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Explanation based on the stationary-point principle for the correlated phase cS-cP. (a) Hypothetical Huygens' sources on the core-mantle boundary (CMB) radiate seismic waves to receivers R1, R2 on the Earth's surface. (b) Red curves show differential travel time of cS and cP ( ) as a function of angular offset between the CMB source and the midpoint of two receivers. The background shows synthetic correlation waveforms of two stations from an explosive source located at the corresponding CMB location. (c) Stacked cross-correlations waveform for all CMB sources demonstrates the emergence of a peak around the stationary point of the differential travel time curves.
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Cross-correlation of seismograms provides new information on the Earth both through the exploitation of ambient noise and specific components of earthquake records. Here, we cross- correlate recordings of large earthquakes on a planetary scale and identify a range of hitherto unobserved seismic phases in Earth’s correlation wavefield. We show that...
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... Figure S3. Explanation based on the stationary-phase principle for other non-causal correlated phases (a) PKP-ScS (b) cPPcP-cS (c) cKS-cS (d) cKS-cP. Their travel time curves are plotted in Figure 2 and Figure S1. For these phases, the stationary sources are at their maximum rather than the minimum for cS-cP ( Figure S2). For details of each panels see the caption of Figure S2. ...
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... origin of the phase cS-cP is closely linked to the core-mantle boundary (CMB), a major internal discontinuity within the Earth with a pronounced seismic contrast between the solid mantle and the liquid outer core comparable to that of the Earth's free surface. When a seismic wavefront reaches the CMB, any point on the CMB can be thought of as a secondary source (i.e., via Huygens' principle -see Figure 3a). Such a virtual source radiates P and S waves that travel along different geometrical ray paths to receivers on the Earth surface. A recorded seismogram can be thought of as a superposition of an infinite number of individual-source seismograms corresponding to those secondary sources. The resulting cross-correlogram is a stack of individual-source cross-correlations [Wapenaar et al., ...
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... cPPcP-cS, cKS-cP, cKS-cS and PKP-ScS, whose stationary-phase results are shown in Figure S3. In all cases, a stationary source for the differential travel times lies either on the CMB, or on the Earth's surface. The stationary point of the differential travel time curves is maximal in these cases, rather than a minimum as for cS-cP. In all cases the ray paths from the stationary sources always arrive at the receivers with the same ray parameter. In consequence, there is a good fit of the predicted differential travel time curves to the anomalous phases in the observed and synthetic cross-correlograms ( Figure 2a, 2b and Figure ...
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... origin of the phase cS-cP is closely linked to the core-mantle boundary (CMB), a major internal discontinuity within the Earth with a pronounced seismic contrast between the solid mantle and the liquid outer core comparable to that of the Earth's free surface. When a seismic wavefront reaches the CMB, any point on the CMB can be thought of as a secondary source (i.e., via Huygens' principle -see Figure 3a). Such a virtual source radiates P and S waves that travel along different geometrical ray paths to receivers on the Earth surface. ...
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... cPPcP-cS, cKS-cP, cKS-cS and PKP-ScS, whose stationary-phase results are shown in Figure S3. In all cases, a stationary source for the differential travel times lies either on the CMB, or on the Earth's surface. ...
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Citations
... Otherwise, one can directly interpret the correlation of seismic recordings as a measurement of differential propagation times between two stations for a given dominant source, either using late coda or ambient noise sources (e.g., Pham et al., 2018;Tkalčić et al., 2020). Boué and Tomasetto (2023) took another look at the daylight imaging concept (Rickett & Claerbout, 1999) and proposed to use oceanic storms lasting a few hours instead of continuous noise records to observe deep Earth seismic propagation (e.g., Nishida & Takagi, 2016;Zhang et al., 2023). ...
Plain Language Summary
Ocean wave interactions are a significant source of constant seismic wave emissions, known as ambient noise. Methods using correlations between seismic recordings recently highlighted surface waves and, more importantly, body waves to extract properties of the Earth's deep interior. These studies either use continuous recordings to infer medium properties, or focus on wave propagation from a specific storm. However, concerns about measurements can come from the broad oceanic source constantly changing in space and time. We model seismic recordings for 3 days during a powerful oceanic storm in southern Greenland, 8–11 December 2014, to assess the source variations' impact on body wave arrival times. We then compare it to data and measure travel time lags. Our findings explain source‐induced delays and also agree with the known structure of the Earth, with some differences. This tool could add body wave travel time measurements and uncertainties from interferometry to image our planet's deep structures.
... This constitutes a less aggressive alternative to improve the balance of sources and leave further selection and weighting for the stacking stage. Selection and weighting proved of importance in the hum cross-correlations (Section III-B) to reduce the contribution of coda waves [63], [64] into the interstation cross-correlations. Rejecting a few cross-correlations with an anomalous energy level and weighting the rest, attenuated by a factor of 10 most of the body-wave signals observed in the EGFs. ...
Seismic ambient noise has a strongly nonstationary time-frequency statistics that demand better interstation correlation methods to improve the balance of highly variable ambient-noise sources, reduce the influence of high-energy poorly-distributed signals, and accelerate the convergence to a robust signal or a broadband empirical Green’s function (EGF). The wavelet cross-correlation method is convenient to analyze the statistics of the cross-correlation of two signals in terms of lag time and scale/frequency. Here we introduce wavelet phase cross-correlation (WPCC) functions better adapted to the statistics of seismic ambient noise by combining the ideas of: using only the instantaneous phase information of the phase cross-correlation (PCC) method to assess amplitude unbiasedness, and analyzing cross-correlations scale by scale of the wavelet cross-correlation to balance strong and weak frequency components. These features allow WPCC to extract clean broadband signals useful for seismic imaging and monitoring studies. Further, we analyze and discuss benefits and limitations of WPCC compared to PCC in two examples using low-frequency seismic ambient noise (hum), but results are easily extrapolated to higher frequencies. In hum autocorrelations, WPCC can correct for the baseline and extract cleaner signals, and in hum cross-correlations, can extract richer and more frequency-balanced EGFs allowing for a significant increase of Rayleigh phase- and group-velocity measurements and an improvement of their accuracy. Finally, we offset the increase in computational cost of WPCC compared to PCC by using the graphics processing unit, and show that WPCC is an efficient approach that permits processing large data volumes as commonly encountered in seismic interferometry studies.
... To improve the spatial sampling of the Earth's deep interior, coda correlation studies [27][28][29] , which exploit correlated features lasting in long earthquake recordings, have emerged as promising tools to probe the Earth's interiors. The correlation wavefield that exploits the similarity of weak signals samples the IC differently from the previous techniques 19,30 (for a recent review, see ref. 31 ). ...
... Their arrival times and slowness properties suggest they are seismic phases reverberating along the entire Earth's diameter, including the inner core, multiple times. Thus, we adopt an abbreviated nomenclature, similar to previous counterparts in the correlation wavefield 29 : PKIKP (I), PKIKP2 (I2), PKIKP3 (I3), PKIKP4 (I4), and PKIKP5 (I5), in which the last digits represent the number of passages reverberating the entire Earth's diameter as compressional waves (see their schematic ray paths Fig. 1B, C). Observations of such exotic arrivals in several other single-event stacks are included in the supplementary material (Fig. S1). ...
... There are features in the global coda correlograms that look similar to PKIKP multiples and were explained to arise due to the similarity of late, weak arrivals after large earthquakes 29 . The emergence of the core-sensitive signals in the coda-correlation wavefield thus inspired us to search for exotic reverberations in the direct seismic wavefield that results in the correlation features' formation. ...
Probing the Earth’s center is critical for understanding planetary formation and evolution. However, geophysical inferences have been challenging due to the lack of seismological probes sensitive to the Earth’s center. Here, by stacking waveforms recorded by a growing number of global seismic stations, we observe up-to-fivefold reverberating waves from selected earthquakes along the Earth’s diameter. Differential travel times of these exotic arrival pairs, hitherto unreported in seismological literature, complement and improve currently available information. The inferred transversely isotropic inner-core model contains a ~650-km thick innermost ball with P-wave speeds ~4% slower at ~50° from the Earth’s rotation axis. In contrast, the inner core’s outer shell displays much weaker anisotropy with the slowest direction in the equatorial plane. Our findings strengthen the evidence for an anisotropically-distinctive innermost inner core and its transition to a weakly anisotropic outer shell, which could be a fossilized record of a significant global event from the past.
... The stacked cross-correlations of earthquake late-coda records between worldwide receivers exhibit prominent features and form a new type of dataset for imaging the Earth's interior, which can circumvent the source-receiver separation restrictions 19 . The correlation features in correlograms-two-dimensional representations of cross-correlations as a function of inter-receiver distance on a global scale-are manifestations of waveform similarities among numerous near-vertical take-off seismic waves [19][20][21] . These deep-travelling seismic waves, being the reverberations from the Earth's free surface and internal discontinuities in the late coda of several hours length, sample the whole of the Earth's interior regardless of the locations of the sources and receivers 21 . ...
... The intersource correlogram constructed without any selectiveness is void of noticeable features (Fig. 1b). However, after the rigorous selection criteria are applied, the correlogram exhibits many prominent features (Fig. 1c) similar to those in interstation correlograms 20 . The number of source pairs after the selection criteria is ten times smaller than the number before the selection criteria ( Fig. 1f,g), demonstrating that only a small percentage of source pairs constructively contribute to the formation of the correlation features, while the other contributions are destructive. ...
... We obtain and pre-process data following the methods in interstation correlation studies 20 . We select globally distributed earthquakes in 2000-2020 with magnitudes M W > 6.5 from the National Earthquake Information Center (NEIC; available at https://earthquake.usgs. ...
The network of seismographs on Earth allows us to gather enough data to reveal the properties of the metallic core hidden in the centre of the planet’s mantle envelope. In contrast, the small number of seismographs deployed on the Moon or Mars limits the sampling of their interiors and makes inferences challenging. Here we show that a single seismograph and global-scale waveform cross-correlations between seismic events can be used to scan planetary cores. We demonstrate that this technique allows us to constrain the sizes of the cores of Earth and Mars and we confirm that the Martian core is large. This technique provides an opportunity to investigate the structure of planetary interiors with currently realizable resources. A method that uses intersource correlograms measured by a single-station seismograph to constrain planetary interiors is presented. Applied to Mars, it measures a core radius of 1,812 ± 20 km, consistent with InSight direct-seismic-wave measurements. Such a method is useful in planetary exploration where the deployment of a full network of seismographs is unlikely.
... An obvious significant advantage over previous approaches was that a new class of studies could be performed without earthquakes, relying merely on a constant ground motion due to the interaction among solid Earth, oceans, and atmosphere. Like in the ambient noise methods, a 2-D cross-correlation stack organized in inter-receiver distance bins can be obtained using the earthquake late coda (e.g., Boué et al., 2014;Phạm et al., 2018). This 2D representation of crosscorrelation as a function of inter-receiver distance is a global correlogram (for a recent review, see . ...
... spurious phases). The prominent signals, known as "the correlation features", can exhibit noticeable timing similarities with the regular seismic phases in time-distance stacks (e.g., Ruigrok et al., 2008;Boué et al., 2014;Phạm et al., 2018). Poli et al. (2017) attributed the seismic-phase-like features to the interference of high-order normal modes. ...
... Poli et al. (2017) attributed the seismic-phase-like features to the interference of high-order normal modes. Phạm et al. (2018) demonstrated these features arise from the similarity of multiple body-wave cross-terms with the same slowness at the receiver pairs. Kennett and Phạm (2018) demonstrated the same principle using the generalized ray theory, and Wang and Tkalčić (2020a) presented observational proof that each feature is made of multiple constituents. ...
Increasing seismic evidence has accumulated, suggesting that the Earth's outer core consists of distinct zones of low P-wave velocities in the top and bottom regions relative to the Preliminary Reference Earth Model (PREM). Seismically detected low velocities in the outer core could be linked with the stratification, essential for understanding the geodynamo and thermochemical evolution of the liquid core. However, a consistent globally-averaged radial structure of the outer core has not been obtained due to the incomplete coverage of sampling body waves. To remedy this problem, we explore the seismic structure of Earth's outer core by employing a new theoretical and observational concept termed coda correlation wavefield. We construct the global correlogram in the 15–50 s period range by stacking cross-correlations of the long-duration coda waves from the selected ten large earthquakes. We then assemble a dataset of prominent correlation features from the global correlogram that are sensitive to the outer core. The waveforms of these features are fit by computing synthetic correlograms through various outer core models. The obtained optimal model displays P-wave velocities in both the outer core's top and bottom, consistent with Coda Correlation Reference Earth Model (CCREM) and reduced relative to PREM. The P-wave velocity is ∼1% lower in the core's top than that in PREM, and the slow anomaly gradually approaches zero at about 800 km below the core-mantle boundary. The low seismic velocities in the top of the outer core could likely imply the formation of a thermal and/or compositional stratification.
... To improve the spatial sampling of the Earth's deep interior, coda correlation studies [27][28][29] , which exploit correlated features lasting in long earthquake recordings, have emerged as promising tools to probe the Earth's interiors. The correlation wave eld that exploits the similarity of weak signals samples the IC differently from the previous techniques 19,30 (for a recent review, see ref. 31 ). ...
... Their arrival times and slowness properties suggest they are seismic phases reverberating along the entire Earth's diameter, including the inner core, multiple times. Thus, we adopt an abbreviated nomenclature, similar to previously counterparts in the correlation wave eld 29 Figure S1). They present similar quality exotic phases of three-or fourfold reverberations that can be routinely observed. ...
... Additionally, the attenuation effect for ~ 10second periods is weak in the IC's upper part ( Figure S3), which is believed to be the most attenuative region in the Earth's interior 24 . The combination of these favorable conditions helps sustain signi cant energy for the PKIKP multiple passages through the Earth's bulk, which is best demonstrated by the pronounced expression of PKIKP multiple counterparts in the correlation wave eld 29 utilizing coda records several hours after the origin time. ...
Probing the Earth’s center is critical for understanding planetary formation and evolution. However, geophysical inferences have been challenging due to the lack of seismological probes sensitive to the Earth’s center. Here, by stacking waveforms recorded by a growing number of global seismic stations, we observe up-to-fivefold reverberating waves from selected earthquakes along the Earth's diameter. Differential travel times of these “exotic” arrival pairs, hitherto unreported in seismological literature, complement and improve currently available information. The inferred transversely isotropic inner-core model contains a ~ 650-km thick innermost ball with P-wave speeds ~ 4% slower at ~ 50° from the Earth’s rotation axis. In contrast, the inner core’s outer shell displays much weaker anisotropy with the slowest direction in the equatorial plane. Our findings strengthen the evidence for an anisotropically-distinctive innermost inner core and its transition to a weakly anisotropic outer shell, which could be a fossilized record of a significant global event from the past.
... Despite these difficulties, recent studies have led to a clearer picture and kept researchers motivated to find new techniques and methods for advancements. Most recently, harnessing shear-wave energy contained in the coda-correlation wavefield, Tkalčić & Pha . m (2018) devised a method and made novel observations that provided new opportunities and research directions. Here, we review historical and contemporary studies for the shear properties of the IC. First, we focus on detections of a solid IC and constraining shear-wave speed (Section 2). This is followed by a presentation of specific and detail ...
... e ; for a recent book covering the topic of waveform correlation, see Kennett & Fichtner 2021). Notably, the similarity between the two weak signals in the late earthquake coda becomes more prominent than the weak signals themselves. J waves manifested themselves via their similarity with other seismic core phases in the coda-correlation wavefield (Tkalčić & Pha . m 2018). Specifically, a pair of seismic phases (xPKIKPPKIKP-xPKJKP), with similar slowness, and hence, waveforms, can result in a cross-correlation peak and the feature named I2-PKJKP (I2-J). The "x" represents any seismic phase (Figure 3b,c). For example, "x" can be replaced with PcP, and as a result, the pair that contributes to the formatio ...
... . When all contributions described above are stacked, the I2-J amplitude is enhanced and becomes visible in a global correlogram. As shown in Figure 5, the I2-J is identified as a cusp of energy in the synthetic correlogram whose timing was shown as dependent on IC shear-wave speed (shown in figure 2 to investigate shear-wave properties in the IC. Tkalčić & Pha . m (2018) obtained evidence for a solid but soft (high Poisson ratio) Earth's IC, with shear-wave speeds and shear moduli of 3.42 ± 0.02 km/s and 149.0 ± 1.6 GPa near the ICB and 3.58 ± 0.02 km/s and 167.4 ± 1.6 GPa in Earth's center, values that are 2.5% lower than those reported in the PREM (Dziewoński & Anderson 1981). Interestingly, all the J ...
Understanding how Earth's inner core (IC) develops and evolves, including fine details of its structure and energy exchange across the boundary with the liquid outer core, helps us constrain its age, relationship with the planetary differentiation, and other significant global events throughout Earth's history, as well as the changing magnetic field. Since its discovery in 1936 and the solidity hypothesis in 1940, Earth's IC has never ceased to inspire geoscientists. However, while there are many seismological observations of compressional waves and normal modes sensitive to the IC's compressional and shear structure, the shear waves that provide direct evidence for the IC's solidity have remained elusive and have been reported in only a few publications. Further advances in the emerging correlation-wavefield paradigm, which explores waveform similarities, may hold the keys to refined measurements of all inner-core shear properties, informing dynamical models and strengthening interpretations of the IC's anisotropic structure and viscosity.
▪ What are the shear properties of the inner core, such as the shear-wave speed, shear modulus, shear attenuation, and shear-wave anisotropy?
Can the shear properties be measured seismologically and confirmed experimentally?
Expected final online publication date for the Annual Review of Earth and Planetary Sciences, Volume 50 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
... Many of the algorithm drivers discussed in this paper have also played an important role in deep earth research. In addition to being widely used for studying the crust and upper mantle, the development of seismic interferometry has also found application for extracting signals of new seismic phases that penetrate the lowermost mantle and core (Pham et al., 2018). The use of unsupervised machine learning to separate the signature of seismic wave scattering from effects due to radial variations in Earth properties has been used to map the presence of lateral heterogeneity near the core-mantle boundary (Kim et al., 2020). ...
The discipline of seismology is based on observations of ground motion that are inherently undersampled in space and time. Our basic understanding of earthquake processes and our ability to resolve 4D Earth structure are fundamentally limited by data volume. Today, Big Data Seismology is an emergent revolution involving the use of large, data‐dense inquiries that is providing new opportunities to make fundamental advances in these areas. This article reviews recent scientific advances enabled by Big Data Seismology through the context of three major drivers: the development of new data‐dense sensor systems, improvements in computing, and the development of new types of techniques and algorithms. Each driver is explored in the context of both global and exploration seismology, alongside collaborative opportunities that combine the features of long‐duration data collections (common to global seismology) with dense networks of sensors (common to exploration seismology). The review explores some of the unique challenges and opportunities that Big Data Seismology presents, drawing on parallels from other fields facing similar issues. Finally, recent scientific findings enabled by dense seismic data sets are discussed, and we assess the opportunities for significant advances made possible with Big Data Seismology. This review is designed to be a primer for seismologists who are interested in getting up‐to‐speed with how the Big Data revolution is advancing the field of seismology.
... Where t pp is the arrival time of the PP wave at the second receiver; t p is the arrival time of the P wave at the first station t green is the arrival time of the P wave between the two receivers, and T is the dominant period. This can be generalized for phases (e.g., Colombi et al., 2014;Roux et al., 2005b) and all cross-terms between two phases that share same ray parameter (slowness) (e.g., Pham et al., 2018). ...
Seismologists eagerly seek new and preferably low-cost ways to map the complex structure of the top few kilometers of the crust. Passive seismic imaging appears as a novel, low-cost, and environmentally-friendly approach for exploring the sub-surface in the mining context. Usually, passive seismic interferometry relies on blind correlations within long time series of seismic noise or coda waves. In this thesis, we propose a complementary approach: seismic interferometry using opportune sources, specifically moving sources that are not stationary in time. This new approach relies on an accurate understanding of the seismic source's mechanism, a careful signal time-window and station pairs selection, and seismic phase identification (surface and body waves).Massive freight trains were only recently recognized as a persistent, powerful cultural (human activity-caused) seismic source. For example, one train passage may generate a tremor with an energy output equivalent of a magnitude M1 earthquake and be detectable for up to 100 km from the track. Thus, these train signals can be considered an opportune seismic source for passive seismic interferometry because they are readily available, detectable, repeatable, and generate high-frequency broadband energy. To illustrate this novel method's potential, we show a case study in a mineral exploration context at the Marathon site, Ontario, Canada.The Marathon dataset consists of 30 days of continuous seismic data recorded by a dense array of 1020 1-component nodes. First, the sources of ambient seismic noise, including train signals, are identified and characterized, and the source mechanisms of train signals are discussed. Second, we developed the theory of seismic interferometry applied to opportune sources and designed a novel workflow to process and analyze this kind of data. By doing so, body- and surface-wave propagating between pairs of stations carefully oriented are retrieved. Finally, these arrivals are picked to generate a 3D seismic velocity model of the Marathon area near-surface. We discuss the pros and cons of the method compared to more standard approaches with the help of numerical modeling, specifically focusing on the potential for body-wave imaging and the retrieval of azimuthal anisotropy. Far from being restrained to near-surface imaging, this new way of analyzing opportune seismic sources can be applied in various contexts and scales using natural or man-generated signals.
... This phase is strongest in the secondary microcosmic band (0.1-1 Hz) but is also weakly present at longer periods (Fig. 2b, c). Whereas the origin of this phase could not be conclusively ascertained, it likely arises from the interference of multiple body wave phases (Pham et al., 2018). The fundamental mode Rayleigh waves group velocity dispersion curve was measured with the multiple filter technique (MFT) (Dziewonski et al., 1969;Herrmann, 1973;Levshin et al., 1989). ...
The Ethiopian Rift is a unique natural environment to study the different stages of evolution from initial continental rifting to embryonic seafloor spreading. We used transdimensional hierarchical Bayesian seismic ambient noise tomography to first construct group velocity maps across the Afar, Main Ethiopian Rift, and the adjoining plateaus, and then inverted these for a shear wave velocity model. The uppermost mantle shear wave velocity ranges between 3.9 and 4.3 km/s, 5–15% lower than the upper mantle velocity in the PREM model. The combined effect of temperature and partial melt is needed to explain a 15% shear wave velocity reduction in the uppermost mantle. Tectonic and magmatic activities are not limited to the rift center, but instead are widespread within the upper crust beneath the Main Ethiopian Rift and Afar. The Main Ethiopian Rift is dominated by two velocity belts, the Wonji Fault Belt along the rift axis and the Silti-Debre Zeit Fault Zone on the western side of the Central Main Ethiopian Rift; the Boru-Toru structural high appears to serve as a transfer zone between them, exhibiting relatively high crustal velocities (3.6 km/s) at 14 km depth. Low velocities persist in the crust beneath the rift flanks and border faults, indicating that they are still tectonically and magmatically active. The crust beneath the western plateau is characterized by a low-velocity anomaly, implying that the plateau is also active. Low-velocity linear belts are further imaged beneath the western and eastern plateaus, away from the active rift axes. These off-axis belts could represent failed or buried rifts.
