Earth's Free Oscillations Research Articles

Probing signals of atmospheric gravity waves excited by the July 29, 2021 MW8.2 Alaska earthquake

It is commonly believed that the atmosphere is decoupled from the solid Earth. Thus, it is difficult for the seismic wave energy inside the Earth to propagate into the atmosphere, and atmospheric pressure wave signals excited by earthquakes are unlikely to exist in atmospheric observations. An increasing number of studies have shown that earthquakes, volcanoes, and tsunamis can perturb the Earth's atmosphere due to various coupling effects. However, the observations mainly focus on acoustic waves with periods of less than 10 min and inertial gravity waves with periods of greater than 1 h. There are almost no clear observations of gravity waves that coincide with observations of low-frequency signals of the Earth's free oscillation frequency band within 1 h. This paper investigates atmospheric gravity wave signals within 1 h of surface-atmosphere observations using the periodogram method based on seismometer and microbarometer observations from the global seismic network before and after the July 29, 2021 MW8.2 Alaska earthquake in the United States. The numerical results show that the atmospheric gravity wave signals with frequencies similar to those of the Earth's free oscillations 0S2 and 0T2 can be detected in the microbarometer observations. The results confirm the existence of atmospheric gravity waves, indicating that the atmosphere and the solid Earth are not decoupled within this frequency band and that seismic wave energy excited by earthquakes can propagate from the interior of the Earth to the atmosphere and enhance the atmospheric gravity wave signals within 1 h.

Solar Flare 1/f Fluctuations from Amplitude-Modulated Five-Minute Oscillation.

We first report that the solar flare time sequence exhibits a fluctuation characterized by its power spectral density being inversely proportional to the signal frequency. This is the 1/f fluctuation, or pink noise, observed ubiquitously in nature. Using GOES16 data, we found that low-energy flares (E≤Emean) display 1/f fluctuations, whereas high-energy flares (E>Emean) show a flat spectrum. Furthermore, we found that the timing sequence of the flares reveals clearer 1/f fluctuations. These observations suggest that the solar flare 1/f fluctuations are associated with low-energy phenomena. We investigated the origin of these 1/f fluctuations based on our recent hypothesis: 1/f fluctuations arise from amplitude modulation and demodulation. We propose that this amplitude modulation is encoded by the resonance with the solar five-minute oscillation (SFO) and demodulated by magnetic reconnections. We partially demonstrate this scenario by analyzing the SFO eigenmodes resolving the frequency degeneration in the azimuthal order number m using the solar rotation and resonance. Given the robust nature of 1/f fluctuations, we speculated that the solar flare 1/f fluctuations may be inherited by the various phenomena around the Sun, such as the sunspot numbers and cosmic rays. In addition, we draw parallels between solar flares and earthquakes, both exhibiting 1/f fluctuations. Interestingly, the analysis applied to solar flares can also be adapted to earthquakes if we read the SFO as Earth's free oscillation and magnetic reconnections as fault ruptures. Moreover, we point out the possibility that the same analysis also applies to the activity of a black hole/disk system if we read the SFO as the quasi-periodic oscillation of a black hole.

Constraint on the focal mechanism of the 2011 Tohoku earthquake from the radial modes

Different from other normal modes of the Earth's free oscillation that depend on all the six components (Mrr, Mtt, Mpp, Mrt, Mrp, and Mtp) of the centroid moment tensor, the amplitudes of the radial modes depend on the Mrr component (e.g., scalar moment (M0), dip (δ), and slip (λ)) and hypocenter depth of the focal mechanism, and hence can be easily used to constrain these parameters of the focal mechanism. In this study, we use the superconducting gravimeter (SG) records after the 2011 Tohoku earthquake to analyze the radial modes 0S0 and 1S0. Based on the solutions of the focal mechanism provided by the GCMT and USGS, we can obtain the theoretical amplitudes of these two radial modes. Comparing the theoretical amplitudes with the observation amplitudes, it is found that there are obvious differences between the former and the latter, which means that the GCMT and USGS focal mechanisms cannot well represent the real focal mechanism of the 2011 event. Taking the GCMT solution as a reference and changing the depth and the three parameters of the Mrr moment, the scalar moment (M0) and the dip (δ) have significant influences, but the effects of the slip (λ) and the depth are minor. After comparisons, we provide a new constraint (M0 = 5.8 ± 0.09 × 1022 N·m, δ = 10.1 ± 0.08°, λ = 88°, and depth = 20 km) for the focal mechanism of the 2011 event. In addition, we further determine the center frequency (1.631567 ± 2.6e-6 mHz) and quality factor (2046.4± 50.1) of the 1S0 mode.

Effect of Earth-Moon’s gravity on TianQin’s range acceleration noise. III. An analytical model

TianQin is a proposed space-based gravitational-wave detector designed to operate in circular high Earth orbits. As a sequel to [Zhang et al. Phys. Rev. D 103, 062001 (2021)], this work provides an analytical model to account for the perturbing effect of the Earth's gravity field on the range acceleration noise between two TianQin satellites. For such an ``orbital noise,'' the Earth's contribution dominates above $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{Hz}$ in the frequency spectrum, and the noise calibration and mitigation, if needed, can benefit from in-depth noise modeling. Our model derivation is based on Kaula's theory of satellite gravimetry with Fourier-style decomposition and uses circular reference orbits as an approximation. To validate the model, we compare the analytical and numerical results in two main scenarios. First, in the case of the Earth's static gravity field, both noise spectra are shown to agree well with each other at various orbital inclinations and radii, confirming our previous numerical work while providing more insight. Second, the model is extended to incorporate the Earth's time-variable gravity. Particularly relevant to TianQin, we augment the formulas to capture the disturbance from the Earth's free oscillations triggered by earthquakes, of which the mode frequencies enter TianQin's measurement band above 0.1 mHz. The analytical model may find applications in gravity environment monitoring and noise-reduction pipelines for TianQin.

Observation of free oscillations after the 2010 Chile and 2011 Japan earthquakes by superconducting gravimeter in Kutch, Gujarat, India

In this paper, we present observations of free oscillations of the Earth after major earthquakes in Chile (February 27, 2010, MW8.8) and Japan (March 11, 2011, MW9.1) using data from the dual-sphere superconducting gravimeter (SG - 055), installed at Badargadh (23°0.47 N, 70°0.62 E), Kutch, Gujarat, India in March 2009. To see the noise characteristics, we calculated the power spectral density of the gravity time series of 5 quiet days in the frequency band 0.05–20 mHz using the new low noise model (NLNM) as a reference. We compared the noise level of the Badargadh site to other SG sites around the world. This shows that the Badargadh SG is in a low noise state. We find that the noise increases at frequencies below 1 mHz. Such a characteristic is also observed in Djougou (Afrique, Benin) and Strasbourg (France). Using theoretical tides for Gujarat, we estimated a scale factor of about −814 nm/s2/V for Grav1 (lower-sphere) and about −775 nm/s2/V for Grav2 (upper-sphere). We corrected the influence of atmospheric pressure from the one-second gravity data before switching to the frequency domain. We extracted a total of 53 Earth's Free Oscillations (EFO) modes during the earthquake in Japan and about 47 EFO modes during the earthquake in Chile. We are able to extract the lowest 0S2 spheroidal mode (0.30945 mHz or 54 min) and 0S0 radial mode (0.81439 mHz or 20 min). The longer time series shows individual 0S2 singlets and 0S3 (0.46855 mHz) singlets due to the Coriolis splitting effect. We cross-referenced the frequencies of these modes using the PREM model and previous global observations. The correlation coefficient between the observed and the PREM model for these two events are 0.999 for Japan earthquake and 0.993 for Chile earthquake. This validates the quality of the data useful for low-frequency studies in seismology. We also calculated the relative deviations of our observed fundamental modes with previously determined observed and theoretical values. We found that the relative deviations of our observed free oscillations do not exceed 0.5%, indicating good correlations.

Terrestrial Resonant Oscillations During the 11 April 2012 Sumatra Doublet Earthquake

AbstractThe Earth's background free oscillations at ∼3.7 and ∼4.4 mHz resonantly couple with the atmospheric acoustic modes and thus energy cross‐talk between the earth‐atmosphere system is maximum at these frequencies. The present study proposes resonant coupling between the Earth's surface and atmosphere during the 11 April 2012 Sumatra doublet earthquake and offer a possible explanation to this occurrence. Following both these earthquakes, prolonged ionospheric oscillations centered at frequency of ∼4 mHz were observed in GPS (Global Positioning System) derived total electron content (TEC) towards north‐northeast of the epicenters. We scrutinize these oscillations in terms of the manifestations of plausible non‐tectonic and tectonic forcing mechanisms surrounding the epicentral region. Non‐tectonic forcing such as the geomagnetic field coupling factor and observation geometry played a critical role in determining the amplitude anisotropy of resonant ionospheric signatures. Further, the Rayleigh waves of the first earthquake (Mw 8.6) were already characterized by an excess of energy at ∼4 mHz. We propose this could make the Mw 8.6 earthquake particularly efficient to excite the 4 mHz resonance in the atmosphere. The resonant ionospheric signatures after the second earthquake (Mw 8.2) were observed to be closely associated with the Earth's free oscillations caused by R2 Rayleigh wave train of the Mw 8.6 earthquake event. Together, all the above point to a scenario where the resonant ionospheric signatures during the Sumatra doublet event were indeed related to the seismic source. Therefore, resonant co‐seismic ionospheric signatures could provide additional information on the low‐frequency features of seismic ruptures.

Book Review of ‘Seismic Ambient Noise’

This book on seismic ambient noise provides a convenient and timely text on theoretical aspects, observations and interpretation of the ubiquitous background signal in continuous seismic time-series collected around the world. The principal editor team managed to commit experts in various complementary fields in ambient-noise research and application to a wide range of frequencies from Earth's free oscillations to ultrasound waves. The product of their efforts is a comprehensive treatise that many have been waiting for. Each of the chapters is well written, and the book could well serve as the principal textbook for a graduate-level course on the topic. The text is dominated by the causes and interpretation of ambient noise in broadband seismic time-series. But the reader will also find the theoretical treatise on and implementation for active and passive ambient noise applications at high frequencies, for example to explore material properties in the laboratory. Because multiple authors contributed to the book, the text is not strictly structured along a main train of thought, and the chapters are largely self-contained. In fact, there is often an overlap, for example on the processing of cross-correlations. This allows an interested reader to select a specific chapter without having to worry about skipping relevant subject matter.

Gravitational Changes of the Earth's Free Oscillation From Earthquakes: Theory and Feasibility Study Using GRACE Inter‐satellite Tracking

AbstractGRACE satellites have detected regional‐scale preseismic, coseismic, and postseismic gravity changes associated with great earthquakes during the GRACE era (2002‐2017). Earthquakes also excite global‐scale transient gravity changes associated with free oscillations that may be discerned for a few days. In this study, we examine such global gravity changes due to Earth's free oscillations and quantify how they affect GRACE measurements. We employ the normal mode formalism to synthesize the global gravity changes after the 2004 Sumatra earthquake and simulate the (gravitational) free oscillation signals manifested in the GRACE K‐band ranging (KBR) measurements. Using the Kaula orbit perturbation theory, we show how GRACE inter‐satellite distances are perturbed through a complex coupling of eigenfrequencies of the normal modes with the Earth's rotation rate and the GRACE satellites' orbital frequency. It is found that a few gravest normal modes can generate range‐rate perturbations as large as 0.2 μm/s, which are comparable to actual errors of GRACE KBR ranging and accelerometer instruments. Wavelet time‐frequency analysis of the GRACE KBR residual data in December 2004 reveals the existence of a significant transient signal after the 2004 Sumatra earthquake. This transient signal is characterized by a frequency of ~0.022 mHz that could be potentially associated with the largest excitation due to the “football” mode of the Earth's free oscillation. However, the results are also affected by low‐frequency noise of the GRACE accelerometers. Improved space‐borne gravitational instrumentation may open new opportunities to study the Earth's interior and earthquakes independently from global seismological analysis.

Application of Stabilized AR‐z Spectrum in Harmonic Analysis for Geophysics

AbstractThe 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 signal‐to‐noise ratio is low. As such, it can be prone to random fluctuations in the form of spurious variances of the noise spectrum. Here we develop a stabilized AR‐z spectrum taking advantage of a Monte Carlo noise‐assisted bootstrap scheme, and demonstrate its effectiveness in obtaining more robust spectral estimates for single record. We apply the stabilized AR‐z spectrum, and compare it with the Fourier and maximum‐entropy spectra, to a number of global geophysical observables of the Earth, including the elastic free oscillations, length of day variation (ΔLOD), dynamic oblateness (ΔJ2), polar motion, Earth's nutation, and global mean sea level variation. We report the findings about hitherto unresolved fine structures, including those for the Mf and Mm tidal clusters in the ΔLOD, ΔJ2, polar motion and the Earth's nutation, and the modal splittings of the Earth's free oscillations. Furthermore, a number of long‐period signals of certain nominal periodicities are detected (or confirmed) in the stabilized AR‐z spectra, including the 6‐year signals in ΔLOD, the 18.6‐year signals expected in ΔLOD and ΔJ2, and certain quasiperiodic interannual to decadal periodicities whose origins have yet to be identified. Overall, the stabilized AR‐z spectrum demonstrates a momentous performance in the quest for numerical harmonic analysis methods.

Detection of Earth's free oscillation excited by the Japan Mw9.0 Earthquake using different tiltmeter and strainmeter

The observatory network of the Crustal Deformation China Seismological Bureau was equipped with vertical pendulum tiltmeter, borehole tiltmeter, tunnel extension meters, multi-component borehole strainmeter, body strainmeter and other tilt and strain observation instruments. All of these instruments have recorded the Earth's free oscillation excited by the Japan Mw9.0 Earthquake. By analyzing those observations, all of the spheroidal oscillation modes (0S3—0S30) and toroidal oscillation modes (0T3—0T20) excited by the Japan Mw9.0 Earthquake were detected in this paper. In addition, comparing the different observation results which obtained by those instruments, we revealed their capacity to observe different kinds of oscillation and different frequency band modes, and analyzed report the reason. We found that the body strainmeter and the vertical pendulum tiltmeter have better observing results for spheroidal oscillation. Because of high noise in low frequency band, the borehole tiltmeter cannot observe the low-order spheroidal oscillation. In terms of observing the toroidal oscillation, the multi-component borehole strainmeter got a best result. The vertical pendulum tiltmeter observes a few toroidal oscillation modes, and the tunnel extension meters can only observe some low-order modes.

Earth's free oscillations excited by the 2011 TohokuMw9.0 earthquake detected with a groundwater level array in mainland China

Earth's free oscillations excited by the 2011 Tohoku<i>M</i>_w9.0 earthquake detected with a groundwater level array in mainland China

Data stacking methods for isolation of normal‐mode singlets of Earth's free oscillation: Extensions, comparisons, and applications

AbstractWe 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 (multistation experiment), that take advantage of the spatial orthogonality of the (scalar and vector) spherical harmonic functions. We further extend these methods to broader applicability as appropriate, in particular SHS extended to matrix‐SHS (MSHS) to better accounting for the nonglobal distribution of recording stations, and OSE and MSE extended to transverse components and arbitrary harmonic degrees. We conduct synthetic numerical experiments and conclude that OSE and MSHS stackings yield superior results. Based on the lessons learned, we apply the methods on real global seismic records after the 2004 Sumatra earthquake and report the complete resolution of all singlets for 13 selected multiplets: 8 are mantle‐sensitive (1S2, 0S4, 1S4, 0S5, 0S6, 1T2, 0T4, and 0T6) and 5 inner‐core sensitive and of anomalous splitting (13S2, 10S2, 2S3, 3S2, and 11S1), among them the singlet resolution of 1T2, 0T4, 10S2, 2S3, 3S2, and 11S1 are reported for the first time.

Estimation of the complex frequency of a harmonic signal based on a linear least squares method

In this study, we propose a simple linear least squares estimation method (LLS) based on a Fourier transform to estimate the complex frequency of a harmonic signal. We first use a synthetically-generated noisy time series to validate the accuracy and effectiveness of LLS by comparing it with the commonly used linear autoregressive method (AR). For an input frequency of 0.5 mHz, the calculated deviations from the theoretical value were 0.004‰ and 0.008‰ for the LLS and AR methods respectively; and for an input 5 × 10−6 attenuation, the calculated deviations for the LLS and AR methods were 2.4% and 1.6%. Though the theory of the AR method is more complex than that of LLS, the results show LLS is a useful alternative method. Finally, we use LLS to estimate the complex frequencies of the five singlets of the 0S2 mode of the Earth's free oscillation. Not only are the results consistent with previous studies, the method has high estimation precisions, which may prove helpful in determining constraints on the Earth's interior structures.

Normal mode coupling observations with a rotation sensor

We present observations of cross coupled spheroidal modes in the Earth's free oscillation spectrum recorded by the vertical component G-ring laser (Geodetical Station Wettzell) of the 2011 Mw 9.0 Tohoku-Oki earthquake. In an attempt to determine which are the mechanisms responsible for spheroidal energy in a vertical axes rotational spectra, we first rule out instrumental effects as well as the effect of local heterogeneity. Secondly, we carry out simulations of an ideal rotational sensor taking into account the effects of the Earth's rotation, its hydrostatic ellipticity and structural heterogeneity, which results in a good fit to the data. Simulations considering each effect separately are performed in order to evaluate the sensitivity of rotational motions to various phenomena compared to traditional translation measurements.

Constraining the gravitational wave energy density of the Universe using Earth’s ring

The search for gravitational waves is one of today's major scientific endeavors. A gravitational wave can interact with matter by exciting vibrations of elastic bodies. Earth itself is a large elastic body whose so-called normal-mode oscillations ring up when a gravitational wave passes. Therefore, precise measurement of vibration amplitudes can be used to search for the elusive gravitational-wave signals. Earth's free oscillations that can be observed after high-magnitude earthquakes have been studied extensively with gravimeters and low-frequency seismometers over many decades leading to invaluable insight into Earth's structure. Making use of our detailed understanding of Earth's normal modes, numerical models are employed for the first time to accurately calculate Earth's gravitational-wave response, and thereby turn a network of sensors that so far has served to improve our understanding of Earth, into an astrophysical observatory exploring our Universe. In this paper, we constrain the energy density of gravitational waves to values in the range 0.035--0.15 normalized by the critical energy density of the Universe at frequencies between 0.3 and 5 mHz, using ten years of data from the gravimeter network of the Global Geodynamics Project that continuously monitors Earth's oscillations. This work is the first step towards a systematic investigation of the sensitivity of gravimeter networks to gravitational waves. Further advances in gravimeter technology could improve sensitivity of these networks and possibly lead to gravitational-wave detection.

Real-Time Assessment of the Broadband Coseismic Deformation of the 2011 Tohoku-Oki Earthquake Using an Adaptive Kalman Filter

Online Material: Matlab scripts and example data for adaptive Kalman filter. The 2011 M w 9.0 Tohoku‐Oki earthquake was the most disastrous known event in Japan,triggering a powerful tsunami wave with a maximum amplitude of ∼40 m (Mori et al. , 2012). At least 15,883 people were killed and over 6145 injured, with a total economic loss of more than $235 billion U.S., making it the costliest natural disaster in world history (Emergency Disaster Countermeasures Headquarters, 2011; Hennessy‐Fiske, 2011). The earthquake occurred at 14:46:24 Japan Standard Time (05:46:24 UTC), with epicenter location at 38.297° N, 142.372° E and depth of 30 km (U.S. Geological Survey Earthquake Hazards Program, 2011). Seismic waveforms were recorded by continuous Global Navigation Satellite Systems (GNSS) monitoring network of GNSS Earth Observation Network (GEONET) (Sagiya et al. , 2001) and strong‐motion seismograph networks of the Kyoshin Network (K‐NET) and Kiban Kyoshin Network (KiK‐net) (Aoi et al. , 2004). These have been separately or jointly applied to rapid earthquake magnitude determination (Ohta et al. , 2012; Wright et al. , 2012; Melgar, Crowell, et al. , 2013), tsunami warning (Melgar and Bock, 2013), earthquake rupture process inversion (Ide et al. , 2011; Suzuki et al. , 2011; Yagi and Fukahata, 2011; Yokota et al. , 2011; Yue and Lay, 2011; Frankel, 2013), ionosphere perturbation detection (Heki, 2011; Tsugawa et al. , 2011; Komjathy et al. , 2012), study of Earth free oscillation (Mitsui and Heki, 2012), etc. For those studies, the acquisition of robust seismic waveforms is vital but defective, especially in a real‐time mode. High‐rate Global Positioning System (GPS) is capable of recording seismic waveforms with centimeter‐level accuracy (Genrich and Bock, 2006), regardless of relative kinematic positioning mode (Nikolaidis et al. , 2001; Larson et al. , 2003; Blewitt et al. , 2006, 2009; Bilich et al. , 2008; Crowell …

Constraints on the Moment Tensor of the 2011 Tohoku-Oki Earthquake from Earth's Free Oscillations

Free oscillations of the Earth provide crucial constraints for seismic source properties of very large earthquakes, especially on the seismic moment. In this work, the scalar moment and mechanism of the 11 March 2011 Tohoku‐Oki earthquake are examined through the analysis of 15 modes. The approach utilizes receiver strips that compress mode excitation information, and are also used to set up an objective data weighting scheme. The moment tensor inversion is performed in two steps. An initial solution is obtained from a linear inversion by fitting the real and imaginary components of the receiver‐strip spectra. In order to take advantage of the difference in the robustness of the amplitude and phase spectra, the second procedure solves a nonlinear problem in an iterative approach. Because the 2011 Tohoku‐Oki earthquake is at a shallow depth, special attention is needed to treat the dip‐slip components of the moment tensor. Low‐frequency modes are practically insensitive to these components, and presents a challenge in estimating the mechanism and seismic moment based purely upon free‐oscillation data. The final result is consistent with the thrust mechanism reported elsewhere, and gives a scalar moment corresponding to M w 9.1.

Anisotropy gradients from QL surface waves: Evidence for vertically coherent deformation in the Tibet region

Abstract The India–Eurasia continental collision has not only caused the high uplift of the Tibetan Plateau, but also created a broad diffuse deformation zone in Central Asia. We relate the well-constrained extent of crustal deformation in the Tibet region with underlying mantle deformation by interpreting the quasi-Love (QL) surface wave scattering in the legacy data of Tibet. QL waves are waveform anomalies generated from cross-mode coupling of Earth's free oscillations, mainly through azimuthal anisotropy. Over 50 events with QL observations are identified using recordings in Tibet. The predominant frequency content of the QL waves is near 10 mHz, and reflects peak sensitivity of anisotropy at 150 km depth in the mantle assuming horizontally-oriented symmetry axes. By calculating the delay times between the QL waves and the main Love waves, we back-project the scatterers to cluster in areas like SE Tibet, Sayan Mountain and Iran. Noticeably the spatial distribution of these scatterers borders the crustal deformation pattern quite well, especially at the deformation limits of Central Asia. This linkage suggests a vertically coherent boundary condition through the crust and the upper mantle for the India–Eurasia continental collision in Central Asia.

Earth's Background Free Oscillations

Earth's background free oscillations, known as Earth's hum, were discovered in 1998. Excited modes of the oscillations are almost exclusively fundamental spheroidal and toroidal modes from 2 to 20 mHz. Seasonal variations in the source distribution suggest that the dominant sources are ocean infragravity waves in the shallow and deep oceans. A probable excitation mechanism is random shear traction acting on the sea bottom owing to linear topographic coupling of the infragravity waves. Excitation by pressure sources on Earth's surface is also significant for a frequency below 5 mHz. A possible pressure source is atmospheric turbulence, which can cause observed resonant oscillations between the solid modes and atmospheric acoustic modes.

A new catalogue of normal-mode splitting function measurements up to 10 mHz

The splitting of the Earth's free-oscillation spectra places important constraints on the wave speed and density structure of the Earth's mantle and core. We present a new set of 164 self-coupled and 32 cross-coupled splitting functions. They are derived from modal spectra up to 10 mHz for 91 events with Mw ≥ 7.4 from the last 34 yr (1976–2010). Our data include the 2001 June 23 Peru event (Mw = 8.4), the Sumatra events of 2004 (Mw = 9.0) and 2005 (Mw = 8.6), the 2008 Wenchuan, China event (Mw = 7.9) and the 2010 Chile event (Mw = 8.8). The new events provide significant improvement of data coverage particularly in continental areas. Almost half of the splitting functions have never been measured before. In particular, we measured 33 new modes sensitive to mantle compressional wave velocity, 10 new inner-core sensitive modes and 22 new cross-coupled splitting functions. These provide new constraints on the large-scale compressional structure of the mantle and the odd-degree structure of the mantle and inner core and can be used in future inversions of heterogeneous Earth structure. Our new splitting function coefficient data set will be available online.