CHAPTER 15

MEASUREMENT OF LOCAL HORIZONTAL VELOCITIES ON THE SLUMGULLION LANDSLIDE USING THE GLOBAL POSITIONING SYSTEM

by Michael E. Jackson, Paul W. Bodin, William Z. Savage, and Elizabeth M. Nel

Introduction

Determination of landslide velocity fields has traditionally relied on cadastral survey techniques, which require multi-year surveys (Varnes and others, 1993). A recent experiment on the Slumgullion landslide suggests that the rate of change of high precision Global Positioning System (GPS) coordinates can be used to determine slide velocities within 10 percent on a time scale of a few days.

The presently active part of the Slumgullion landslide has apparently been moving for the last 300 years (Crandell and Varnes, 1961; Varnes and others, 1993). Traditional control surveys conducted during the past 35 years suggest that the narrow middle part and toe of the active slide are moving at average velocities of approximately 1.6 cm/day, and 0.4 cm/day, respectively.

Introduction to GPS Geodesy

The Global Positioning System is a constellation of 24 Department of Defense satellites orbiting at 21,000 km above the Earth. The satellites transmit precisely timed radio signals (pseudo-random codes called C/A and P-codes, and sine/cosine-shaped carrier phase signals called the L1 and L2 carrier) to ground-based receivers. In this study, both the L1 and L2 carrier phase data (L1 and L2 carrier phase are radio frequency signals transmitted at 1,575.42 MHz, wavelength () 20 cm, and 1,227.60 MHz, 25 cm, respectively) are used to attain the highest measurement precision possible. GPS satellites and receivers are equipped with precise clocks, and, by comparing the time of GPS signal reception with the time of transmission and multiplying this difference by the speed of light, the distance between the satellite and receiver is calculated. Simultaneous measurement to four satellites is required to solve for the receivers' latitude, longitude, and height. Repeating these measurements over discrete time intervals allows the change in station coordinates with time to be determined to a high degree of precision.

For high-precision work, the time of flight of the radio signals needs to be corrected for small offsets in the satellite and receiver clocks. This is accomplished by post-processing simultaneous GPS data from a minimum of two ground receivers. Satellite clock errors are removed by combining the data from two receivers that have the same satellites in view (this is called a single-difference calculation). Because the satellite clock error is common to both receivers, combining the data eliminates that error. Similarly, receiver clock errors are removed by combining two single-difference data files for two satellite pairs. In this case, the receiver clock errors are common in both single-difference files, and the combination removes the receiver clock error. Combinations of the L1 and L2 signals are, in turn, used to remove the distortion encountered as the GPS signal passes through the ionosphere. As previously mentioned, the L1 and L2 signals are each shaped like a continuous sine/cosine function. Therefore, any break in the continuous wave train impedes the ability to correctly calculate the distance between the satellite and the receiver. A further combination of the L1 and L2 carrier phase data, called the wide-lane combination, helps in recovering the distance using the carrier phase data.

GPS Observations

A GPS survey was initiated in June 1993 to determine if satellite geodesy can rapidly map the slide velocity field, describe the spatial and temporal distribution of velocity, and determine whether the inactive slide is moving relative to a stable benchmark well off the slide. A total of seven GPS stations (baselines < 5 km) were installed: five on the active slide, one on the inactive slide, and one on the stable portion near the slide main scarp (fig. 1).

Station benchmarks consist of 1-m sections of capped steel pipe driven flush with the landslide surface. The stations were occupied with Trimble 4000 SST, 8-channel, dual-frequency phase and C/A code receivers, which observed all satellites above a 15^o horizon. Each station was measured for at least two, 4- to 6-hour sessions with most stations being occupied for four, 4- to 6-hour sessions. The baseline between stations SEI1, which is assumed to be stable, and GP01, located on the fastest moving portion of the active slide, was measured for a total of nine consecutive 4- to 6-hour sessions. Relative coordinates for the network were carried from the Pietown fiducial tracking site in northern New Mexico to a reference station (SEI1 - lat 37^o59'29.3392"N.; long 107^o15'19.6388" W., HAE (height above ellipsoid) 3,157.98 m) in the landslide network to a precision of 3, 3.5, and 5 cm in the north, east, and up components, respectively.

GPS Data Processing

The GPS data were analyzed with software designed for high-accuracy geodetic surveys. Precise GPS satellite orbits, with an estimated error of ~ 0.01 ppm, provided by Scripps Institute of Oceanography (Bock and others, 1993) were used to establish the Slumgullion GPS network within the geodetic reference frame. The coordinates of station SEI1 were held fixed, and single differences between network stations were formed to remove satellite and receiver clock errors. The single-difference files were preprocessed to fix carrier phase cycle slips or breaks in the carrier phase data caused by obstructions between satellites and receivers. Trees on the landslide often blocked the GPS signal, particularly at low satellite elevation angles (15^o - 30^o) and caused frequent, but repairable, cycle slips. Double difference combinations were then formed to estimate phase integer ambiguities in the L1 and L2 signals. Once station ambiguities were resolved, station coordinates were estimated relative to station SEI1 using the L1, L2, and L3 (ionosphere-free) double-difference phase combinations. Because the baseline distances on the landslide were short, the ionosphere bias was negligible between stations and there was no significant difference between the L1 and L3 coordinate solutions within the measurement uncertainties. Landslide bench mark displacements were calculated by comparing successive L1-frequency coordinate solutions for each station while assuming no movement of station SEI1. The cumulative displacements at each station and the time interval between measurements were used to calculate bench mark velocities.

Results

Figure 1 shows velocities of bench marks determined during a 4-day measurement period. The motion of station T03A, which is in the inactive portion of the landslide and near the slide main scarp, may be caused by monument instability. Table 1 and figure 1 show that stations in the center of the active slide are moving at velocities of 1.2 - 1.5 cm/day. These GPS-determined velocities are similar to slide velocities determined from traditional surveys (Crandell and Varnes, 1961), creepmeter measurements (Savage and Fleming, this volume; Bodin and others, 1993, Gomberg and others, this volume), and photogrammetric methods (Smith, 1993, this volume; Powers and Chiarle, this volume).

References Cited

Bock, Y., Agnew, D. C., Fang, P., Genrich, J. F., Hagar, B. H., Herring, T. A., Hudnut, K.W., King, R.W., Larson, S. L., Minster, J. B. and others, 1993, Detection of crustal deformation from the Landers earthquake sequence using continuous geodetic measurements: Nature, v. 361, p. 337-340.

Bodin, P.W., Savage, W.Z., Gomberg, J.S., and Jackson, M.E., 1993, An analog to crustal-scale tectonics?: EOS, Transactions, American Geophysical Union, v. 43, p. 67.

Crandell, D.R. and Varnes, D.J., 1961, Movement of the Slumgullion earthflow near Lake City Colorado, U.S. Geological Survey Research: U.S. Geological Survey Professional Paper 424-B, p. 136-139.

Smith, W.K., 1993, Photogrammetric determination of movement on the Slumgullion Slide, Hinsdale County, Colorado 1985-1990: U.S. Geological Survey Open-File Report 93-597, 17 p., 2 pl.

Varnes, D.J., W.K. Smith, W.Z. Savage, and Varnes, K.L., 1993, Control and deformation surveys at the Slumgullion Slide, Hinsdale County, Colorado -- A progress report: U.S. Geological Survey Open File Report, 93-577, 15 pages, 1 plate.