A Taiwan Airborne Gravity Survey

To obtain this solution, the standard stochastic model of the GPS-phase observables was used (Seeber, 2003). In this case, the double-differenced phase observables between the aircraft and the eight tracking stations are selected and used to obtain the final coordinates. The initial values of the kinematic positions (parameter subset x₂) are required for the linearization of the nonlinear GPS observation equations.

5.3 A Taiwan Airborne Gravity Survey 5.3.1 Survey Campaign

The survey lines are shown in Fig 5-1(a). These lines consist of 64 north–south, 22 east–west, 10 northeast–southwest, and 6 northwest–southeast oriented lines with a spacing of 4.5 km, 20 km, 5 km, and 30 km, respectively. The west–east and northwest–southeast lines are mainly used for crossover analyses. The survey area covers the whole of Taiwan Island and its offshore regions. The survey area is approximately 75,000 km² and the total distance covered by the survey lines is approximately 53,000 km.

A scalar-type gravimeter called LaCoste and Romberg (LCR) Air-Sea Gravity System II (serial number: S-133) (Fig 5-1(b)) mounted on a laser gyro-stabilized platform is used to record the airborne gravity data at 1 Hz. This gravimeter has a resolution of 0.01 mgal and an accuracy of 1 mgal, as seen from the shipborne test (LCR, 2003). It uses spring tension and beam velocity measurements to obtain the relative gravity variations. Additional information on the Air-Sea Gravity System II gravimeter is summarized in Table 5-1. The gravimeter is placed in a medium-size

aircraft, Beechcraft-200 (Fig 5-1(c)), flying at an average altitude of 5156 m (The spatial resolution is approximately 6 km (Torge, 1989)) at a mean ground speed of approximately 306 km/h. Both the airborne gravimeter and aircraft belong to the Ministry of the Interior, Taiwan.

The King-Air Beechcraft-200 is equipped with a Trimble 5700 GPS receiver (Fig 5-1(d)) that samples data at 2 Hz. For the kinematic positioning of the aircraft, eight ground-based GPS reference stations (Fig 5-1(a)) around Taiwan are used to determine the kinematic solutions. The eight stations are YMSM, SNAM, KDNM, PKGM, TMAM, FLNM, KMNM, and MZUM. The sampling rate of these reference stations is 2 Hz except that of SNAM station, which is 1 Hz. CCK, shown in Fig 5-1(a), is the Taichung airport, where aircraft take off and landing occurred.

The reference gravity value can be determined by a land gravimeter based on the absolute gravity reference points at the Taichung FG5 (Micro-g, 1999) absolute gravity station. The gravity value at the aircraft parking spot was recorded using a Graviton-EG gravimeter (LCR, 2002). The standard error of this gravity value is 0.04 mGal based on the relative gravity network adjustment. A number of gravity base readings of the airborne gravity system need to be obtained during the field survey period to obtain a smooth drift of the airborne gravimeter.

The airborne gravity survey was carried out from May 2004 to May 2005. The survey took 43 days, including 3 days of re-flights where bad data were found. The number of flight hours exceeds 200.

Table 5-1 Overview of the L & R Air-Sea Gravity System II Resolution 0.01 mGal

Accuracy <1.00 mGal Size 71 × 56 × 84 cm

Weight 116 kg

Power supply 240 W (avg), 450 W (max) Sampling rate 1 Hz

(a) (b)

(c) (d)

Fig. 5-1 (a) Airborne gravity survey lines and GPS tracking stations (solid circles) for precise aircraft positioning. The star represents the Taichung (CCK) airport, where the King-Air Beechcraft-200 is based. (b) The L&R Air-Sea Gravity System II gravimeter and (c) the King-Air Beechcraft-200 aircraft; the circle denotes the antenna. (d) Inside of the King-Air Beechcraft-200; the L&R Air-Sea Gravity System II and Trimble 5700 are mounted inside the aircraft.

5.3.2 Data Processing

Kinematic GPS solutions are obtained by using the combination of eight different GPS based stations and processed using Bernese 5.0 (Beutler et al., 2004) and the IGS precise ephemeris ( http://igscb.jpl.nasa.gov/ ). In order to determine the velocity and acceleration of the aircraft, we use the program DERIV of the International Mathematical and Statistical Library (IMSL) to perform the numerical differentiations. DERIV first computes the spline interpolants to the input functions (i.e., coordinate components x, y, and z) and then differentiates the spline interpolants to obtain their derivatives (Hwang et al., 2006b). Following the GPS procedure, two data processing techniques have to be considered: correction for time shift and filtering of raw gravity observations.

The time systems of the raw GPS and the gravimeter observations are inconsistent. The gravimeter time associated with a gravity reading is obtained from the clock of the computer attached to the gravimeter. Therefore, the gravimeter is not synchronous with the GPS clock and requires correction. In order to synchronize the two time systems, the time series of the raw gravity reading and vertical aircraft acceleration can be used (Olesen, 2003). Because gravity signals are much smaller than the vertical accelerations of the aircraft in common weather conditions, most raw readings recorded by the gravimeter are those of the vertical accelerations of the aircraft. Thus, the patterns of the raw gravity readings of the gravimeter and vertical acceleration readings of the GPS receiver are very similar. According to this characteristic, the shift between these two time series can be determined using a correlation analysis (Hwang et al., 2006b).

It is necessary to use an along track filter for raw airborne gravity data containing considerable noise due to turbulence. We use a Gaussian filter with a filter width of 150 s to eliminate high-frequency signals. The chosen filter width is a trade-off between noise reduction and gravity signal preservation and is proved to be the optimum width in the latter part of this study.

A description of the software that fulfils many of the requirements summarized above can be found in Shih (2004), Hwang (2005), and Hwang et al. (2006b and 2007b). The procedure for the airborne data processing is summarized in Fig 5-2.

Fig. 5-2 Flow chart of the airborne gravity data process implemented by NCTU. f , _x f , and n f are the three components of the gravimeter measurements. _u

ϕ

represent the three components of the velocities and accelerations of the aircraft, respectively. g is the output gravity at the flight altitude.

Airborne gravimeter

GPS receiver

f ,x f ,_n f _u

ϕ

‧Bernese software

‧IGS precise ephemeris

ϕ_& λ& h&

ϕ&& λ&& h&&

Numerical differential

g

‧Time-shift adjustment

‧Eto&&vo&&s correction

‧Tilt correction