The use of different spherical radial basis functions to combine terrestrial and airborne measurements for regional gravity field refinement

2020 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Laura Sánchez
Keyword(s):  
Gravity Data ◽  
Basis Functions ◽  
Airborne Gravity ◽  
Shannon Function ◽  
Airborne Measurements ◽  
Different Types ◽  
Low Pass ◽  
Spherical Radial Basis Functions ◽  
Regional Gravity ◽  
Terrestrial Data

<p>The objective of this study is the combination of different types of basis functions applied separately to different kinds of gravity observations. We use two types of regional data sets: terrestrial gravity data and airborne gravity data, covering an area of about 500 km × 800 km in Colorado, USA. These data are available within the “1 cm geoid experiment” (also known as the “Colorado Experiment”). We apply an approach for regional gravity modeling based on series expansions in terms of spherical radial basis functions (SRBF). Two types of basis functions covering the same spectral domain are used, one for the terrestrial data and another one for the airborne measurements. To be more specific, the non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The Cubic Polynomial (CuP) function is applied to the airborne data as a low-pass filter, and the smoothing features of this type of SRBF are used for filtering the high-frequency noise in the airborne data. In the parameter estimation procedure, these two modeling parts are combined to calculate the quasi-geoid.</p><p>The performance of our regional quasi-geoid model is validated by comparing the results with the mean solution of independent computations delivered by fourteen institutions from all over the world. The comparison shows that the low-pass filtering of the airborne gravity data by the CuP function improves the model accuracy by 5% compared to that using the Shannon function. This result also makes evident the advantage of combining different SRBFs covering the same spectral domain for different types of observations.</p>

scholarly journals Regional gravity field refinement for (quasi-) geoid determination based on spherical radial basis functions in Colorado

2020 ◽  
Vol 94 (10) ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Laura Sánchez ◽  
Martin Willberg
Keyword(s):  
Gravity Data ◽  
Basis Functions ◽  
Height Anomaly ◽  
Shannon Function ◽  
Validation Data ◽  
Topographic Model ◽  
Spherical Radial Basis Functions ◽  
The Mean ◽  
Rms Error ◽  
Terrestrial Data

Abstract This study presents a solution of the ‘1 cm Geoid Experiment’ (Colorado Experiment) using spherical radial basis functions (SRBFs). As the only group using SRBFs among the fourteen participated institutions from all over the world, we highlight the methodology of SRBFs in this paper. Detailed explanations are given regarding the settings of the four most important factors that influence the performance of SRBFs in gravity field modeling, namely (1) the choosing bandwidth, (2) the locations of the SRBFs, (3) the type of the SRBFs as well as (4) the extensions of the data zone for reducing the edge effect. Two types of basis functions covering the same spectral range are used for the terrestrial and the airborne measurements, respectively. The non-smoothing Shannon function is applied to the terrestrial data to avoid the loss of spectral information. The cubic polynomial (CuP) function which has smoothing features is applied to the airborne data as a low-pass filter for filtering the high-frequency noise. Although the idea of combining different SRBFs for different observations was proven in theory to be possible, it is applied to real data for the first time, in this study. The RMS error of our height anomaly result along the GSVS17 benchmarks w.r.t the validation data (which is the mean results of the other contributions in the ‘Colorado Experiment’) drops by 5% when combining the Shannon function for the terrestrial data and the CuP function for the airborne data, compared to those obtained by using the Shannon function for both the two data sets. This improvement indicates the validity and benefits of using different SRBFs for different observation types. Global gravity model (GGM), topographic model, the terrestrial gravity data, as well as the airborne gravity data are combined, and the contribution of each data set to the final solution is discussed. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the height anomaly result w.r.t the validation data drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data. Comparisons with the mean results of all the contributions show that our height anomaly and geoid height solutions at the GSVS17 benchmarks have an RMS error of 1.0 cm and 1.3 cm, respectively; and our height anomaly results give an RMS value of 1.6 cm in the whole study area, which are all the smallest among the participants.

The combination and contribution of different gravity measurements in regional quasi-geoid determination based on spherical radial basis functions

2021 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Laura Sánchez
Keyword(s):  
Radial Basis Functions ◽  
Gravity Data ◽  
Basis Functions ◽  
Airborne Gravity ◽  
Frequency Noise ◽  
Geoid Model ◽  
Topographic Model ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Terrestrial Data

<p>In this study, we investigate the optimal combination of local gravity observations and their contributions to the regional quasi-geoid model. The study area is located in Colorado, USA, with two types of regional data sets, namely terrestrial gravity data and airborne gravity data, available within the “1 cm geoid experiment”. The approach based on series expansions in terms of spherical radial basis functions (SRBF) is applied, which has been developed at DGFI-TUM in the last two decades. We use two different types of basis functions covering the same spectral domain separately for the terrestrial and the airborne measurements. The Shannon function is applied to the terrestrial data, and the Cubic Polynomial (CuP) function which has smoothing features is applied to the airborne data for filtering their high-frequency noise.</p><p>To assess the contributions of the regional terrestrial and airborne gravity data to the final quasi-geoid model, four solutions are compared, namely the combined solution, the terrestrial only, the airborne only, and finally the model only solution, i.e., only the global gravity model and the topographic model are used without any gravity data from regional measurements. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the quasi-geoid model w.r.t the validation data (the mean solution of independent computations delivered by fourteen institutions from all over the world) drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data.</p>

Study on Elliptic Filters in Airborne Gravity Data Processing

2013 ◽  
Vol 341-342 ◽  
pp. 999-1004
Author(s):  
Wei Zhou ◽  
Ti Jing Cai
Keyword(s):  
Data Processing ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Optimal Parameters ◽  
Evaluation Indicator ◽  
Filter Order ◽  
Upper Limit ◽  
Optimal Value ◽  
Low Pass ◽  
Stopband Attenuation

For low-pass filtering of airborne gravity data processing, elliptic low-pass digital filters were designed and filtering influences of the elliptic filter order, upper limit passband frequency, maximal passband attenuation and minimal stopband attenuation were studied. The results show that the upper limit passband frequency has the greatest effect on filtering among four parameters; the filter order and the maximal passband attenuation have some influence, but instability will increase with larger order; the effect of the minimal stopband attenuation is not obvious when reaching a certain value, which requires a combination of evaluation indicator accuracy to determine the optimal value. The standard deviations of discrepancies between the elliptic filtered gravity anomaly with optimal parameters and the commercial software result are within 1mGal, and the internal accord accuracy along four survey lines after level adjusting is about 0.620mGal.

scholarly journals Airborne gravimetry: An investigation of filtering

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Vicki A. Childers ◽  
Robin E. Bell ◽  
John M. Brozena
Keyword(s):  
Gravity Data ◽  
Substantial Improvement ◽  
Airborne Gravity ◽  
Airborne Gravimetry ◽  
Pass Filter ◽  
Low Pass Filter ◽  
West Antarctic ◽  
Low Pass ◽  
Filter Approach ◽  
Gravity Signal

Low‐pass filtering in airborne gravimetry data processing plays a fundamental role in determining the spectral content and amplitude of the free‐air anomaly. Traditional filters used in airborne gravimetry, the 6 × 20-s resistor‐capacitor (RC) filter and the 300-s Gaussian filter, heavily attenuate the waveband of the gravity signal. As we strive to reduce the overall error budget to the sub-mGal level, an important step is to evaluate the choice and design of the low‐pass filter employed in airborne gravimetry to optimize gravity anomaly recovery and noise attenuation. This study evaluates low‐pass filtering options and presents a survey‐specific frequency domain filter that employs the fast Fourier transform (FFT) for airborne gravity data. This study recommends a new approach to low‐pass filtering airborne data. For a given survey, the filter is designed to maximize the target gravity signal based upon survey parameters and the character of measurement noise. This survey‐specific low‐pass filter approach is applied to two aerogravimetry surveys: one conducted in West Antarctica and the other in the eastern Pacific off the California coast. A reflight comparison with the West Antarctic survey shows that anomaly amplitudes are increased while slightly improving the rms fit between the reflown survey lines when an appropriately designed FFT filter is employed instead of the traditionally used filters. A comparison of the East Pacific survey with high‐resolution shipboard gravity data indicates anomaly amplitude improvements of up to 20 mGal and a 49% improvement of the rms fit from 3.99 mGal to 2.04 mGal with the appropriately designed FFT filter. These results demonstrate that substantial improvement in anomaly amplitude and wavelength can be attained by tailoring the filter to the survey.

scholarly journals Regularization methods for the combination of heterogeneous observations using spherical radial basis functions

2019 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Roland Pail ◽  
Martin Willberg
Keyword(s):  
Radial Basis Functions ◽  
Regularization Parameter ◽  
Basis Functions ◽  
Parameter Determination ◽  
Data Sets ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Ill Posed ◽  
Curve Method ◽  
Regional Gravity

Abstract. Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBF) for regional gravity field refinement. However, this process is in most cases ill-posed, and thus, regularization is indispensable. We discuss two frequently used methods for choosing the regularization parameter which are the L-curve method and variance component estimation (VCE). Based on these two methods, we propose two new approaches for the regularization parameter determination, which combine the L-curve method and VCE. The first approach, denoted as ‘VCE + L-curve method’, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights the L-curve method is applied to determine the regularization parameter. In the second approach, called ‘L-curve method + VCE’, the L-curve method determines first the regularization parameter and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. These methods are investigated based on two different estimation concepts for combining various observation techniques. All the methods are applied and compared in six study cases using four types of observations in Europe. The results show that the ‘VCE + L-curve method’ delivers the best results in all the six cases, no matter using SRBFs with smoothing or non-smoothing features. The ‘L-curve method + VCE’ also gives rather good results, generally outperforming the cases just using the L-curve method or VCE. Therefore, we conclude that the newly proposed methods are decent and stable for regularization parameter determination when different data sets are combined and can be recommended regardless of the type of SRBFs used.

scholarly journals DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

2021 ◽  
Vol 6 (24) ◽  
pp. 213-225
Author(s):  
Shazad Jamal Jalal ◽  
Tajul Ariffin Musa ◽  
Ami Hassan Md Din ◽  
Wan Anom Wan Aris
Keyword(s):  
Gravity Data ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Gravity Survey ◽  
Mountainous Areas ◽  
Entire Study ◽  
Terrestrial Gravity ◽  
The Past ◽  
Regional Gravity ◽  
Entire Study Area

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

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