5:15 PM - 7:15 PM
[SGD02-P01] A Stable and Precise Computational Method for the Analytical Downward Continuation of Helmert Gravity Anomalies
Keywords:Geoid, Gravity, Downward Continuation
The procedure for reducing gravity anomaly values observed on or above the Earth's surface into those on the geoid or ellipsoid is called "downward continuation." This procedure plays a crucial role in determining geoid undulations and estimating the Earth's internal structure based on gravimetric methods. Methods for calculating downward continuation widely include the analytical approach using Taylor series expansion (Moritz, 1980) and the numerical approach based on the Poisson integral formula (Vaníček et al., 1996). The former is referred to as "analytical downward continuation," while the latter is called "Poisson downward continuation."
Downward continuation is known to be a mathematically ill-posed problem. In particular, the amplification of short-wavelength noise poses a significant challenge, necessitating calculations to be performed under optimal conditions. For example, Martinec (1996) demonstrated that in regions with steep terrain, such as the Canadian Rocky Mountains, setting the gravity anomaly grid spacing (grid step size) to 5 arcseconds (approximately 9 km) or larger enables stable downward continuation calculations. Similarly, Goli (2024) investigated the stability of analytical down continuation for free-air gravity anomalies in Iran and its surrounding areas. They found that calculations diverge easily with a grid spacing of 1 arcsecond (approximately 2 km), whereas a grid spacing of 2 arcseconds (approximately 4 km) maintains stability even at different noise levels.
In this study, we aimed to enhance gravimetric geoid computation based on the Stokes-Helmert method by examining optimal downward continuation methods for Helmert gravity anomalies using analytical downward continuation. The study focused on the following four factors: (1) condensation depth of topography, (2) the order of Taylor series expansion, (3) the presence or absence of iterative computation, and (4) the resolution of the gravity grid used in calculations. The methodology involved performing downward continuation calculations of Helmert gravity anomalies under various settings for these factors, followed by gravimetric geoid computation based on the results. The computed geoid was then compared with GNSS/leveling geoid data to evaluate consistency and identify the optimal settings for each factor. The study region selected for this evaluation was the state of Colorado, USA, where high-quality gravity data and reference geoid data are available.
As a result of the evaluation, the most stable and precise results were obtained under the following conditions: (1) condensation depth of topography = 0 km, (2) Taylor series expansion order = 3, (3) iterative computation enabled, and (4) gravity grid spacing = 5 arcseconds (approximately 9 km). The reasons for these results include: (1) minimization of indirect effects, (2) and (3) proper amplification of short-wavelength signals, and (4) mitigation of short-wavelength noise divergence. However, these optimal conditions depend on the topographic characteristics of the target region and the quality of the available gravity data. Therefore, it is necessary to explore optimal settings for each specific region.
Downward continuation is known to be a mathematically ill-posed problem. In particular, the amplification of short-wavelength noise poses a significant challenge, necessitating calculations to be performed under optimal conditions. For example, Martinec (1996) demonstrated that in regions with steep terrain, such as the Canadian Rocky Mountains, setting the gravity anomaly grid spacing (grid step size) to 5 arcseconds (approximately 9 km) or larger enables stable downward continuation calculations. Similarly, Goli (2024) investigated the stability of analytical down continuation for free-air gravity anomalies in Iran and its surrounding areas. They found that calculations diverge easily with a grid spacing of 1 arcsecond (approximately 2 km), whereas a grid spacing of 2 arcseconds (approximately 4 km) maintains stability even at different noise levels.
In this study, we aimed to enhance gravimetric geoid computation based on the Stokes-Helmert method by examining optimal downward continuation methods for Helmert gravity anomalies using analytical downward continuation. The study focused on the following four factors: (1) condensation depth of topography, (2) the order of Taylor series expansion, (3) the presence or absence of iterative computation, and (4) the resolution of the gravity grid used in calculations. The methodology involved performing downward continuation calculations of Helmert gravity anomalies under various settings for these factors, followed by gravimetric geoid computation based on the results. The computed geoid was then compared with GNSS/leveling geoid data to evaluate consistency and identify the optimal settings for each factor. The study region selected for this evaluation was the state of Colorado, USA, where high-quality gravity data and reference geoid data are available.
As a result of the evaluation, the most stable and precise results were obtained under the following conditions: (1) condensation depth of topography = 0 km, (2) Taylor series expansion order = 3, (3) iterative computation enabled, and (4) gravity grid spacing = 5 arcseconds (approximately 9 km). The reasons for these results include: (1) minimization of indirect effects, (2) and (3) proper amplification of short-wavelength signals, and (4) mitigation of short-wavelength noise divergence. However, these optimal conditions depend on the topographic characteristics of the target region and the quality of the available gravity data. Therefore, it is necessary to explore optimal settings for each specific region.