Determination of the complex frequencies of the Earth's normal modes by autoregressive method

U ovom radu prezentirana su mjerenja svojstvenih frekvencija singleta i faktora dobrote za pet normalnih modova Zemlje, četiri fundamentalna moda 0S0, 0S2, 0S3, 0S4 i jedan viši harmonik 2S1. Normalni modovi Zemlje, zbog osjetljivosti na rotaciju, eliptičnost, lateralne heterogenosti i anizotropiju pod utjecajem su procesa razdvajanja, kada umjesto degenerirane frekvencije moda uočavamo njegovo razdvajanje na singlete. Za mjerenje svojstvenih frekvencija singleta modova korištena je autoregresijska metoda u frekvencijskoj domeni. Korištena je velika skupina podataka i po prvi put kombinirana su mjerenja gravimetra i seizmometra. Odnosno, ukupno je korišteno 113 gravimetara i seizmometara nakon 5 mega potresa iz 2004. (otočje Sumatra-Andaman, Indonezija), 2010. (Maule regija, Čile), 2011. (Tohoku, Japan), 2012. (Aceh, Indonezija) i 2015. (Illapel, Čile) godine, magnituda većih od 8, zabilježenih na 46 postaja u svijetu. Rezultati izračunatih svojstvenih frekvencija i faktora dobrote singleta mjerenih modova pokazuju dobro slaganje s prijašnjim radovima. Pogreške, koje su dobivene bootstrap eksperimentima, pokazale su se realističnima i konzistentnima. Takoder, očekivano mjerenja su ukazala na odstupanja vrijednosti svojstvenih frekvencija singleta od teorijskih vrijednosti definiranih modelom Zemlje PREM. To potvrduje činjenicu da korišteni model nije dovoljan za opis efekata koje opažamo na realnim podacima zbog Zemljine kompleksnosti. Iako je metoda dala zadovoljavajuće rezultate, osjetljiva je na nelinearnosti u vremenskim nizovima koje mogu prouzrokovati pristranost mjerenja

Influence des ondes gravitationnelles sur les modes propres de la Terre

We have revisited and developed an analytical model of the interaction between the gravitational waves and the Earth in terms of normal modes excitation. We have first reevaluated the induced response for a spherical, radially heterogeneous and non-rotating model to monochromatic gravitational wave sources in terms of radial displacement at the Earth’s surface. Then we have developed a new analytical solution for a rotating elliptical model with lateral heterogeneities. We have considered sources of the gravitational waves that are the double white-dwarf binary systems. We have shown that for both models the only normal modes that are being excited are the quadrupole ones. The final responses highly depend on the gravitational wave frequencies, the largest response being at resonance with a normal mode. However, the detection of these elusive signals in gravimetric and seismological data is very difficult due to large environmental noise present in the data, even after using some signal processing techniques like the matched filtering. There are ten orders of magnitude difference between the calculated Earth’s normal modes response and the ambient noise level. Finally, we have highlighted some limitation of the signal processing techniques used for the search and analysis of the weak signals. In particular, some biases can be introduced when using different station distributions at the surface of the globe in the frame of normal mode studies.Nous avons révisé et développé une modélisation analytique de l’interaction des ondes gravitationnelles avec la Terre en termes d’excitation des modes propres. Nous avons, dans un premier temps, réévalué la réponse d’une Terre sphérique, sans rotation et radialement stratifiée à des sources d’ondes gravitationnelles monochromatiques en termes de déplacement radial induit à la surface. Nous avons ensuite développé une nouvelle solution pour une Terre en rotation, ellipsoïdale et latéralement hétérogène. Nous avons considéré comme sources d’ondes gravitationnelles les systèmes binaires de naines blanches. Dans les deux cas, les seuls modes propres qui sont excités sont les modes quadripolaires. La réponse finale dépend fortement de la fréquence de l’onde gravitationnelle, la plus grande excitation étant à résonance avec des modes propres. Cependant, la détection de ces faibles signaux dans des données gravimétriques ou sismologiques est très difficile de par la présence d’un bruit trop élevé dans ces observations et ce même après l’utilisation de techniques de traitement du signal, comme le filtrage adaptatif. La réponse de la Terre en termes d’excitation des modes propres est dix ordres de grandeur plus faible que le niveau de bruit ambiant sur Terre. Finalement, nous avons mis en évidence certaines limites d’outils de traitement du signal utilisés pour la recherche et l’analyse de petits signaux. En particulier, la distribution des stations à la surface du globe peut introduire des biais dans l’étude des modes propres

Perturbation of the Earth's rotation by monochromatic gravitational waves from astrophysical sources

International audienceGravitational waves (GWs) of astrophysical origin were detected for the first time in 2015 through strain deformation measured at the Earth's surface. The inertia tensor of the deformable Earth is also disturbed resulting in the perturbation of its rotation vector and excitation of the rotational normal modes. Using a linearized theory of gravitation and the linearized equations of conservation √ Hz for fg = 10 −4 Hz and h0 = 10 −16. The strain amplitudes of such centrifugal deformation are beyond the detectability of current laser strainmeters used to detect GWs. In the future, improvement in the sensitivities of geophysical instruments to measure Earth's rotation fluctuations, particularly at sub-daily periods, and the development of the Laser Interferometer Space Antenna would make the present quantifications worth considering

Erratum: Earth’s spheroidal motion induced by a gravitational wave in flat spacetime [Phys. Rev. D 100 , 044048 (2019)]

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Earth’s spheroidal motion induced by a gravitational wave in flat spacetime

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Designing Convolutional Neural Network Pipeline for Near‐Fault Earthquake Catalog Extension Using Single‐Station Waveforms

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Interpreting convolutional neural network decision for earthquake detection with feature map visualization, backward optimization and layer-wise relevance propagation methods

International audienceSUMMARY In the recent years, the seismological community has adopted deep learning (DL) models for many diverse tasks such as discrimination and classification of seismic events, identification of P- and S-phase wave arrivals or earthquake early warning systems. Numerous models recently developed are showing high accuracy values, and it has been attested for several tasks that DL models perform better than the classical seismological state-of-art models. However, their performances strongly depend on the DL architecture, the training hyperparameters, and the training data sets. Moreover, due to their complex nature, we are unable to understand how the model is learning and therefore how it is making a prediction. Thus, DL models are usually referred to as a ‘black-box’. In this study, we propose to apply three complementary techniques to address the interpretability of a convolutional neural network (CNN) model for the earthquake detection. The implemented techniques are: feature map visualization, backward optimization and layer-wise relevance propagation. Since our model reaches a good accuracy performance (97%), we can suppose that the CNN detector model extracts relevant characteristics from the data, however a question remains: can we identify these characteristics? The proposed techniques help to answer the following questions: How is an earthquake processed by a CNN model? What is the optimal earthquake signal according to a CNN? Which parts of the earthquake signal are more relevant for the model to correctly classify an earthquake sample? The answer to these questions help understand why the model works and where it might fail, and whether the model is designed well for the predefined task. The CNN used in this study had been trained for single-station detection, where an input sample is a 25 s three-component waveform. The model outputs a binary target: earthquake (positive) or noise (negative) class. The training database contains a balanced number of samples from both classes. Our results shows that the CNN model correctly learned to recognize where is the earthquake within the sample window, even though the position of the earthquake in the window is not explicitly given during the training. Moreover, we give insights on how a neural network builds its decision process: while some aspects can be linked to clear physical characteristics, such as the frequency content and the P and S waves, we also see how different a DL detection is compared to a visual expertise or an STA/LTA detection. On top of improving our model designs, we also think that understanding how such models work, how they perceive an earthquake, can be useful for the comprehension of events that are not fully understood yet such as tremors or low frequency earthquakes

Testing performances of the optimal sequence estimation and autoregressive method in the frequency domain for estimating eigenfrequencies and zonal structure coefficients of low-frequency normal modes

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Lunar Gravitational-Wave Detection

A new era of lunar exploration has begun bringing immense opportunities for science as well. It has been proposed to deploy a new generation of observatories on the lunar surface for deep studies of our Universe. This includes radio antennas, which would be protected on the far side of the Moon from terrestrial radio interference, and gravitational-wave (GW) detectors, which would profit from the extremely low level of seismic disturbances on the Moon. In recent years, novel concepts have been proposed for lunar GW detectors based on long-baseline laser interferometry or on compact sensors measuring the lunar surface vibrations caused by GWs. In this article, we review the concepts and science opportunities for such instruments on the Moon. In addition to promising breakthrough discoveries in astrophysics and cosmology, lunar GW detectors would also be formidable probes of the lunar internal structure and improve our understanding of the lunar geophysical environment.ISSN:1572-9672ISSN:0038-630

Lunar Gravitational-Wave Detection

International audienceAbstract A new era of lunar exploration has begun bringing immense opportunities for science as well. It has been proposed to deploy a new generation of observatories on the lunar surface for deep studies of our Universe. This includes radio antennas, which would be protected on the far side of the Moon from terrestrial radio interference, and gravitational-wave (GW) detectors, which would profit from the extremely low level of seismic disturbances on the Moon. In recent years, novel concepts have been proposed for lunar GW detectors based on long-baseline laser interferometry or on compact sensors measuring the lunar surface vibrations caused by GWs. In this article, we review the concepts and science opportunities for such instruments on the Moon. In addition to promising breakthrough discoveries in astrophysics and cosmology, lunar GW detectors would also be formidable probes of the lunar internal structure and improve our understanding of the lunar geophysical environment