No abstract

Using an updated data set of ballistic PKIKP travel time data at antipodal distances, we test different models of anisotropy in the Earth's innermost inner core (IMIC) and obtain significantly better fits for a fast axis aligned with Earth's rotation axis, rather than a quasi‐equatorial direction, as proposed recently. Reviewing recent results on the single crystal structure and elasticity of iron at core conditions, we find that an hcp structure with the fast c axis parallel to Earth's rotation is more likely but a body‐centered cubic structure with the [111] axis aligned in that direction results in very similar predictions for seismic anisotropy. These models are therefore not distinguishable based on current seismological data. In addition, to match the seismological observations, the inferred strength of anisotropy in the IMIC (6–7%) implies almost perfect alignment of iron crystals, an intriguing, albeit unlikely situation, especially in the presence of heterogeneity, which calls for further studies.

Abstract-The aim of this paper is to present a study on the potential and limits of the -transform and its inverses. The -transform is an extension of the short-time Fourier transform with characteristics of the wavelet transform. It is mostly used for time-frequency analyses. Two different inverse -transforms have been presented in the literature. We explain why the most recent one is an approximation but a very good one. The level of approximation is calculated in this paper. We then discuss the relative merits of both inverses. A careful study enables us to show that, although both inverses are nearly exact in the infinite continuous domain, this is not true anymore in the practical finite discrete domain. Side effects are quantified, and typical examples are given. Time-frequency filtering is one of the main applications of the -transform. We evaluate the effects that occur when using the -transform and its inverses for filtering.

Stacks of ambient noise correlations are routinely used to extract empirical Green's functions (EGFs) between station pairs. The time-frequency phase-weighted stack (tf-PWS) is a physically intuitive nonlinear denoising method that uses the phase coherence to improve EGF convergence when the performance of conventional linear averaging methods is not sufficient. The high computational cost of a continuous approach to the time-frequency transformation is currently a main limitation in ambient noise studies. We introduce the timescale phaseweighted stack (ts-PWS) as an alternative extension of the phase-weighted stack that uses complex frames of wavelets to build a time-frequency representation that is much more efficient and fast to compute and that preserve the performance and flexibility of the tf-PWS. In addition, we propose two strategies: the unbiased phase coherence and the two-stage ts-PWS methods to further improve noise attenuation, quality of the extracted signals and convergence speed. We demonstrate that these approaches enable to extract minor-and major-arc Rayleigh waves (up to the sixth Rayleigh wave train) from many years of data from the GEOSCOPE global network. Finally we also show that fundamental spheroidal modes can be extracted from these EGF.

This electronic supplement contains amplitude spectra for the gravest modes of the 11 March 2011 TohokuOki earthquake as recorded on GEOSCOPE station TAM (Tamanrasset, Algeria) in Algeria. Gravest Modes of the 2011 TohokuOki Earthquake The main goal of the article is to examine the performance of the different autocorrelations, based on the conventional cross correlation (CC; equation 1 in the main article), geometrically normalized cross correlation (CCGN; equation 2 in the main article), and phase cross correlation (PCC; equation 3 in the main article) on ambient noise

Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the dataset after subtraction. Due to the high crosscorrelation between their waveform, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation and, despite its simplicity, narrows the gap between 1D and standard adaptive 2D methods on field data * .

SS precursor observations are a powerful tool to study the topography and character of transition zone discontinuities, especially in regions such as ocean basins where few seismic stations exist, precluding other high resolution approaches. Still, the available coverage is limited by the distribution of sources and stations, but also by the level of noise and by the fact that, in some distance ranges, interfering seismic phases mask the weak signal from the SS precursors. We introduce an array data processing tool, the local slant-stack filter, to address these challenges and clean up the otherwise noisy SS precursor record sections. We show that these filters are a powerful tool for extracting the weak yet coherent SS precursor signals while removing interfering seismic phases as well as random noise, yielding robust precursor traveltime measurements with spatial resolution higher than what can be achieved by the conventional common midpoint stacking method. The effectiveness of the filters are demonstrated by application to synthetic and real data. We systematically apply this filtering method to an SS precursor data set recorded by the U.S. Transportable Array that samples a vast region of the Pacific Ocean and its northwest margin, and present maps of 410 and 660 discontinuity topography. We discuss correlations observed between our discontinuity images and several fine-scale heterogeneities revealed by mantle shear wave tomography in the vicinity of Hawaii and the Pacific Superswell.

Interstation correlation is the basic operation in seismic noise and coda-wave interferometry for signal extraction in imaging and monitoring applications. Conventional cross-correlations evaluate the similarity between two signals along lag time, and they are efficiently computed by the fast Fourier transform (FFT), valuable to manage the large data volumes that ambient noise applications demand. The phase cross-correlation (PCC) method contributes to increase convergence, a key issue in seismic ambient noise imaging and monitoring; however, it is much more computationally demanding. PCC evaluates similarity by subtracting the modulus of the sum and difference of the instantaneous phase of two signals. We introduce solutions to dramatically reduce the high-computational cost of PCC. We show that PCC can be rewritten as a complex cross-correlation and computed by the FFT when the moduli are raised to the power of 2, and we demonstrate PCC can improve waveform coherence and increase convergence compared with the default processing flow of 1-bit amplitude normalization and standard cross-correlation. Moreover, we develop a graphics processing unit implementation to accelerate computations when using powers other than 2 and particularly when using the power of 1. Finally, we extract Rayleigh-and body-wave signals from many years of data from seismic stations distributed worldwide using PCC without a significant increase in computational cost compared with conventional cross-correlation.