The Spectral Analysis and Application of Low-degree Modified Spheroidal Hotine Kernel

The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modified is introduced in this research,which is exampled by the Hotine kernel.In addition,the low-degree modified spheroidal kernel is proposed.Either cosine or linear modification factors can be utilized.The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel.Furthermore,the modified kernel augments the contribution rate of the measured data to height anomaly in the modified frequency domain.The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel.And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high-and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same.Since the computational efficiency of the low-degree modified kernel is much higher,the low-degree modified kernel behaves better in constructing the(quasi-)geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.

Low-degree toroidal modes from the Sumatra-Andaman event observed by superconducting gravimeters

The complex frequencies of the low-degree toroidal modes are helpful in constraining the mantle structure.In the early years,the traditional method to detect the low-degree toroidal modes is seismic approach,which is primarily limited by the horizontal noise of seismometers.Recently,it has been proved that gravity method is competitive.Therefore,we re-estimated or newly estimated the complex frequencies of the toroidal modes below 1.5 mHz excited by the 2004 Sumatra-Andaman event using gravity method in this paper.The results show that(1)The quality factors of0 T5-0 T9 and1 T2-1 T3 are estimated from superconducting gravity data for the first time;(2)The estimated frequencies and quality factors for0 T2-0 T9 and1 T2-1 T3 are consistent with those provided by previous publications,which verifies the correctness and effectiveness of our estimations;(3)The maximum difference of frequencies between our results and those from CPREM is on the order of 0.01 mHz and the maximum difference of quality factors is at the level of 10.

Effect of low-degree astigmatism on the objective visual quality

AIM:To evaluate the effect of low-degree astigmatism on objective visual quality through the Optical Quality Analysis System(OQAS).METHODS:This study enrolled 46 participants(aged 23 to 30y,90 eyes)with normal or corrected-to-normal vision.The cylindrical lenses(0,0.5,0.75,1.0,and 1.25 D)were placed at the axial direction(180°,45°,90°,and 135°)in front of the eyes with the best correction to form 16 types of regular low-degree astigmatism.OQAS was used to detect the objective visual quality,recorded as the objective scattering index(OSI),OQAS values at contrasts of 100%,20%,and 9%predictive visual acuity(OV100%,OV20%,and OV9%),modulation transfer function cut-off(MTFcut-off)and Strehl ratio(SR).The mixed effect linear model was used to compare objective visual quality differences between groups and examine associations between astigmatic magnitude and objective visual quality parameters.RESULTS:Apparent negative relationships between the magnitude of low astigmatism and objective visual quality were observed.The increase of OSI per degree of astigmatism at 180°,45°,90°,and 135°axis were 0.38(95%CI:0.35,0.42),0.50(95%CI:0.46,0.53),0.49(95%CI:0.45,0.54)and 0.37(95%CI:0.34,0.41),respectively.The decrease of MTFcut-off per degree of astigmatism at 180°,45°,90°,and 135°axis were-10.30(95%CI:-11.43,-9.16),-12.73(95%CI:-13.62,-11.86),-12.75(95%CI:-13.79,-11.70),and-9.97(95%CI:-10.92,-9.03),respectively.At the same astigmatism degree,OSI at 45°and 90°axis were higher than that at 0°and 135°axis,while MTFcut-off were lower.CONCLUSION:Low astigmatism of only 0.50 D can significantly reduce the objective visual quality.