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A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the Earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the Earth.
A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the earth. Previously announced in STAR as N83-29893
Deep learning has emerged as a transformative tool for enhancing the extraction of reliable information from seismograms, addressing the increasing demand for precise and efficient seismic data analysis. We introduce an innovative encoder–decoder deep learning model, named WaveDenoiser, designed for noise reduction in the time domain, thereby eliminating the need for spectrogram computations that have been used for existing deep learning tools and significantly improving processing speed. Utilizing the benchmark dataset that is Stanford Earthquake Dataset, we developed three models of varying sizes: base, medium, and large. Notably, the large (referred to as WaveDenoiser) model demonstrated superior performance, achieving a median signal‐to‐noise ratio improvement of 8.8 dB on in‐distribution unseen data (in the same geographic region) and 7.7 dB on out‐distribution unseen data (in a new geographic region), outpacing both the base and medium models. Further evaluation of the WaveDenoiser model revealed a reduction in median arrival‐time errors by 0.02 s for P waves and 0.01 s for S waves when processing waveforms prior to phase picking using PhaseNet on in‐distribution unseen data. When tested on out‐distribution unseen data, the model also effectively reduced the P‐wave median arrival‐time error by 0.02 and 0.01 s in median arrival‐time error for S waves. Importantly, the application of WaveDenoiser resulted in a significant reduction of phase picking outliers by 1.1% to 3.6% for both P and S waves. In addition, we achieved over five times acceleration in processing speed compared with the seisBench implementation of DeepDenoiser. Our findings underscore the potential of WaveDenoiser as a powerful tool for improving seismic data analysis and processing efficiency.
Discriminating low-yield underground nuclear explosions from small earthquakes is a key task in monitoring nuclear test ban treaties. P/S amplitude ratios have been an effective discriminant for moderate-sized events recorded at regional distances, but it is unclear if they are as effective in discriminating small seismic events recorded at local distances (<150 km). The difference between local magnitude (M L ) and coda duration magnitude (M c ) has been proposed as a new discriminant that may complement P/S amplitude ratios at local distances. Here, in this work, we calculate high-frequency (up to ∼4 Hz) synthetic seismograms at epicentral distances of 0–30 km in realistic models of the Salt Lake basin (Utah, United States) to better understand how variations in source type and depth affect M L −M c values. The Earth models incorporate simplified 1D and deterministic 3D structures, small-wavelength stochastic velocity perturbations, and surface topography. Coda waves are enhanced for the more complicated models compared to the base 1D model, but still underpredict observed durations by about a factor of two, which results in overprediction of amplitude to duration ratios (i.e., M L −M c values) for a near-surface explosion and a 7 km deep earthquake. For both source types, the predicted M L and M c values decrease as source depth increases, and M L −M c shows only minor variation with depth; however, M L −M c is on average ∼0.5 units smaller for explosions than earthquakes. This finding may imply that M L −M c has sensitivity to source type, in addition to being a depth discriminant, but more modeling is needed given the limitations of the current study. Future modeling should incorporate higher-frequency (≳5 Hz) simulations over a larger distance range (0–150 km), where M L and M c are commonly measured, while honoring low shear velocities (<300 m/s) near the surface and sampling a wider range of earthquake and explosion source mechanisms.
Spheroidal-type seismogram study of wave generation, propagation, dispersion and attenuation in realistic spherical Earth models, especially Gutenberg-Bullen A-prime model
Torsional disturbances due to source buried below surface in Gutenberg-Bullen A prime heterogeneous spherical earth model, calculating seismograms
Seismic wave generation, propagation, dispersion and attenuation in gravitating sphere having homogeneous elastic mantle and liquid core, giving theoretical seismograms
Spheroidal disturbances theoretical seismograms on surface of gravitating elastic sphere with homogeneous mantle and liquid core, considering gravity and polar radial stress effects
Traveling wave propagation, modal vibrations and elastic transmission medium studies from theoretical seismograms for realistic gravitating heterogeneous spherical earth model
The use of polarization filters is demonstrated on lunar seismograms. Body-wave arrivals from artificial impacts are identified as surface reflections, which may be used for improving our knowledge of the lunar interior or to relocate surface events if an approximate location is known as well as an approximate model.
The damping in theoretical waveforms is described phenomenologically and a classification is proposed. A method for studying the Earth's crust was developed which includes this damping as derived from reflection seismograms. Seismic wave propagation by absorption, attenuation of seismic waves by scattering, and dispersion relations are considered. Absorption of seismic waves within the Earth as well as reflection and transmission of elastic waves seen through boundary layer absorption are also discussed.
Long-period lunar seismograms were studied with the aim of identifying consistent sets of direct shear and secondary wave arrivals, thus constraining the velocities in the lunar mantle and the depths of the velocity discontinuities. Two velocity models were used to locate the natural impacts and the shallow moonquakes and to obtain the travel time residuals. Seismic sections were made of the radial, transverse, and vertical components of ground motion for impacts, shallow, and deep moonquakes in order to search for consistent sets of secondary wave arrivals. No conclusive set of secondary arrivals could be recognized on the seismic sections and thus the velocities and depths of the velocity discontinuities cannot be severely constrained by secondary arrivals. It is likely that the crust is thinner than 50 km and that a first-order discontinuity separates the upper and lower crust at a depth of between 20 and 30 km.
Marley (1990) and Marley and Porco (1993) proposed that f-mode oscillations of Saturn could excite resonant density and bending waves in the inner C-ring. They hypothesized that certain wave features discovered by Rosen et al. (1991) that were not associated with known satellite resonances could be the result of such resonant interactions with the planetary oscillation modes. They also predicted that if this was the case the waves would be found to be density (and not bending) waves by Cassini and predicted the azimuthal wave number of the C-ring waves m. Employing Cassini VIMS stellar occultation data Hedman and Nicholson (2013) have now confirmed the predictions and demonstrated that at least some of the C-ring features identified by Rosen et al. are indeed likely caused by resonant oscillation modes of Saturn. Given this context we have taken a fresh look at the Saturn ring seismology. First we propose that an apparent bending wave denoted 'j' by Rosen may be a second order outer vertical resonance with the l=3, m=2 f-mode of Saturn and discuss the locations of other plausible second order resonances in the rings. Since only a handful of ring resonances have been identified, measuring even one or two additional planetary mode frequencies would substantially assist the process of inverting mode frequencies to constrain Saturn interior's structure. Using the available mode frequencies, modern inversion technique employed in stellar seismology, and a recent set of Saturn interior models we provide an initial estimation of what available mode frequencies are telling us about the interior structure of the planet. Since the f-modes are confined relatively closely to the planetary surface, most of the observed modes probe only the outermost layers of the planet that are already comparatively well understood. However the l = 2 mode does probe relatively deeply into the planet and we will discuss the potential the measurement of this mode frequency has for placing new constraints on the interior structure.
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Secondary ejecta explanation to seismograph of Apollo 12 LM impact
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Normal mode theory, extended to the slightly laterally heterogeneous Earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the Earth's lateral heterogeneity at l=2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l=2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5% in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the earth's lateral heterogeneity at l = 2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l = 2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 percent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.