates along the south-central segment of the San Andreas fault suggest that the M 8 1857 earthquake is a characteristic earthquake for this segment. Comparisons of earthquake recurrence relationships on both the Wasatch and San Andreas faults based on historical seismicity data and geologic data show that a linear (constant b value) extrapolation of the cumulative recurrence curve from the smaller magnitudes leads to gross underestimates of the frequency of occurrence of the large or characteristic earthquakes. Only by assuming a low b value in the moderate magnitude range can the seismicity data on small earthquakes be reconciled with geologic data on large earthquakes. The characteristic earthquake appears to be a fundamental aspect of the behavior of the Wasatch and San Andreas faults and may apply to many other faults as well.

Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas Fault Zones

This book gives an account of certain observed irregularities on the rotation of the Earth, both in its rate of rotation (giving a variable length of day) and in the position of its axis. These irregularities are caused by events on and within the Earth and provide a means of studying a number of geophysical problems. Seasonal shifts in air masses and variable winds are causes of short-period fluctuations in the rotation. Climatic changes and their attendant sea levels are in part responsible for long-term fluctuations. Modern observations of the Moon and descriptions of ancient elipses both establish a secular increase in the length of day. The interpretation involves atmospheric, oceanic and bodily tides. The book provides a unified treatment of the rotation of the Earth, making this method of studying geophysical phenomena more readily accessible to geophysicists and others.

The rotation of the earth: a geophysical discussion.

Geostationary satellites have provided routine, high temporal resolution Earth observations since the 1970s. Despite the long period of record, use of these data in climate studies has been limited for numerous reasons, among them that no central archive of geostationary data for all international satellites exists, full temporal and spatial resolution data are voluminous, and diverse calibration and navigation formats encumber the uniform processing needed for multisatellite climate studies. The International Satellite Cloud Climatology Project (ISCCP) set the stage for overcoming these issues by archiving a subset of the full-resolution geostationary data at ~10-km resolution at 3-hourly intervals since 1983. Recent efforts at NOAA's National Climatic Data Center to provide convenient access to these data include remapping the data to a standard map projection, recalibrating the data to optimize temporal homogeneity, extending the record of observations back to 1980, and reformatting the data for broad ...

/pdf/globally-gridded-satellite-observations-for-climate-studies-2oq6ez1ouk.pdf

Globally Gridded Satellite Observations for Climate Studies

Changes in the earth's rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the International Latitude Service data and also in the estimates of the nontidal acceleration of the length of the day. We have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere, a viscoelastic mantle, and an inviscid core. Forcings from the two major ice sheets, Laurentide and Fennoscandia, have been considered. Sensitivity analysis of the parameters governing the external forcings, such as the length and the time of termination of the deglaciation phase, show in general that there exist two families of mean mantle viscosities, 0(1022 P) and 0(1023 P), which can match the data satisfactorily. However, we find it an improvement to incorporate some amount of shrinkage from the Antarctic ice sheet, obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions. Hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data. We have also solved the initial value problem of the components of instantaneous angular velocity by means of the Laplace transform for applied loads characterizing the continental ice sheets, which since the mid-Pliocene have periodically expanded and contracted over the northern hemisphere. In consequence of this continual forcing, polar wander of around 5–10 degrees can take place for a mean mantle viscosity 0 (1022 P). Recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m.y. These calculations thus provide a physical explanation for the observed movement of the rotation axis. Membrane stresses of 0 (10) bars can develop from this secular polar motion.

Polar wandering and the forced responses of a rotating, multilayered, viscoelastic planet

The dual frequency radio signals of the Global Positioning System (GPS) allow measurements of the total number of electrons, called total electron content (TEC), along a ray path from GPS satellite to receiver. We have developed a new technique to construct two-dimensional maps of absolute TEC over Japan by using GPS data from more than 1000 GPS receivers. A least squares fitting procedure is used to remove instrumental biases inherent in the GPS satellite and receiver. Two-dimensional maps of absolute vertical TEC are derived with time resolution of 30 seconds and spatial resolution of 0.15° × 0.15° in latitude and longitude. Our method is validated in two ways. First, TECs along ray paths from the GPS satellites are simulated using a model for electron contents based on the IRI-95 model. It is found that TEC from our method is underestimated by less than 3 TECU. Then, estimated vertical GPS TEC is compared with ionospheric TEC that is calculated from simultaneous electron density profile obtained with the MU radar. Diurnal and day-to-day variation of the GPS TEC follows the TEC behavior derived from MU radar observation but the GPS TEC is 2 TECU larger than the MU radar TEC on average. This difference can be attributed to the plasmaspheric electron content along the GPS ray path. This method is also applied to GPS data during a magnetic storm of September 25, 1998. An intense TEC enhancement, probably caused by a northward expansion of the equatorial anomaly, was observed in the southern part of Japan in the evening during the main phase of the storm.

A new technique for mapping of total electron content using GPS network in Japan

In order properly to apply transformations when using data derived from different GPS solutions, the effects of plate motion on the coordinates should be accurately taken into consideration. Only then can a rigorous comparison be established between results observed at different epochs. Equations are given to relate GPS-derived Cartesian coordinates and velocities affected by changes of their reference frames and epochs.

/pdf/a-compendium-of-transformation-formulas-useful-in-gps-work-2nhv7oh4vv.pdf

A compendium of transformation formulas useful in GPS work

In order to properly apply transformations when using data derived from different space techniques, the corresponding frames should be clearly stated. Only then can a rigorous comparison of results be established. This review is an attempt to expound some of the basic definitions and concepts of reference frames to users from diverse backgrounds, who are not familiar with the geodetic terminology.

/pdf/coordinate-systems-used-in-geodesy-basic-definitions-and-4itf6wso0x.pdf

Coordinate Systems Used in Geodesy: Basic Definitions and Concepts

This study demonstrates the usefulness of an approach based on the Online Positioning User Service (OPUS) provided by the National Geodetic Survey (NGS) of the National Oceanic and Atmospheric Administration (NOAA) to process Global Positioning System (GPS) data and conduct long-term landslide monitoring in the Puerto Rico and Virgin Islands region. Continuous GPS data collected at a creeping landslide site during 2 years were used to evaluate different scenarios for landslide surveying: continuous or campaign, long duration or short duration, morning or afternoon (during different weather conditions). OPUS uses the Continuously Operating Reference Station (CORS) network managed by the NGS as control points and user-collected data to solve for the position of the occupied station (rover). In July 2011, there were 19 NGS CORS sites in the Puerto Rico and Virgin Islands region. This dense GPS network provided a precise and reliable reference frame for subcentimeter-accuracy landslide monitoring in t...

OPUS for Horizontal Subcentimeter-Accuracy Landslide Monitoring: Case Study in the Puerto Rico and Virgin Islands Region

SUMMARY The applications of eigentheory to many branches of mathematical physics (e.g., rotational dynamics, continuum mechanics) is an unquestionable fact. This work expands the conventional methodology by introducing equations to compute the covariance matrices of eigenvalues and eigenvectors of second-rank 3-D symmetric tensors in terms of their six distinct elements error estimates. New analytical expressions derived herein are general and should be of interest to anyone concerned with the accuracy of the computed orientation of principal axes and their associated principal quantities (e.g., moments of inertia, stress, strain).

/pdf/on-covariances-of-eigenvalues-and-eigenvectors-of-second-46hnifoth5.pdf

On covariances of eigenvalues and eigenvectors of second-rank symmetric tensors

OPUS-RS is a rapid static form of the National Geodetic Survey’s On-line Positioning User Service (OPUS). Like OPUS, OPUS-RS accepts a user’s GPS tracking data and uses corresponding data from the U.S. Continuously Operating Reference Station (CORS) network to compute the 3-D positional coordinates of the user’s data-collection point called the rover. OPUS-RS uses a new processing engine, called RSGPS, which can generate coordinates with an accuracy of a few centimeters for data sets spanning as little as 15 min of time. OPUS-RS achieves such results by interpolating (or extrapolating) the atmospheric delays, measured at several CORS located within 250 km of the rover, to predict the atmospheric delays experienced at the rover. Consequently, standard errors of computed coordinates depend highly on the local geometry of the CORS network and on the distances between the rover and the local CORS. We introduce a unitless parameter called the interpolative dilution of precision (IDOP) to quantify the local geometry of the CORS network relative to the rover, and we quantify the standard errors of the coordinates, obtained via OPUS-RS, by using functions of the form $$ \sigma ({\text{IDOP}},{\text{RMSD}}) = \sqrt {(\alpha \cdot {\text{IDOP}})^{2} + (\beta \cdot {\text{RMSD}})^{2} } $$
 here α and β are empirically determined constants, and RMSD is the root-mean-square distance between the rover and the individual CORS involved in the OPUS-RS computations. We found that α = 6.7 ± 0.7 cm and β = 0.15 ± 0.03 ppm in the vertical dimension and α = 1.8 ± 0.2 cm and β = 0.05 ± 0.01 ppm in either the east–west or north–south dimension.

https://geodesy.noaa.gov/CORS/Articles/SchwarzetalGPSSOL09.pdf

Tomás Soler

Papers

A compendium of transformation formulas useful in GPS work

Coordinate Systems Used in Geodesy: Basic Definitions and Concepts

OPUS for Horizontal Subcentimeter-Accuracy Landslide Monitoring: Case Study in the Puerto Rico and Virgin Islands Region

On covariances of eigenvalues and eigenvectors of second-rank symmetric tensors

Accuracy assessment of the National Geodetic Survey's OPUS-RS utility