Problems of theoretical seismology and physics of the earth's interior <voprosy teoreticheskoi seismologii i fiziki zemnykh nedr<
Theoretical seismology and physics of earth core and mantle
SEISMOLOGY↗
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Numerical modelling of impact seismic sources using the stress glut theory
SUMMARY Meteorite impacts have proved to be a significant source of seismic signal on the Moon, and have now been recorded on Mars by InSight seismometers. Understanding how impacts produce seismic signal is key to the interpretation of this unique data, and to improve their identification in continuous seismic records. Here, we use the seismic Representation Theorem, and particularly the stress glut theory, to model the seismic motion resulting from impact cratering. The source is described by equivalent forces, some resulting from the impactor momentum transfer, and others from the stress glut, which represents the mechanical effect of plasticity and non linear processes in the source region. We condense these equivalent forces into a point-source with a time-varying single force and nine-component moment tensor. This analytical representation bridges the gap between the complex dynamics of crater formation, and the linear point-source representation classically used in seismology. Using the multiphysics modelling software HOSS, we develop a method to compute the stress glut of an impact, and the associated point-source from hypervelocity impact simulations. For a vertical and an oblique impact at 1000 m s−1, we show that the moment tensor presents a significant deviatoric component. Hence, the source is not an ideal isotropic explosion contrary to previous assumptions, and draws closer to a double couple for the oblique impact. The contribution of the point force to the seismic signal appears negligible. We verify this model by comparing two signals: (1) HOSS is coupled to SPECFEM3D to propagate the near-source signal elastically to remote seismic stations; (2) the point-source model derived from the stress-glut theory is used to generate displacements at the same distance. The comparison shows that the point-source model is accurately simulating the low-frequency impact seismic waveform, and its seismic moment is in trend with Lunar and Martian impact data. High-frequencies discrepancies exist, which are partly related to finite-source effects, but might be further explained by the difference in mathematical framework between classical seismology and HOSS’ numerical modelling.
79 ASTRONOMY AND ASTROPHYSICS↗
Observational and theoretical investigations in solar seismology
This is the final report on a project to develop a theoretical basis for interpreting solar oscillation data in terms of the interior dynamics and structure of the Sun. The topics covered include the following: (1) studies of the helioseismic signatures of differential rotation and convection in the solar interior; (2) wave generation by turbulent convection; and (3) the study of antipodal sunspot imaging of an active region tomography.
Noyes, Robert W.↗
Seismic moment tensor classification using elliptical distribution functions on the hypersphere
Discrimination of underground explosions from naturally occurring earthquakes and other anthropogenic sources is one of the fundamental challenges of nuclear explosion monitoring. In an operational setting, the number of events that can be thoroughly investigated by analysts is limited by available resources. The capability to rapidly screen out events that can be robustly identified as not being explosions is, therefore, of great potential benefit. Nevertheless, possible mis-classification of explosions as earthquakes currently limits the use of screening methods for verification of test-ban treaties. Moment tensors provide a physics-based classification tool for the characterization of different seismic sources and have enabled the advent of new techniques for discriminating between earthquakes and explosions. Following normalization and projection of their six-degree vectors onto the hypersphere, existing screening approaches use spherically symmetric metrics to determine whether any new moment tensor may have been an explosion. Here, we show that populations of moment tensors for both earthquakes and explosions are anisotropically distributed on the hypersphere. Distributions possessing elliptical symmetry, such as the scaled von Mises–Fisher distribution, therefore provide a better description of these populations than the existing spherically symmetric models. We describe a method that uses these elliptical distributions in combination with a Bayesian classifier to achieve successful classification rates of 99 per cent for explosions and 98 per cent for earthquakes using existing catalogues of events from the western United States. The 1983 May 5 Crowdie underground nuclear test and 2018 July 20 DAG-1 deep-borehole chemical explosion are the only two explosions out of 140 that are incorrectly classified. Application of the method to the 2006–2017 nuclear tests in the Democratic People’s Republic of Korea yields 100 per cent identification rates and we provide a simple routine MTid for general usage. The approach provides a means to rapidly assess the likelihood of an event being an explosion and can be built into monitoring workflows that rely on simultaneously assessing multiple different discrimination metrics.
58 GEOSCIENCES↗
Seismology - Responsibilities and requirements of a growing science. Part 2 - problems and prospects
Theoretical and applied seismology, earthquake engineering, earth structure, industrial uses, facilities, and underground nuclear explosion detection
Source record↗
Magnectic Probing of Core Geodynamics
To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth s core and uncertainty. If this agrees with the seismologic value, then the hypotheses pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth s core, this yields a JGR-PI, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change.In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length- scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto- geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core- source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.
Voorhies, Coerte↗
Magnetic Probing of Core Geodynamics
To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynamical hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothesis passes the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale range. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at length-scale 1/k, if one presumes kinetic energy is converted in either eddy-overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small-scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magnetogeostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core-mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order 120 years is pseudo-scale-invariant. Magnetic spectra of other planets may differ; however, if a transition to non-conducting fluid hydrogen in Jupiter acts as a barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.
Voorhies, Coerte V.↗
Magnetic Probing of Core Geodynamics
To better understand geomagnetic theory and observation, we can use spatial magnetic spectra for the main field and secular variation to test core dynmcal hypotheses against seismology. The hypotheses lead to theoretical spectra which are fitted to observational spectra. Each fit yields an estimate of the radius of Earth's core and uncertainty. If this agrees with the seismologic value, then the hypothes pass the test. A new way to obtain theoretical spectra extends the hydromagnetic scale analysis of Benton to scale-variant field and flow. For narrow scale flow and a dynamically weak field by the top of Earth's core, this yields a generalized Stevenson-McLeod spectrum for the core-source field, and a secular variation spectrum modulated by a cubic polynomial in spherical harmonic degree n. The former passes the tests. The latter passes many tests, but does not describe rapid dipole decline and quadrupole rebound; some tests suggest it is a bit hard, or rich in narrow scale change. In a core geodynamo, motion of the fluid conductor does work against the Lorentz force. This converts kinetic into magnetic energy which, in turn, is lost to heat via Ohmic dissipation. In the analysis at lentgh-scale l/k, if one presumes kinetic energy is converted in either eddy- overturning or magnetic free-decay time-scales, then Kolmogorov or other spectra in conflict with observational spectra can result. Instead, the rate work is done roughly balances the dissipation rate, which is consistent with small scale flow. The conversion time-scale depends on dynamical constraints. These are summarized by the magneto-geostrophic vertical vorticity balance by the top of the core, which includes anisotropic effects of rotation, the magnetic field, and the core- mantle boundary. The resulting theoretical spectra for the core-source field and its SV are far more compatible with observation. The conversion time-scale of order l20 years is pseudo-scale-invarient. Magnetic spectra of other planets may differ; however, if a transition to non-conductmg fluid hydrogen in Jupiter acts as barrier to vertical flow, as well as current, then the shape of the jovi-magnetic spectrum could be remarkably Earth-like.
Voorhies, Coerte V.↗
Preface to the Focus Section on Geophysical Observations of the OSIRIS-REx Sample Return Capsule Re-Entry
Here, this focus issue of Seismological Research Letters compiles observational results and theoretical interpretations related to the OSIRIS-REx SRC re-entry and multidisciplinary analyses highlighting broader scientific applications of such events (Carr et al., 2025; Clemente et al., 2025; Fernando et al., 2025; KC et al., 2025; Silber and Bowman, 2025). The articles contribute toward a geophysical understanding of how hypersonic objects interact with Earth’s atmosphere and how generated acoustic waves propagate through the atmosphere and couple into the ground as measurable seismic signals.
58 GEOSCIENCES↗
The Topographic Torque on a Bounding Surface of a Rotating Gravitating Fluid and the Excitation by Core Motions of Decadal Fluctuations in the Earth's Rotation
General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.
Hide, Raymond↗
The five-minute oscillations: What's left to be done
Current observational methods for studying these oscillations at large horizontal wavenumbers are discussed in detail and several two dimensional power spectra obtained with a CID camera on the main spectrograph of the McMath telescope at Kitt Peak National Observatory are described. The best-resolved observations of the p-mode obtained at chromospheric elevations are also presented. Recent progress in studies of the p-modes at low wavenumbers with full-disk velocity detection schemes is summarized. These full-disk observations of radial and low-degree non-radial modes were shown to place severe constraints on the theoretical calculation of solar interior structure. Progress in making fully-consistent solar models which fit both the high- and low-wave number observations is described. Finally, the observational and theoretical improvements that are necessary for further progress in solar seismology are summarized.
Rhodes, E. J., Jr.↗
Sunspot dynamics
The goal of this research was the understanding of the various oscillatory, transient, and quasi-steady motions in sunspots and the basic structure of a sunspot. The research involved both theoretical modeling (based on thermohydrodynamic theory) and observations of dynamical phenomena in sunspots. The principal topics of the research were sunspot seismology (the interaction of solar p-modes with a sunspot as a probe of the subsurface structure of a sunspot); three minute umbral oscillations and their relation to the structure of the umbral atmosphere; siphon flows in isolated magnetic flux tubes and their relation to the photospheric Evershed flow and to intense magnetic elements outside of sunspots; and more general theoretical work on magneto-atmospheric waves. Here, a summary of results is given.
Thomas, John H.↗
Deep Learning Models for Planetary Seismicity Detection
Research in planetary seismology is fundamentally constrained by a lack of data. Seismo-logical science products of future missions can typically only be informed by theoretical signal/noise characteristics of the environment or likely Earth-analogues. Although objectives can be re-assessed after some initial data-collection upon lander arrival, transfer of high-resolution data back to Earth is costly on lander power usage. Over the last several years, development of GPU computing techniques and open-source high-level APIs have led to rapid advances in deep learning within the fields of computer vision, natural language processing, and collaborative filtering. These techniques are actively being adapted in seismology for a variety of tasks, including: earthquake detection, seismic phase discrimination, and ground-motion prediction. Until the recent detection of mars quakes during the Mars InSight mission, the only other measurements of seismicity recorded outside of Earth was on the Moon during the Apollo missions between 1969 to 1977. These unique data sets have been periodically revisited using new seismological methods, including ambient noise interferometry and Hidden Markov Models. Our objective is to develop a deep learning seismic detector and use it to catalog moonquakes from the Apollo 17 Lunar Seismic Profiling Experiment (LSPE) and compare the results with those obtained by other methods. Additionally, we will assess the accuracy tradeoff between using a training set of lunar data and one composed of Earth seismicity. In this document, we present preliminary results using a prototype classifier trained on a small set of earthquakes that was able to obtain detections for LSPE moonquakes with a greater accuracy than a recent study using Hidden Markov Models.
Civilini, F.↗
More on Magnetic Spectra from Correlated Crustal Sources on Mars
The spectral method for distinguishing crustal from core-source magnetic fields has been re-examined, modified and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. These observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we found fields from a core of radius 3512 plus or minus 64 km, in accord with the 3480 km seismologic radius, and a crust represented by a shell of random dipolar sources at radius 6367 plus or minus 14 km, just beneath the 6371.0 km mean radius. For Mars we found only a field from a crust represented in same way, but 46 plus or minus 10 km below the planetary mean radius of 3389.5 km, and with sources about 9.6 plus or minus 3.2 times stronger than Earth's. It is remarkable that the same simple theoretical form should fairly fit crustal magnetic spectra for both worlds and return crustal-source depth estimates of plausible magnitude. Evidently, the idea of an ensemble of compact, quasi-independent, magnetized regions within these planetary crusts has some merit. Yet such estimates, at best a kind of average, depend upon both the observational spectrum fitted and the physical basis of the theoretical spectrum.
Voorhies, C. V.↗
Scientific Rationale and Requirements for a Global Seismic Network on Mars
Following a brief overview of the mission concepts for a Mars Global Network Mission as of the time of the workshop, we present the principal scientific objectives to be achieved by a Mars seismic network. We review the lessons for extraterrestrial seismology gained from experience to date on the Moon and on Mars. An important unknown on Mars is the expected rate of seismicity, but theoretical expectations and extrapolation from lunar experience both support the view that seismicity rates, wave propagation characteristics, and signal-to-noise ratios are favorable to the collection of a scientifically rich dataset during the multiyear operation of a global seismic experiment. We discuss how particular types of seismic waves will provide the most useful information to address each of the scientific objectives, and this discussion provides the basis for a strategy for station siting. Finally, we define the necessary technical requirements for the seismic stations.
Solomon, Sean C.↗
An extensive bibliography on long baseline interferometry
Long baseline interferometry has grown from a simple concept of an optical device for detecting light fringes to a highly theoretical and sophisticated system assisted by computers and modern electronic components. The areas of applications include radio astronomy, radio science, geodesy, tectonics, space navigation, and seismology.
Benjauthrit, B.↗
The theory of sunspots
This review covers the present state of our theoretical understanding of the physics of sunspots, along with the principal observational results that need to be explained. The topics covered range from the detailed structure of an individual sunspot to the broad connection between sunspots and the global solar magnetic field and the solar cycle. Our aim is to give a critical discussion of the theoretical ideas and models without presenting mathematical details. After outlining the historical development of the basic concepts associated with the magnetohydrodynamic theory of sunspots, we discuss recent treatments of their properties and structure, placing special emphasis on developments that have occurred within the last ten years. There have been remarkable improvements in the theoretical modelling of sunspots, led by new ideas and by more elaborate and realistic numerical simulations. At the same time, new observations have raised new theoretical questions or caused old ones to be reconsidered. In particular, measurements of oscillations in and around sunspots have opened up the new field of sunspot seismology, while recent high-resolution observations have forced us to rethink the structure of a sunspot penumbra.
Thomas, John H.↗
On Magnetic Spectra of Earth and Mars
The spectral method for distinguishing crustal from core-source magnetic fields is reexamined, modified, and applied to both a comprehensive geomagnetic field model and an altitude normalized magnetic map of Mars. The observational spectra are fairly fitted by theoretical forms expected from certain elementary classes of magnetic sources. For Earth we find fields from a core of radius 3512 +/- 64 km, in accord with the seismologic core radius of 3480 km, and a crust represented by a shell of random dipolar sources at radius 6367 +/- 14 km, near the planetary mean radius of 6371.2 km. For Mars we find no sign of a core-source field, only a field from a crust represented in same way, but at radius 3344 +/- 10 km, about 46 km below the planetary mean radius of 3389.5 km, and with sources about 9.6 +/- 3.2 times stronger.
Voorhies, C. V.↗