Abstract
Gravity surveys are an important research topic in geophysics and geodynamics. This paper investigates a method for high accuracy large scale gravity anomaly data reconstruction. Based on the airborne gravimetry technology, a flight test was carried out in China with the strap-down airborne gravimeter (SGA-WZ) developed by the Laboratory of Inertial Technology of the National University of Defense Technology. Taking into account the sparsity of airborne gravimetry by the discrete Fourier transform (DFT), this paper proposes a method for gravity anomaly data reconstruction using the theory of compressed sensing (CS). The gravity anomaly data reconstruction is an ill-posed inverse problem, which can be transformed into a sparse optimization problem. This paper uses the zero-norm as the objective function and presents a greedy algorithm called Orthogonal Matching Pursuit (OMP) to solve the corresponding minimization problem. The test results have revealed that the compressed sampling rate is approximately 14%, the standard deviation of the reconstruction error by OMP is 0.03 mGal and the signal-to-noise ratio (SNR) is 56.48 dB. In contrast, the standard deviation of the reconstruction error by the existing nearest-interpolation method (NIPM) is 0.15 mGal and the SNR is 42.29 dB. These results have shown that the OMP algorithm can reconstruct the gravity anomaly data with higher accuracy and fewer measurements.
Highlights
The Earth’s gravity field is a fundamental physical field, which reflects the distribution, motion and variety of the Earth’s interior matter
Equation (2) is an equivalent form of Equation (1), where g is the gravity anomaly to be determined, vD is the vertical component of the vehicle acceleration obtained from GPS, f D is the vertical component of the specific force measured by the accelerometers of an inertial measuring unit, f D0 is the vertical component of the specific force obtained from the static data on the parking apron, called base reading, g b is the gravity of reference point on the parking apron and aE includes all kinds of the error correction [16]
This paper has presented a new investigation on a method for high accuracy large scale gravity anomaly data reconstruction
Summary
The Earth’s gravity field is a fundamental physical field, which reflects the distribution, motion and variety of the Earth’s interior matter. Gravity surveys can support fundamental geophysical investigations, which are beneficial to determine the density of the Earth’s interior matter and help explain many physical phenomena of the Earth. Candès, Romberg, Tao and Donoho showed that a signal having a sparse representation can be reconstructed from a small set of linear, non-adaptive measurements [7,8,9,10,11] This result suggests that it may be possible to sense sparse signals by taking far fewer flight measurements, and such as a method is named Compressed Sensing (CS). Taking into account the sparsity of airborne gravimetry by DFT, this paper firstly proposes a method for the reconstruction of gravity anomaly data using the CS theory. Shown that the OMP algorithm can reconstruct the gravity anomaly data with higher accuracy and fewer measurements than existing methods
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