High-resolution regional gravity field model of Pakistan based on best residual terrain model (RTM) of topography and interpolation techniques

Abstract

This study focuses on the development of absolute gravity model for Pakistan based on best possible residual terrain model of gravity using residual terrain modeling technique. The datasets used for the development of model are observed gravity, global gravity models, and Shuttle Radar Topographic Mission (SRTM30) elevation data. The residual terrain modeling technique has been used in the remove-restore procedure for smoothing the observed gravity field. Different topographic elevation models were tested in the model selection and one best possible model with minimum mean and standard deviation was selected for residual terrain effects. Least square collocation technique has been used for quality control and error estimates. The best possible covariance model was established from residual gravity for onward prediction of gravity anomalies at the earth surface for error and prediction analysis. The residual terrain effect of gravity, value of free air anomaly from EGM96, and observed free air anomaly are added to normal gravity to compute the absolute gravity at earth surface. The prediction of these parameters is made by employing Lagrange interpolation with least square adjustment. The results are compared with ∼5% randomly selected data points not utilized for the development of covariance function and/or model development. Spline interpolation technique has also been used for the prediction of gravity field-related parameters. Lagrange interpolation exhibits relatively superior results over spline-based interpolation. This is as per expectation due to the reason that additional gridding for spline interpolation filters the signal part as well. This fact is evident from the results of spline interpolation of Grid-I and Grid-II with relatively better prediction results in Grid-I. This version of the model is capable of prediction having limiting error of 30 mGal. The predicted results show that 96.16% of prediction data falls within above-mentioned limit with Lagrange interpolation technique with least square adjustment for whole Pakistan area. The adverse effect of gridding is absent in case of Grid-I due to relatively flat areas and predicted data matches totally with control values for both spline as well as Lagrange interpolations. However, in case of Grid-II which includes high mountains of Himalaya, gridding effect is present and the accuracy of the predicted results falls to ∼92%. The computed results have been compared with absolute values predicted using EGM96 and EGM2008 models as well. The gravity field recovered with PAKGM model is much better, i.e., ∼ 96.16%, than both with EGM96 and EGM2008 which is about 85% only.