REPORT:
Trilateration and Distance-Measuring Techniques Used at Cascades and Other Volcanoes

Abstract

From 1980 to 1989, scientists of the U.S.Geological Survey's Cascades Volcano Observatory established trilateration and distance-measuring networks on Mount Baker, Mount Rainier, and Mount St. Helens in Washington; Mount Hood, South Sister, Newberry, and Crater Lake in Oregon; Medicine Lake, Mount Shasta, Lassen Peak, and Mammoth Lakes in California; and Augustine Island in Alaska. The networks were installed to provide baseline information on potentially active and dangerous volcanoes. The experience gained in monitoring Mount St. Helens has helped in designing guidelines for establishing these networks. One improved method of measuring air temperatures (for atmospheric corrections to the distance) at each bench mark has led to considerable savings in helicopter time by not requiring continuous temperature measurements along the path of the infrared signal. Bench-mark stability is critical and must be carefully evaluated both during installation and later if movement is measured. The equipment and methods currently in use are sufficient to meet the precision (+/- 2-3 ppm about any given distance) that is required for baseline data.

Introduction

Trilateration and distance-measuring networks have been established on 12 potentially active volcanoes in the Pacific Coast States beginning in 1980. These networks, once the baseline information has been collected, can detect surface deformation that may reflect magma movement up the conduit. The rates of deformation increase as magma approaches the surface, and these measurements can therefore help determine where and when an eruption may occur (Lipman and others, 1981). Before 1980, electronic distance meters (EDM's) had been used primarily to monitor horizontal deformation during inflation and deflation of shield volcanoes (Kinoshita and others, 1974). Little horizontal deformation monitoring had been attempted on stratovolcanoes with the exception of Usu volcano, Japan, where up to 160 meters of movement was observed using trilateration techniques to monitor cyrptodomes forming in the summit area in 1977-78 (Yokoyama and others, 1981). Several distances at Mount St. Helens and Mount Hood were measured in 1972 but were not remeasured prior to the reawakening of Mount St. Helens in 1980. Several distances were measured twice at Mount Hood in the summer of 1980, owing to an earthquake swarm, but no complete network was established and no significant changes were observed.

In mid-April 1980, measurements of distances and angles were initiated at Mount St. Helens, primarily to monitor the rate of deformation of the bulge on the north side of the volcano. Displacements of 1.4-1.6 meters/day were measured on the bulge prior to May 18, but there was little or no significant change outside the bulge area (Lipman and others, 1981). A complete EDM network was established at Mount St. Helens shortly after the catastrophic eruption on May 18, 1980 (Swanson and others, 1981; Iwatsubo, Topinka, and Swanson, chapter 8).

Monitoring networks were established at other volcanoes in the Pacific Coast States, including Augustine Island, Alaska, between 1981 and 1989 (fig. 10.1, table 10.1). All networks, except the Medicine Lake and partially completed Mammoth Lake networks (both installed 1989), have been reoccupied at least once. Periodic reoccupation of these networks is planned as part of an overall long-term monitoring program. Reoccupation serves as a check on previous data, solidifies the baseline information, and provides an assessment of the state of the volcano.

Figure 10.1: Volcanoes at which personnel of Cascades Volcano Observatory have installed horizontal deformation monitoring networks. Not included is Augustine Island, Alaska.

Techniques and equipment developed in the 1980's have helped to reduce costs for monitoring volcanoes without compromising the precision of the data. We explain in this report the techniques and procedures used by Cascades Volcano Observatory (CVO) scientists to measure distances at volcanoes. For further information on general trilateration and distance-measuring techniques, see Brinker and Minnick (1987) and Davis and others (1981).

Equipment

Most of the equipment used for surveying can be purchased commercially (see appendix). The methods we use to install bench marks and to measure distances, angles, barometric pressure, humidity, and air temperature are described below. These methods, in use in 1990, have been evolving since 1981 and should continue to improve in the future.

Bench-mark Installation

Surveying Equipment

The dimensions of an EDM are critical when used in moderate to high winds. The bulky HP3808A can catch wind and vibrate constantly, making it difficult to complete measurements. Each HP3808A measurement takes as long as 1 minute, depending on the length of the shot, even on calm days. When wind causes instrument vibration, measurement can take up to several minutes to complete and may even fail. The Geodimeter 114 takes 14-25 seconds for the first measurement, then repeats the measurement every 4.5 seconds. Often, the Geodimeter 114 can read 10 measurements before the HP3808A can measure one. This is a big advantage in marginal conditions.

The lightweight Geodimeter 114 is preferable for backpacking. A backpack frame is available for the HP3808A and is essential for most field applications; the carrying case for the Geodimeter 114 comes with straps that can be used as a backpack. Both EDM's use a 12-volt battery as the main power source. The HP3808A battery fits into the bottom of the instrument, whereas the Geodimeter 114 battery is connected to the EDM by an external cable. We advise purchasing an additional battery cable that can be used with a separate 12-volt sealed or automobile battery. This battery should be carried in the field as a backup power supply. If trips are planned to remote areas for extended periods and the recharging of batteries is impossible, several batteries must be carried.

The HP3808A has an internal telescope for sighting and is mounted on the tripod using its built-in yoke. The Geodimeter 114 does not have an internal telescope but can be used in two ways. The Geodimeter 114 is designed to fit on the telescope of the theodolite, which is used for sighting on the target. A yoke with a telescope (4-7X magnification) mounted on it can also be used, and we recommend purchasing the most powerful telescope (30X magnification minimum) available. Because of budget limitations we did not purchase the powerful telescope, and the 4-7X magnification telescope on the yoke is not powerful enough for our applications. Therefore we always mount the Geodimeter 114 on the theodolite.

When the EDM is yoke-mounted, the optical center or vertical axis of the EDM always remains the same, regardless of the tilt of the EDM. In other words, the EDM pivots over the center of the bench mark. However, when the EDM is mounted on a theodolite telescope, the optical center of the telescope pivots over the center of the bench mark, but the optical center of the EDM does not. The difference between the optical centers of the theodolite and of the EDM when tilted is the eccentricity error. To correct for this error, either a zenith or vertical angle must be measured and incorporated into the slope distance reduction. The formula to correct the slope distance (SD) for the eccentricity error (corr) is:

           corr = e * cos(Z)
           corrected SD = raw SD - corr, where Z  <90 degrees
           corrected SD = raw SD + corr, where Z  >90 degrees

where e is the distance between the optical center of the theodolite and the EDM, and Z is the zenith angle (Bevin and Dip, 1983).

To measure zenith angles for the eccentricity error and to calculate station elevations, we use a Wild T2 (new style) theodolite. The Wild T2 is manually read to the nearest 1 second; any good-quality 1-second theodolite is recommended for measuring angles. The advent of microprocessors has revolutionized most surveying equipment, including the theodolite. Wild manufactures the T2000 theodolite, that is accurate to 0.5 second and digitally reads out to 0.1 second ( Ewert, chapter 15 Instruments and reflectors are typically mounted on Kern tripods with centering rods, but standard tripods with optical tribrachs can also be used. For more detailed discussion of tripods, see Iwatsubo and Swanson (chapter 6).

For reflectors, we use standard (accuracy within +/-2 arc seconds), 7.3-centimeter diameter, glass corner-cube prisms in a triple nontilting mount assembly (a triad). When using the HP3808A, we carry two triads in each reflector backpack. For almost all of the measurements, two triads are sufficient. With the Geodimeter 114, four triads are carried in each reflector backpack, with 2-3 triads normally being set up for the average 3-5 kilometer line. Recently, tilting mounts with smaller diameter (5.9 centimeter) prisms became available. Tilting mounts are superior to nontilting mounts when steep lines are measured, because they can be aimed directly at the EDM increasing the return signal strength. Steep lines can be measured with nontilting mounts but may require more reflectors.

Atmospheric System

a 1 degree C change in air temperature,
a 3.4 mbar change in barometric pressure, or
a 22.66 mbar change in water vapor pressure (Bevin and Dip, 1983).

Humidity has a very small effect on the measurements but nonetheless is included in all data reduction.

A complete atmospheric package, including pressure, humidity, and temperature sensors, is carried in all reflector and instrument packs. A barometric-pressure sensor we initially used to record barometric pressure performed well but was bulky, consumed considerable power, and needed frequent maintenance. A hand-held digital barometer/altimeter, model AIR-HB-1A, was purchased to replace the barometric-pressure sensor. The AIR-HB-1A is commercially available and has upgraded our barometric pressure measurements. It has a pressure range of 364 to 775 mm Hg with a resolution of 0.1 mm Hg; other specifications are listed in the Appendix. The size, capabilities, and ease of use of this unit make it ideal to be part of the atmospheric package. Another commercial barometer package is the Ultimeter model 12, which has a resolution of 1 mm Hg and a range of 330 to 787 mm Hg. Other pressure indicators, such as the Thommens altimeter/barometer, can be used but should be checked daily, before and after use, against a more accurate instrument (such as the AIR-HB-1A). Each of our reflector packs carries a Thommens altimeter as a backup for the AIR-HB-1A.

Humidity measurements above 0 degrees C are made using a sling psychrometer, which measures a dry-and wet-bulb temperature. When temperatures are below freezing, some other method must be found to measure humidity.

Air temperature is the most important atmospheric parameter measured. This is another area where we have improved our data collecting methods. Endpoint temperatures can be affected by ground radiation, but W.H. Prescott (unpub. USGS report, 1971) showed that measurement of temperatures 7 meter or more above ground level can minimize this problem. We now use a telescoping, 7.6-meter-long fiberglass rod as a pole for the temperature sensor. By using the 7.6-meter rod in place of the previous 6-meter poles (Iwatsubo and others, 1988), we have minimized the ground radiation effects. This longer rod is sufficiently sturdy to stand up in moderate winds and short enough (1.78 meters collapsed) to be used in helicopter operations. The 6-meter fiberglass poles are shorter (1.06 meters collapsed) and lighter, and are still used when considerable hiking is required and there is enough wind to allow good air mixing, thereby helping to minimize ground radiation effects.

To avoid direct sunlight on the temperature sensor, a naturally aspirated shield is used to house the sensor. The shield consists of four thin aluminum plates 10 centimeter square, two above the sensor and two below (fig. 10.2). The pairs of plates are 5-7 millimeters apart, and the temperature sensor is mounted between the two pairs of plates, which are separated 1 centimeter apart. The shield is attached to the top of the leveling rod by threaded aluminum stock. The sides of each plate facing away from the sensor are painted white to reflect light, and the sides facing the sensor are painted black to absorb light. This shield is lightweight and allows adequate air circulation.

A wire for power and signal output connects the temperature sensor to a separate box that contains the power supply, barometer, and a digital display for the temperature sensor. A foam resin case (47x39x17 centimeters; manufactured by Pelican Products, Inc.) that is airtight (with a pressure-release valve), corrosion free, and durable, houses this equipment (fig. 10.3). A central foam section that is easily cut to tightly fit any instrument protects the equipment inside the case. After years of use, no damage has occurred to any of our cases.

We use a National Semiconductor LM335 precision temperature sensor powered by a 5-volt voltage reference; an LM78L05 reference is currently being used (fig. 10.4), but we will update to an REF-02 for better stability. A 12-volt sealed rechargeable battery (6.5 Ah), which allows long periods of use without recharging, powers the 5-volt reference. For short periods, a 9-volt transistor battery can replace the larger 12-volt battery. This is sometimes necessary, when it is not possible to carry both the larger battery and the case because of weight or bulk. The signal output of the temperature sensor is displayed by a digital 4 1/2-digit Fluke multimeter. The LM355 sensor-output signal is a voltage that corresponds to the air temperature and is displayed to the nearest 0.1 degree K. A flow chart (fig. 10.5) shows the path taken to record air temperatures.

The temperature sensors are calibrated at least once a year against a more accurate quartz thermometer. An environmental chamber, quartz-thermometer unit (HP2804A with a fast-responding probe), data-acquisition unit (HP3421A), and a personal computer are used for calibrating sensors. The range of calibration is from -20 to 50 degrees C in 1 degree C in tervals (Iwatsubo and others, 1988).

All of the above equipment, except for the temperature rod and tripod, are packed inside a typical external-frame backpack. The tripod can be strapped to the backpack if desired. The pack is easy to carry and fits into a helicopter. These factors are important when setting up a system that must be portable.

Network Setup and Measuring Procedure

Setting up a network starts with the best topographic map available, preferably one with vegetated areas marked on it. About six instrument stations are selected at the base of the mountain, approximately 60 radial degrees apart relative to the summit. Ideally each instrument station should be visible from the next station so that measurements can be made between them, but this is not critical and is commonly difficult to achieve. Next we select reflector sites at medium to high elevations on the volcano that can be seen from at least two instrument stations. Reflector sites visible from three instrument stations are optimal. If only one instrument station can be seen and the line is considered important, then we install it. We try to form triangles when establishing stations and to connect the whole network together when possible. This ideal can sometimes be accomplished on a map but is rarely met when attempted in the field. Topography, vegetation, snow and ice cover, and bedrock outcrops ultimately dictate what can be established at any volcano. Examples of three monitoring networks are shown in figure 10.6 to demonstrate their diversity.

During installation of a network, one person occupies a potential instrument site, and one is located at each respective reflector site. If a solid rock outcrop or large boulder firmly set in the ground is present and visibility is good, the bench marks are installed. People move around the volcano until the network is completed. It is imperative that visual confirmation be made before the benchmarks are set. There have been times when an instrument site had to be moved several hundred meters to complete a triangle or to be seen from more than one reflector station.

Bench-mark location descriptions should be written at the time of installation and should be improved when the station is reoccupied during the measurement of the lines. Writing clear bench-mark descriptions in the field is important, so that in the future someone who has never been to the bench-mark can locate it. We try to be as complete as possible. Descriptions should include anything that can help locate the station, taking into account any seasonal effects such as snow covering the bench mark, fallen leaves in autumn, and possibly future human intervention. We have had problems with vandalism at some sites where bench marks have been removed or damaged. If we anticipate vandalism, we now bury the bench marks several tens of centimeters below ground and write a careful description of where one needs to dig. Photographs of the bench mark and surrounding rocks are very helpful.

We typically use four people to measure a network, two at the instrument end and two separate reflector people. All parties should have two-way radio communications for a number of reasons; among other things, this ensures that the atmospheric data are collected simultaneously. Most often, it is not possible to locate the reflector from the instrument station without the aid of a signal mirror. Both instrument and reflector people flash toward each other, enabling the instrument person to aim the EDM and the reflector person to aim the prisms. Sometimes a flash from the EDM end of the line can be reflected by the prisms at the reflector end, and there is no need for the reflector person to flash. On cloudy days, bright clothing, flags, or flares are useful. Once the reflector is sighted, the slope distance and zenith angle are measured. Two lines can be measured before someone moves. Measuring the network follows the same procedure as setting it up; people move from site to site in a leap-frog manner until all the lines are completed.

Complete recording at the instrument and reflector sites of all information necessary to reduce the data is critical but easily overlooked. A form that must be filled out completely before leaving the site is one way to minimize problems. We use a data sheet printed on "Rite-in-the-Rain" waterproof paper. Both the instrument and reflector people fill out appropriate parts of the same data sheet. Each backpack is assigned a number that corresponds to a specific calibrated temperature sensor and is referred to as the "BOX #" on the data sheet. Hence the same sensors, tripod, reflector set, and notebook are always together, thereby minimizing potential calibration problems. It is imperative that the height to the optical center of both the EDM and the reflector prisms be recorded in order to reduce the data (we reduce to mark-to-mark distances). The bottom lines on the data sheet are for recording angles. Miscellaneous notes can be recorded on the back of each sheet. Such notes might include the geometry of an unusual prism setup, sketches of landmarks, comments on weather conditions, or condition of the bench mark.

Discussion

The type of equipment and methods used should be determined by the required precision of the data. If the project requires the highest quality data, expect large costs for specialized equipment and helicopter or airplane hours to fly temperature and humidity profiles aling the lines. Precision of 3 millimeters and a proportional error of 0.2 ppm of line length can be attained using such methods with the greatest relative precision at longer distances (Savage and Prescott, 1973). However, we have found that owing to random errors, which include incorrect centering and inaccurate atmospheric conditions, systematic errors such as improper calibration and aiming errors (McDonnell, 1987), and bench-mark instability, our precision is +/-(2.46+/-2.26 ppm) about any given distance. Such changes should be random and not define a pattern, but if a pattern is defined, the possibility of real deformation should be considered and an attempt should be made to reoccupy the network as soon as possible.

From 1981 through 1986, we used a helicopter to fly along each measured line and collect continuous temperature and humidity data. Barometric pressures were collected at each endpoint. An average index of refraction for the line path was calculated from this information and used in the data reduction. This is the standard procedure used for collecting high-precision strain data, when line lengths are typically 20-30 kilometers and relatively flat, such as those used in earthquake studies (Savage and Prescott, 1973). Lines measured on volcanoes are shorter and steeper and are very difficult to fly because they are in mountainous terrain where winds are typically strong and gusty. For these reasons, we compared distances calculated by using two-endpoint air temperature data obtained from the new 7.6-meter rods with those utilizing the continuously recorded temperature and humidity data (table 10.3). There is little difference between the two sets of data; all of the differences are within expected error. Similar comparisons have been made for a number of networks with similar results. Consequently, we no longer fly the lines and have saved up to 50 percent on helicopter hours and time spent to complete a survey. Therefore, we have ultimately reduced the cost of each survey.

We have established networks on the following Cascade volcanoes: Mount Baker, Mount Rainier, Mount St. Helens, Mount Hood, Newberry, South Sister, Crater Lake, Medicine Lake, Mount Shasta, and Lassen Peak. Similar networks were installed at Augustine, Alaska, in 1988 and in late 1989 to help monitor Mammoth Mountain in eastern California. Repeat measurements of each network, except for those at Medicine Lake and Mammoth Mountain, both of which were first installed in 1989, have established baseline data (table 10.1).

Occasional reoccupation helps assess bench-mark instability, the major source of error in such networks. All the Cascade volcanoes have high snowfall, and bench marks are subject to severe freeze-thaw conditions. When establishing the networks, the best bench-mark location available at the time was chosen; in some cases this choice was dependent on the snowpack and led to incorrect assessment of bench-mark stability. Mount Rainier proveds a good example of such a problem.

The network at Mount Rainier (fig. 10.6A) was established in 1982 and partially reoccupied in 1983. No major changes were seen during this interval. In 1988, a portion of the network was once again measured and larger than expected changes were seen on distances to several bench marks in an area where glacial-outburst flooding had periodically occurred since 1987 (T.Pierson, CVO, written commun., 1987). The distance to one reflector station high on the cone (station 13 in figure 10.6A) had contracted 20 centimeters. Stations 14 and 15, both measured from Iron Mountain, had moved -0.036 and 0.057 meters, respectively. We were uncertain is actual deformation was taking place, so the entire network was again measured in 1989. When the network was initially installed in 1982, the rock that contains bench mark 13 was mostly buried in snow and appeared to be solid. In 1989, after a winter with low snowfall, the person who installed the bench mark noted that the snow had melted away from the rock containing the bench mark, revealing that the rock was simply a loose slab lying on a rather steep slope and was clearly not stable. Data from the rest of the 1989 survey, stations 14 and 15 included, ware within the expected error of the 1982 and 1983 surveys.

Potential bench-mark instability must be carefully watched. Instability can lead to large changes that may be interpreted as volcanic deformation. If there is no seismic activity and apparent deformation is seen, we look at the data very critically and do not accept them until the network ahs been reoccupied again and examined for bench-mark instability or atmospheric problems.

     2612.3428        2612.3425        -.0003     -0.11
     5142.2388        5142.2304        -.0084     -1.63
     3787.7485        3787.7478        -.0007     -0.18
     4567.9478        4567.9472        -.0006     -0.13
     3229.0068        3229.0069         .0001      0.03
     3155.4868        3155.4855        -.0013     -0.41
     3994.7571        3944.7550        -.0021     -0.53
     3134.0022        3134.0064         .0042      1.34
     2073.8518        2073.8512        -.0006     -0.29
     3559.6423        3559.6407        -.0016     -0.45
     4558.1172        4558.1149        -.0023     -0.50
     3241.0857        3241.0888         .0031      0.96
     3243.4739        3243.4814         .0075      2.31
     3823.2954        3823.2971         .0017      0.44
     5079.7373        5079.7372        -.0001     -0.02
     6681.5571        6681.5542        -.0029     -0.43
     6101.5864        6101.5870         .0006      0.10
     6391.9248        6391.9245        -.0003     -0.05
     7573.0171        7573.0166        -.0005     -0.07
     4461.7808        4461.7804        -.0004     -0.09
     3502.0552        3502.0570         .0018      0.52
     4507.9756        4507.9696        -.0006     -0.13
     2814.4336        2814.4325        -.0011     -0.39
     3014.4924        3014.4950         .0026      0.86
     2717.0093        2717.0099         .0006      0.22

Summary

Baseline horizontal-distance data have been collected on many potentially active volcanoes. We have saved considerable time and money by continually improving monitoring methods without compromising the data. We have seen that, despite care during installation, bench-mark instability remains a problem and could potentially be misinterpreted as real deformation.

The equipment and methods described in this paper are more than adequate to meet the precision for baseline data. Equipment and methods will no doubt continue to improve over the years, and as networks are reoccupied the baseline data on volcanoes in the Pacific Coast states will also continue to improve, statistically.

The intent of this paper was to describe the equipment and methods used at CVO to monitor volcanoes. We hope that this may serve as a guide for establishing equipment needs, methods, and procedures for similar projects elsewhere.

Acknowledgments

We thank Teresa Atwill, Steve Brantley, Ed Brown, Ken Cameron, Tom Casadevall, Bill Chadwick, Dan Dzurisin, John Ewert, Christina Heliker, Dan Johnson, Jack Kleinman, Jeff Marso, Bobbie Myers, Peter Otway (New Zealand Geological Survey), John Power, Dave Schneider, Ben Talai (Rabaul Volcano Observatory, Papua New Guinea), Lyn Topinka, Richard Waitt, Dave Wieprecht, Ed Wolfe, and Jon and Ken Yamashita for their help at one or more volcanoes. Special thanks go to Lyn Topinka for the majority of the photography, Tom Murray for electronic guidance, and Elliot Endo for computer programming. We also thank the many helicopter pilots who made it possible to complete these measurements.

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