Hao Ding

• PhD
• Wuhan University

Low-frequency signals play an important role in understanding sea level changes and their acceleration. This paper analyzed multidecadal oscillations on a global scale with tide gauge records. A significant stable oscillation of approximately 64 years was identified at 177 globally distributed tide gauges, with an estimated period of 63±4 yr. The a...

The spatiotemporal characteristics of the Antarctic ice sheet (AIS), as constrained by geodetic observations, provide us with a deeper understanding of the current evolution of ice mass balance. However, it still needs further in-depth research on interannual fluctuations and long-term trends of ice mass changes throughout the AIS (Antarctic Ice Sh...

Parameters of mantle anelasticity are crucial for understanding and recognizing the dynamic processes of Earth’s interior and energy dissipation mechanism. So far, the anelastic parameters of the lower mantle mainly rely on inversion and constraints of geodetic observations such as long-period body tides and pole tides; however, there are still obv...

Intradecadal changes in GPS displacements have garnered significant attention within the research community; however, the existence of relatively stable intradecadal signals, as well as their characteristics and excitation sources, remains to be further confirmed. This study aims to comprehensively investigate this topic by reviewing relevant exist...

Numerous practical geodetic and geophysical applications necessitate precise measurements of GNSS displacements at the millimeter or sub-millimeter level. To attain such precision, it is imperative to identify and analyze the unidentified decadal signals inherent in the GPS displacements. In this research, we employ the optimal sequence estimation...

This RAR document contains 5 separate files and is primarily designed to reproduce the result of the 5.9yr signal given in Ding et al. (2024; Science Bulletin; https://doi.org/10.1016/j.scib.2024.03.015). It contains the~5.9yr sequence extracted from LOD and the 43 used surface geomagnetic records which have been filtered and sorted into the availa...

The Ordos block is an important active block in North China during the Cenozoic and modern tectonic activity. Based on a large amount of GPS observation data, an accurate and dense GPS velocity field of the Ordos block is calculated through frame transformation. The results indicate that the estimated internal principal tensile and compressive stra...

The presence of a static tilt between the inner core and mantle is an ongoing discussion encompassing the geodynamic state of the inner core. Here, we confirm an approximate 8.5 yr signal in polar motion is the inner core wobble (ICW), and find that the ICW is also contained in the length-of-day variations of the Earth’s rotation. Based on the dete...

Since the optimal sequence estimation (OSE) method was proposed, it has been proved by different research teams to be the optimal stacking method for dealing with array data and has been successfully applied in many geoscience studies. However, there are still questions about whether the results obtained by OSE are affected by aliasing caused by th...

This Matlab code is used to carry out the OSE method (vertical components).

****The reviewer must have seen this, so I close it now -2023/10/24**** !!!@ Given that AGU don't allow to publish those review comments and responses, I'll delete the attached file soon.@@@@@ In 2022, we initially submitted a manuscript to the Journal of Geophysical Research: Solid Earth (JGR-SE) to examine the absence of a ~5.9yr signal in GPS di...

Since there are complicated changes in the polar motion (PM) from sub-annual to decadal, precisely predicting it is challenging. Here, we provide an advanced multivariate algorithm by combining an iterative oblique singular spectrum analysis (IOSSA) with pseudo data (IOSSApd) and consider more periodic and quasi-periodic signals, especially long-pe...

This file contians two test codes and the g1.0 time series that used in <How to extract the ~64yr signal from the geomagnetic coefficient g10>

In Ding et al. (2021; JGR-SE), we have extracted a ~64yr signal from the Earth's magnetic field dipole change (i.e., the geomagnetic coefficient g 1,0). In that study, we used the normal Morlet wavelet (NMWT) spectrum to extract this oscillation and didn't give more details. Many researchers may not be very familiar with this method, or it is diffi...

Vertical land motion (VLM) involves complex nonlinear geophysical signals, including periodic oscillations and long-term trend. Analyzing the spatial variation characteristics of VLM at different timescales is of great scientific significance for studying the dynamics of mass migration in shallow and deep in the earth. In this study, long-term tren...

Global positioning system (GPS) vertical displacements measuring the elastic response of Earth’s crust to tectonic motion have been used to produce vertical velocity estimates. These accurate estimates require minimal contamination by non-tectonic deformations, mainly including atmospheric-oceanic-hydrologic mass loadings. However, the variability...

This is only a simple example code, we directly use three times zero-padding to enhance the AR-z spectrum (see D&C 2015). For how to implement stabilized AR-z, pls see DC2018. We note that the added noise levels for different frequency bands are very important! This process is similar to EEMD, but the noise level needs to be determined by Fourier s...

To analyze quasi‐periodic signals (with time‐varying complex amplitudes/frequencies) typically contained in geophysical observables is a quest that has seen continual advances in numerical techniques over the decades. In this study, based on transient z‐pole estimation (in Hankel matrices), a state‐space analysis referred to as Hankel Spectral Anal...

The uplift of the Tianshan and Pamir Mountains/Areas are caused by active intracontinental tectonic movements. The dynamic mechanism is controversial and has aroused great interest among scholars. In this study, we investigate the present three‐dimensional (3‐D) crustal deformation in the Tianshan and Pamir areas from multi‐geodetic observations fr...

Nonlinear trends (i.e., quadratic trends, usually defined as accelerations) in Antarctic ice mass loss due primarily to the complex climate warming forcing regimes have induced large uncertainty to future sea level projection. Here, we quantify the nonlinear and spatially varying mass losses in the Antarctic ice-sheet during the last two decades us...

High-precision gravity measurements provide an invaluable approach for exploring the interior of the Earth by detecting geodynamic phenomena generated by different physical processes. China has established a very extensive and diverse gravity observation network, including high-precision superconducting gravimeters, gPhones, and other kinds of grav...

The signal leakage effect in the use of the Gravity Recovery and Climate Experiment (GRACE) level‐2 products limits the accuracy of the mass inversion, especially in small spatial scales (less than ∼100,000 km²). In this study, we try to use GRACE observation to evaluate the basin mass changes in Finland, where the basins are quite small (less than...

To analyze non-stationary harmonic signals typically contained in geophysical observables is a quest that has seen continual advances in numerical techniques over the decades. In this paper, based on transient z-pole estimation (in Hankel matrices), a novel state-space analysis referred to as Hankel Spectral Analysis (HSA), was developed. Depended...

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC (Monte Carlo), SUT (scaled unscented transformation), and SI (sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time,...

Earth's lithospheric deformation in response to geophysical and climatic processes manifests as a wide range of spatio-temporal elastic/viscoelastic deformation, including seismic and tectonic motion, mantle flow, and climate-induced hydrologic-cyrospheric-atmospheric mass transports. We use increasingly accurate contemporary geodetic measurements,...

The period and quality factor of the Chandler wobble (CW) are useful for constraining the Earth's internal structure properties, such as the mantle elasticity. It has been shown that the CW is mainly excited by a combination of atmospheric and oceanic processes; hence based on a deconvolution method, we can remove them from the excitation sequence...

We search in the continuous GPS 3-D displacement data for the signals of the normal modes of Earth’s free oscillation that were excited by the 2011 Mw 9.0 Tohoku earthquake. A previous study has reported such a detection; we here conduct a more comprehensive and detailed study. We use GPS data from three separate networks: (i) about 1000 stations f...

Global geophysical networks provide powerful databases to infer globally coherent signals, and array processing techniques are useful for inferring them. In this study, we comprehensively analyze seven spherical harmonic-based array processing techniques: spherical harmonic stacking (SHS) as well as its gridded form (SHS_GT) and grid-interval weigh...

Long‐period zonal tidal Love numbers are more sensitive to lower‐mantle anelasticity (which is difficult to determine even from laboratory); however, the Love numbers of the zonal tides have not been adequately determined. In this study, we use the optimal sequence estimation method with the Global Positioning System (GPS) displacements to estimate...

The multidecadal fluctuations in sea level changes play an important role in the exact quantification of present‐day global mean sea level (GMSL) rise and its acceleration. Here, we use an array processing technique (optimal sequence estimation) to analyze 44 global tide gauge (TG) sea‐level records with identical January 1933–December 2019 data sp...

Due to poor local accuracy and temporal resolution, the GIM (global ionospheric map) application continues to be of restricted use in obtaining the characteristics of seismic-ionospheric effects. Utilizing spherical harmonic (SH) function and generalized trigonometric series (GTS), the latest 15 min/map GIM with high precision released from the Chi...

The Global Positioning System (GPS) derived bedrock displacements respond to multiple geophysical effects, ranging from surface elastic loads to tectonic sources or viscoelastic uplifts stemming from Earth’s viscous mantle. In this study, the GPS‐inferred vertical crustal velocities are rigorously estimated in mainland China. We integrate the GPS v...

The intradecadal fluctuations in the length‐of‐day variation (∆LOD) are considered likely to play an important role in core motions. Two intradecadal oscillations, with ∼5.9 and ∼8.5 years periods (referred to as SYO and EYO, respectively), have been detected in previous studies. However, whether the SYO and the EYO have exhibited stable damping tr...

Abstract Adaptive and accurate trend estimation of the sea level record is critically important for characterizing its nonlinear variations and its study as a consequence of anthropogenic climate change. Sea level change is a nonstationary or nonlinear process. The present modeling methods, such as least squares fitting, are unable to accommodate n...

The intradecadal fluctuations in the length-of-day variation (∆LOD) are considered likely to play an important role in core motions. Two intradecadal oscillations, with ~5.9-year and ~8.5-year periods (referred to as SYO and EYO, respectively), have been detected in previous studies. However, whether the SYO and the EYO have had stable damping tren...

Abstract Global ocean mass (GOM) change, which is mainly influenced by water outflow from land, has been identified as one of the important contributors to present‐day sea level rise. Here, we delineated GOM change by dividing the land into five parts, which are exorheic river basins, endorheic basins, polar ice sheets, and land glaciers and ice ca...

To advance geodynamics and geophysical research, high precision Global Navigation Satellite System (GNSS) observations of velocity and position are needed. In this study, we construct a 3‐D model of a ~5.9‐year periodic signal for the Earth surface displacements. This model is mainly based on the determined time sequences and the Y22 spatial patter...

The density jump at the inner core boundary of the Earth is poorly constrained by seismic data. One sensitive measure of the jump is the eigenperiod of the inner core wobble (ICW). Although theoretical studies on the ICW have been ongoing for decades, no observed ICW signal has been reported. To increase the detection level, here we use a recently...

The present‐day deformation of the Tianshan Mountain range is largely resulting from the collision between India and the Eurasian plate, but the mechanism causing its uplift remains controversial. In this study, we present the contemporary tectonic and geodynamic processes resulting in the growth of the Tianshan Mountain range as revealed by integr...

The eigenperiods of the translational oscillation modes of the Earth’s solid inner core, also referred to as the Slichter modes or Slichter triplet, are the key parameters that constrain the density jump across the inner core boundary (ICB). Deinite observations of the Slichter triplet are still open. Here, we discuss and investigate this problem u...

Surface and deep potential geophysical signals respond to the spatial redistribution of global mass variations, which may be monitored by geodetic observations. In this study, we analyze dense Global Positioning System (GPS) time series in the Eastern Tibetan Plateau using principal component analysis (PCA) and wavelet time-frequency spectra. The o...

In contrast to most of the coseismic gravity change studies, which are generally based on data from the Gravity field Recovery and Climate Experiment (GRACE) satellite mission, we use observations from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) Satellite Gravity Gradient (SGG) mission to estimate the coseismic gravity and...

We carefully reanalyze the ∼6-yr oscillation (SYO), which has been previously found in the Earth's length of day variation (ΔLOD) and has been considered important for understanding the core–mantle interactions and core dynamics. Based on the Morlet wavelet and AR-z spectra of a long-period yearly ΔLOD record (1760–2018), we identify eight long per...

The AR-z spectrum devised in Ding and Chao (2015a) for analyzing harmonic signals (an extension of the frequency domain autoregressive AR algorithm developed by Chao and Gilbert (1980) based on Prony's method) proves to have significantly higher sensitivity and spectral resolution than the Fourier and maximum-entropy spectra, especially when the si...

Seeking geophysical explanations for the periodic ∼six-year oscillation (SYO) previously found in the Earth's length-of-day variation (ΔLOD), we analyze the global GPS displacement and geomagnetic data using the array processing technique of OSE (Optimal Sequence Estimation), and find clear evidences of the 6-yr signals which manifest as a westward...

The solid Earth deforms elastically in response to variations of surface atmosphere, hydrology, and ice/glacier mass loads. Continuous geodetic observations by Global Positioning System (CGPS) stations and Gravity Recovery and Climate Experiment (GRACE) record such deformations to estimate seasonal and secular mass changes. In this paper, we presen...

Using normal-mode summations we calculate the coseismic changes in a suite of global geodynamic quantities produced by all the 43,304 major earthquakes (above Mw 5) that occurred during 1976-2015 from the Global CMT catalogue. Here we focus in particular on the polar motion excitations due to the few greatest earthquakes in the 21st century. The lo...

Using normal-mode summations we calculate the coseismic changes in a suite of global geodynamic quantities produced by all the 43,304 major earthquakes that occurred during 1976-2015 from the Global CMT catalogue. We calculate changes for the Earth's inertia tensor elements and the ensuing Earth rotation variations, as well as the monopolar changes...

Modeling nonlinear vertical components of a GPS time series is critical to separating sources contributing to mass displacements. Improved vertical precision in GPS positioning at stations for velocity fields is key to resolving the mechanism of certain geophysical phenomena. In this paper, we use ensemble empirical mode decomposition (EEMD) to ana...

The Slichter mode is the triplet oscillational mode of the 3-D translation of the Earth's solid inner core; despite much effort it has so far eluded observation. Here we revisit the search by applying new data-processing methods upon the latest set of available superconducting gravimeter (SG) data. The new methods are the AR-z spectrum [Ding and Ch...

In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531 day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM seires (1962–1977) while cannot b...

We develop a new method referred to as the AR-z spectrum for detecting harmonic signals with exponential decay/growth contained in a noisy time-series by extending the autoregressive (AR) method of Chao & Gilbert. The method consists of (i) ‘blindly’ forcing one 2nd-order AR fit to the signal content in the frequency domain for any chosen frequency...

We review three data stacking methods developed for attaining the splitting parameters of normal modes of the Earth's free oscillation, namely SHS (spherical harmonic stacking), OSE (optimal sequence estimation) and MSE (multi-station experiment), that take advantage of the spatial orthogonality of the (scalar and vector) spherical harmonic functio...

In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531 day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM seires (1962–1977) while cannot b...

We extend the spherical harmonic stacking (SHS) method of Buland et al. [1979] for the radial (vertical) component in the seismogram to the transverse (horizontal) components of the displacement field. Taking advantage of the orthogonality of the spherical harmonic functions (scalar and vectorial), SHS isolates and accentuates the signals of indivi...

Superconducting gravimeter (SG) records after the 2004 Sumatra Mw 9.0, 2010 Maule Mw 8.8 and 2011 Tohoku Mw 9.1 earthquakes are selected to observe the singlets of six spheroidal normal mode multiplets below 1 mHz (0S2, 2S1, 0S3, 0S4, 1S2 and 3S1). To clearly observe their spectral splitting, the ensemble empirical mode decomposition (EEMD) is appl...

Based upon SG (superconducting gravimeter) records, the autoregressive method proposed by Chao and Gilbert [1980] is used to determine the frequencies of the singlets of seven spheroidal modes (S-0(2), S-2(1), S-0(3), S-0(4), S-1(2), S-0(0), and S-3(1)) and the degenerate frequencies of three toroidal modes (T-0(2,) T-0(3), and T-0(4)) below 1 mHz...

Complete isolation of the triplet of the seismic normal mode S-n(1) may better help to tell the complete splitting lines and consequently better constrain the inner structure of the Earth. In theory, the Multi-Station Experiment (MSE) technique and the Spherical Harmonic Stacking (SHS) method can successfully strip the triplet of a mutiplet mode wi...

Based upon seven superconducting gravimeter (SG) records of 20 000 h length after the 2004 Sumatra earthquake, four methods, namely the ensemble empirical mode decomposition (EEMD), the multi-station experiment (MSE) technique, the autoregressive (AR) method and the product spectrum analysis (PSA) method, are chosen jointly together to detect the i...

inner core translational mode (1S1), known as the Slichter triplet, can provide important information particularly on the Earth's inner core and its dynamics. A time domain spectral analysis method, the optimal sequence estimation (OSE), is devised and applied to search for the Slichter modes. Applications of the OSE and the multistation experiment...

The Hilbert-Huang transform (HHT) is used to analyze the time series from nine superconducting gravimeter (SG) stations and 22 broadband seismometers to investigate the anomalous signals prior to the great 2010 Maule earthquake. The results show that seven SG time series and 20 broadband seismometer time series have anomalous signals lasting about...

Using continuous 1-Hz data series recorded by a superconducting gravimeter (SG) at Hsinchu station, Taiwan, we investigate the anomalous gravity signals prior to 71 large earthquakes with seismic moment magnitude larger than 7.0 (Mw7.0) occurred in the period from 1 Jan. 2008 to 31 Dec 2011. For the first time we evaluated the noise level of the SG...

The Earth expansion problem has attracted great interest, and the present study demonstrates that the Earth has been expanding, at least over the recent several decades. Space-geodetic data recorded at stations distributed globally were used (including global positioning system data, very-long-baseline interferometry, satellite laser ranging statio...