Richard A. Snay

Reducing the profile of sparse symmetric matrices

An algorithm for improving the profile of a sparse symmetric matrix is introduced. Tests on normal equation matrices encountered in adjustments of geodetic networks by least squares demonstrate that the algorithm produces significantly lower profiles than the widely used reverse Cuthill-McKee algorithm.

Introducing HTDP 3.1 to transform coordinates across time and spatial reference frames

The National Geodetic Survey, an office within the National Oceanic and Atmospheric Administration, recently released version 3.1 of the Horizontal Time-Dependent Positioning (HTDP) utility for transforming coordinates across time and between spatial reference frames. HTDP 3.1 introduces improved crustal velocity models for both the contiguous United States and Alaska. The new HTDP version also introduces a model for estimating displacements associated with the magnitude 7.2 El Mayor–Cucapah earthquake of April 4, 2010. In addition, HTDP 3.1 enables its users to transform coordinates between the newly adopted International Terrestrial Reference Frame of 2008 (ITRF2008) and IGS08 reference frames and other popular reference frames, including current realizations of NAD 83 and WGS84. A more convenient format to enter a list of coordinates to be transformed has been added. Users can now also enter dates in the decimal year format as well as the month-day-year format. The new HTDP utility, explanatory material and instructions are available at http://www.ngs.noaa.gov/TOOLS/Htdp/Htdp.shtml.

Crustal velocity field near the big bend of California's San Andreas Fault

We use geodetic data spanning the 1920–1992 interval to estimate the horizontal velocity field near the big bend segment of Californias San Andreas fault (SAF). More specifically, we estimate a horizontal velocity vector for each node of a two-dimensional grid that has a 15-min-by-15-min mesh and that extends between latitudes 34.0°N and 36.0°N and longitudes 117.5°W and 120.5°W. For this estimation process, we apply bilinear interpolation to transfer crustal deformation information from geodetic sites to the grid nodes. The data include over a half century of triangulation measurements, over two decades of repeated electronic distance measurements, a decade of repeated very long baseline interferometry measurements, and several years of Global Positioning System measurements. Magnitudes for our estimated velocity vectors have formal standard errors ranging from 0.7 to 6.8 mm/yr. Our derived velocity field shows that (1) relative motion associated with the SAF exceeds 30 mm/yr and is distributed on the Earths surface across a band (>100 km wide) that is roughly centered on this fault; (2) when velocities are expressed relative to a fixed North America plate, the motion within our primary study region has a mean orientation of N44°W ± 2° and the surface trace of the SAF is congruent in shape to nearby contours of constant speed yet this trace is oriented between 5° and 10° counterclockwise relative to these contours; and (3) large strain rates (shear rates > 150 nrad/yr and/or areal dilatation rates < −150 nstr/yr) exist near the Garlock fault, near the White Wolf fault, and in the Ventura basin.

DYNAP: software for estimating crustal deformation from geodetic data

Abstract The acronym DYNAP (DYNamic Adjustment Program) identifies a software package for estimating crustal dynamic parameters from a collection of geodetic data. DYNAP accepts various data types including horizontal directions and angles, distances, azimuths, zenith distances, and intersite vectors such as those obtainable with the Global Positioning System (GPS) or with Very Long Baseline Interferometry (VLBI). DYNAP incorporates the “simultaneous reduction” technique whereby crustal dynamic parameters are estimated simultaneously along with station positional coordinates and various “nuisance” parameters, all via the least squares process. The estimated crustal dynamics parameters come in groups of six or fewer where each group corresponds to a prespecified geographic region and period of time. The six parameters convert mathematically to yield the three components of the horizontal strain rate tensor, the horizontal rotation rate, and the two components of the vertical tilt rate vector. DYNAPs applicability is illustrated with two examples. The first involves over 60 years of triangulation/trilateration data in the Cascadia subduction zone of northwestern California. Here a maximum shearing rate was found of 0.161 ± 0.074μ radians/yr with the corresponding axis of maximum contraction oriented N25° E ± 14°. The second involves a 1980 triangulation/trilateration survey and a 1986 GPS survey both spanning the Imperial fault of southern California. Here a maximum dextral shearing rate was found of 1.073 ± 0.171μ radians/yr in the direction of N31°W ± 5°.

HTDP 3.0: Software for Coping with the Coordinate Changes Associated with Crustal Motion

NOAAs National Geodetic Survey has developed the horizontal time-dependent positioning HTDP software to provide a way for its users to estimate the coordinate changes associated with horizontal crustal motion in the United States. HTDP contains a model for estimating horizontal crustal velocities and separate models for estimating the displacements associated with 29 earthquakes two in Alaska and 27 in California. This software is updated periodically to provide more accurate estimates for crustal velocities and earth- quake displacements, as well as to include models for additional earthquakes. In June 2008, NGS released version 3.0 of HTDP HTDP 3.0 that introduces an improved capability for predicting crustal velocities, based on a tectonic block model of the western contiguous United States CONUS, that is, from the Rockies to the Pacific coast. Values for the model parameters that predict the velocity at any point within the domain were estimated from 4,890 horizontal velocity vectors derived from repeated geodetic observations, 170 fault slip rates, and 258 fault slip vector azimuths. Extensive testing indicates that this model can predict velocities within CONUS with a standard error of less than 2 mm/year in both the north and east components. HTDP 3.0 also introduces a model for the combined coseismic and postseismic displacements associated with the magnitude 7.9 Denali earthquake that occurred in central Alaska on No- vember 3, 2002.

Network design strategies applicable to GPS surveys using three or four receivers

Strategies applicable to the design ofGPS surveys involving deployment of either three or four compatible receivers are presented. During aGPS observing session, the receivers operate simultaneously, producing three-dimensional cartesian coordinate differences for the lines interconnecting the receivers. Different strategies provide the network designer with several options for planning the survey. The designer may opt for a survey in which each mark is occupied three times, that is, during three separate observing sessions, or he may elect a more economical survey in which each mark is occupied only twice. The designer may also choose between two fundamentally different network geometries (a loop geometry or an areal geometry) to design a survey compatible with the spatial distribution of network marks. The strategies can be extended to other geometries. The strategies produce efficient networks in that no two marks are jointly occupied for more than one observing session. This feature produces the maximum number of distinct, directly observed lines for the given number of receivers and observing sessions. The strategies also favor observations over those lines connecting marks near one another. This feature helps survey logistics by reducing travel time between observing sessions.

Horizontal deformation in the Cascadia subduction zone as derived from serendipitous geodetic data

Abstract Data from recent Global Positioning System (GPS) surveys are combined with triangulation/trilateration data to estimate horizontal shear-strain rates for two regions in the Cascadia subduction zone. Near Bellingham, Washington, we estimate that the maximum horizontal shear rate (γ) equals 0.116 ± 0.089 μrad/yr and the direction of maximum horizontal contraction (θ) orients N71°E ± 21° for data spanning the 1905–1985 interval. The corresponding estimates for a region near Portland, Oregon, are 0.057 ± 0.027 μrad/yr and N95°E±14° for data spanning the 1881–1988 interval. These estimates are consistent with estimates from independent geodetic data in the area. Moreover, the estimates for θ are consistent with the N68°E direction of ongoing convergence between the Juan de Fuca plate and the North American plate as predicted by the NUVEL-1 plate motion model. This consistency between θ-estimates and the direction of plate convergence supports the argument for the possibility of a great subduction earthquake occurring in the Cascadia subduction zone. The low shear rates, however, imply that the recurrence interval between such earthquakes would be several centuries long.

Modeling 3-D crustal velocities in the United States and Canada

A numerical model for three-dimensional (3-D) crustal velocities has been derived for most of the United States and Canada, primarily from repeated geodetic data. This model provides a foundation for a prototype of the TRANS4D software. TRANS4D is being developed to enable geospatial professionals and others to transform 3-D positional coordinates across time. The derived model reveals several macroscopic features of the 3-D velocity field, including the pervasive presence of the glacial isostatic adjustment associated with the past melting of the ice fields that formed more than 19,000 years ago during the Last Glacial Maximum. In this study, the present-day 3-D velocity field associated with this melting (as estimated via the recently published ICE-6G_C (VM5a) model) was subtracted from this studys total 3-D velocity field to identify features of the residual velocity field. In particular, this study introduces the NA_ICE-6G reference frame in which residual horizontal velocities have magnitudes that are less than 2 mm/yr everywhere east of longitude 104°W and south of latitude 60°N, except in southern Texas. Residual horizontal velocities of greater magnitude are found west and/or north of these two boundaries, and they are due mostly to interactions among tectonic plates with localized pockets due to other geophysical phenomena. Large residual vertical velocities, some with values exceeding 30 mm/yr, are found in southeastern Alaska. The uplift occurring here is due to present-day melting of glaciers and ice fields formed during the Little Ice Age glacial advance that occurred between 1550 A.D. and 1850 A.D.

The Effect of the MAPS Weather Model on GPS-Determined Ellipsoidal Heights

We investigated a current numerical weather model, known as MAPS (Mesoscale Analysis and Prediction System), to determine if it could precisely define the behavior of GPS signals in the tropospere, ultimately leading to improved GPS-determined ellipsoidal heights. MAPS is the research version of the Rapid Update Cycle (RUC2) generated by NOAAs Forecast System Laboratory. MAPS is generated on an hourly basis and provides coverage in the contiguous United States at a 40-km grid spacing. We processed numerous subsets of GPS data collected over a months-long period on 23 static baselines ranging in length from 62 to 304 km. The GPS data were processed in 1/2-hr, 1-hr, 2-hr, and 4-hr session lengths. The primary effort was to compare the precision of heights obtained using a commonly adopted seasonal weather model with the precision of heights obtained using the MAPS weather model. Our analysis shows that the current version of MAPS can lead to improvement in GPS height precision when session lengths are shorter than two hours. For sessions longer than two hours, comparably precise heights may be obtained using a less accurate seasonal model by introducing appropriate nuisance parameters into the height estimation process.

Crustal Motion Models Developed for Version 3.2 of the Horizon- tal Time-Dependent Positioning Utility

Abstract The Horizontal Time-Dependent Positioning (HTDP) software allows users to transform positional coordinates across time and between spatial reference frames. To provide this capability, the software includes numerical models for estimating interseismic horizontal crustal velocities in and around the United States, as well as numerical models for estimating the displacements associated with major (magnitude > 6.0) earthquakes in these same areas. Version 3.2 of HTDP was released in August 2012. This HTDP version introduces: (a) an improved model for estimating interseismic horizontal velocities in Alaska, (b) a model for estimating the postseismic motion associated with the M7.9 Denali Fault earthquake that occurred in central Alaska on November 3, 2002, and (c) an improved model for estimating interseismic horizontal velocities in the region of the conterminous United States, which is located east of longitude 107°W. The development and nature of these new models are discussed in this paper.