GPH 492/692 Spring 2010 Field Exercise

GPH 492/692 Spring 2010 Field Exercise

Positional Survey Methods and Results

Jay Goldfarb

Courtney Murphy

Gary Richardson

Jason Henderson

The survey data for the gravity profiles is contained in the Excel workbook “SurveyData - rev 3.xls”.

Methods:

The first method we used to measure elevations for th Hidden Valley gravity points was trigonometric leveling, a conventional survey method, using a theodolite, range pole, and prism. We recorded both forward and reverse shots for each point to collect vertical data so as to cancel important systematic errors. We used this method to measure points HVG96 through HVG100A. In addition, we subsequently reoccupied several of these points with the Trimble ProXH mapping-grade GPS to verify point identification.

We collected th remaining points at Hidden Valley and on Prater Way using a Trimble ProXH in carrier-phase mode[1]. These data were post-processed differentially using data from continuously-operating reference stations downloaded via the internet.

We collected GPS data with the ProXH on one City of Sparks benchmark to provide another measure of survey quality.

Results:

The horizontal datum (for latitudes and longitudes) is World Geodetic System of 1984/North American Datum of 1983 (WGS84/NAD83). (For our purposes, these datums are the same.) The vertical datum (for orthometric heights) is the North American Vertical Datum of 1988 (NAVD88). Note that many older maps and reports are based on the National Geodetic

The “UTM” coordinates shown on the spreadsheets are based on the NAD27 datum. (By definition, UTM are based on NAD27.) Note that the conversion used to transform the WGS84/NAD83 latitudes and longitudes to NAD27 (NADCON) is not intended to preserve survey accuracy but is instead intended for mapping applications. The proper way to establish coordinates in a particular datum is to occupy control points which have

The (average) standard deviation of the errors for the theodolite for the Hidden Valley measurements HVG96- HVG100A was 0.06 meters. This was determined by computing the absolute differences between the forward and the reverse shots measured with the theodolite and then taking the standard deviation of the difference. The maximum elevation error from the theodolite measurements was 0.20 meters.

The total error in the orthometric heights given in the spreadsheets is the result of a number of sources. The important sources of error in the trigonometric leveling are (in approximate decreasing order of importance) are:

• random and unaccounted-for systematic errors in measurements
• failure to account for earth curvature
• atmospheric refraction

Curvature and refraction effects in our survey are negligible. Our longest sight line did not exceed 500 m, and the total correction for earth curvature and refraction over this distance would be less than two centimeters.

The important factors contributing to errors in GPS-derived heights are

• satellite geometry (as reflected by Dilution of Precision or DOP factor)
• uncertainties in geoid model (used to convert ellipsoid heights to
• receiver noise
• multipath

The “SigmaH GPS” values shown in the spreadsheet only predict the uncertainty in the GPS ellipsoid heights (at a 68.3% confidence level). There is additional uncertainty inherent in the conversion from ellipsoid to orthometric height. Nevertheless, because the geoid is so flat in this area (as evidenced by the near-constant calculated geoid heights), this should not contribute more than a centimeter or so to the total uncertainty. (Note that that geoid model uncertainties also contribute to the errors in the calculated heights for the conventionally-surveyed points because the elevation of the initial control point for this survey was determined using GPS.)

For the purpose of characterizing the predicted vertical accuracy, the surveyed gravity stations can be divided into three groups:

1. The upper Hidden Valley points (#96-108) from the eastern limit of the residential area to the highest point on the hillside: These elevations were determined by trigonometric leveling. The elevation of the initial control point was determined by GPS under relatively-good satellite geometry (relatively low GDOP). Based on the single estimated GPS elevation uncertainty and on the spread between the forward and direct total-station elevation difference readings at station, we estimate the vertical accuracy for this group of stations to be between 10-20 centimeters at the one-sigma (68.3%) confidence level. Because there is insufficient redundancy in the data to obtain a rigorous statistical estimate of precision, these values reflect judgment based on our experience in surveying.
2. The lower Hidden Valley points (#65-95) – from McCarran Boulevard to the eastern limit of the residential area: Based on the precision estimates from the GPS processing, we estimate the vertical accuracy for this group of stations to be between 10-25 centimeters, one-sigma.
3. All points along Prater Way: Based on the precision estimates from the GPS processing, we estimate the vertical accuracy for this group of stations to be between 45-75 centimeters, one-sigma. This lower accuracy is due to the poorer satellite geometry which was present during the afternoon survey.
4. City gravity reference points: Based on the precision estimates from the GPS processing, we estimate the vertical accuracy for this group of stations to be between 20-55 centimeters, one-sigma. The lower-accuracy points were those collected in the afternoon. Note that these values have an additional, unknown, error due to the fact that the location of the original points is not well known.

Errors in horizontal position and in elevation propagate into errors in calculated anomalous gravity. In this survey, the effect of horizontal position errors is negligible. The horizontal effect is due to the variation of gravity due to centripetal acceleration, which depends only on latitude. Using the Geodetic Reference System (GRS) International Gravity Formula (IGF)

where g0 is normal gravity in gals and  is the latitude, we calculate that an error in latitude of 30 meters results in an error in calculated normal gravity of less than 0.001 milligals at Reno's latitude, which is well below the effective resolution of our gravity meter.

Differences in vertical position have much more influence on calculated gravity than do differences in horizontal position. Based on the simple formla

where dg is gravity in milligals and  is an average crustal density (taken here to be 2.67 grams per cubic centimeter) an elevation error of 20 centimeters results in a gravity error of 0.04 milligals, while an elevation error of 75 centimeters results in a gravity error of 0.15 milligals.

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[1]From the information provided in Trimble's white paper on the ProXH, it is not clear whether the unit uses true carrier-phase data or instead uses less-precise carrier-smoothed pseudorange data.