Constraints on Moon's orbit 3.2 billion years ago from tidal bundle data

The angular momentum of the Earth-Moon system was initially dominated by Earth's rotation with a short solar day of around 4 hours duration. Since then, Earth gradually transferred angular momentum through tidal friction to the orbit of the Moon, resulting in an increasing orbital radius and a deceleration of Earth's rotation. Geologic observations of tidal deposits can be used to verify and constrain models of lunar orbital evolution. In this work we reexamine the oldest tidal record suitable for analysis from the Moodies Group, South Africa with an age of 3.22 billion years. Time frequency analysis of the series of thicknesses of the sandstone layers yields a periodicity at 15.0 layers, taking into account the possibility of missing laminae. Assuming a mixed tidal system, the duration of two neap-spring-neap cycles was 30.0 lunar days for dominant semidiurnal or 30.0 sidereal days for dominant diurnal tides. We derive the relationship between this observation and the past Earth-Moon distance and re-visit related published work. We find that the Earth-Moon distance 3.22 billion years ago was around 70% of today's value. The Archean solar day was around 13 hours long with around 700 solar days per year. The ratio of solar to lunar tide-raising torque controls the leakage of angular momentum from the Earth-Moon system, but deviation from the assumed ratio of 0.211 results in only moderate changes. A duration of a postulated 21-hour atmospheric resonance shorter than 200 million years would be consistent with our observation; it would significantly alter Earth-Moon distance

Seismic scattering and absorption parameters in the W-Bohemia/Vogtland region from elastic and acoustic radiative transfer theory

In this study, frequency-dependent seismic scattering and intrinsic attenuation parameters for the crustal structure beneath the W-Bohemia/Vogtland swarm earthquake region close to the border of Czech Republic and Germany are estimated. Synthetic seismogram envelopes are modelled using elastic and acoustic radiative transfer theory. Scattering and absorption parameters are determined by fitting these synthetic envelopes to observed seismogram envelopes from 14 shallow local events from the October 2008 W-Bohemia/Vogtland earthquake swarm. The two different simulation approaches yield similar results for the estimated crustal parameters and show a comparable frequency dependence of both transport mean free path and intrinsic absorption path length. Both methods suggest that intrinsic attenuation is dominant over scattering attenuation in the W-Bohemia/Vogtland region for the investigated epicentral distance range and frequency bands from 3 to 24 Hz. Elastic simulations of seismogram envelopes suggest that forward scattering is required to explain the data, however, the degree of forward scattering is not resolvable. Errors in the parameter estimation are smaller in the elastic case compared to results from the acoustic simulations. The frequency decay of the transport mean free path suggests a random medium described by a nearly exponential autocorrelation function. The fluctuation strength and correlation length of the random medium cannot be estimated independently, but only a combination of the parameters related to the transport mean free path of the medium can be computed. Furthermore, our elastic simulations show, that using our numerical method, it is not possible to resolve the value of the mean free path of the random medium

Fast and robust earthquake source spectra and moment magnitudes from envelope inversion

With the present study we introduce a fast and robust method to calculate the source displacement spectra of small earthquakes on a local to regional scale. The work is based on the publicly available Qopen method of full envelope inversion which is further tuned for the given purpose. Important source parameters -- seismic moment, moment magnitude, corner frequency and high-frequency fall-off -- are determined from the source spectra by fitting a simple earthquake source model. The method is demonstrated by means of a data set comprising the 2018 West Bohemia earthquake swarm. We report moment magnitudes, corner frequencies, and centroid moment tensors inverted from short period body waves with the Grond package for all earthquakes with a local magnitude larger than 1.8. Moment magnitudes calculated by envelope inversion show a very good agreement to moment magnitudes resulting from the probabilisitc moment tensor inversion. Furthermore, source displacement spectra from envelope inversion show a good agreement with spectra obtained by multiple taper analysis of the direct onsets of body waves, but are not affected by the large scatter of the second. The seismic moments obtained with the envelope inversion scale with corner frequencies according to $M_0 \propto f_{\mathrm{c}}^{-4.7}$. Earthquakes of the present data set result in a smaller stress drop for smaller magnitudes. Self-similarity of earthquake rupture is not observed. Additionally, we report frequency-dependent site amplification at the used stations.Comment: Version after peer-revie

Probing the in situ Elastic Nonlinearity of Rocks with Earth Tides and Seismic Noise

Heterogeneous materials such as rocks, concrete, and granular materials exhibit a strong elastic nonlinearity. The sensitivity of the elastic nonlinearity to the applied stress and pore pressure in principle allows the use of seismic waves for remote observations of stress or pore pressure changes. Yet the nonlinearity of rocks is difficult to quantify in situ as active deformation tests are not possible in the field. We investigate the elastic nonlinearity in a fully natural experiment using the ambient seismic noise of a single seismic station to sense changes of the seismic velocity in the subsurface reaching 0.026% in response to the minute deformation caused by various constituents of the tidal forces exerted by the Sun and Moon

Coseismic drop of seismic velocity caused by the 2023 Turkey–Syria earthquakes

The Mw 7.8 earthquake in Turkey on 6 February 2023 was extraordinary for various reasons. It originated in depth of only 10 km, ruptured along a fault plane around 300 km long and the surface was covered by an extensive network of high-quality seismic instruments. The strong motions resulted in a vast number of tragic casualties and huge material losses in Turkey and Syria. However, abundant and proximate seismic observations of this event and numerous aftershocks give an opportunity to deepen the understanding of earthquake processes. In this study, we carried out an assessment of coseismic changes of seismic velocity using Passive Image Interferometry. We used data from one strong-motion and twenty-four broadband sensors. We observed coseismic drops of seismic velocity, which reached up to -1.79 per cent at a location directly at the ruptured East Anatolian Fault Zone. Along the Mw 7.8 earthquake fault, we observe frequency dependence of the velocity changes. At frequencies above 0.5 Hz, the velocity drops seem to be higher at locations close to the ruptured faults than in the more distant areas

Magnitude estimates of earthquakes induced by the geothermal stimulations in Espoo/Helsinki, southern Finland : a comparison of different approaches

In 2018 and 2020, two weeks-long geothermal reservoir stimulations were performed some 6 km below the Helsinki capital area, Finland. The seismic activity was recorded by a set of surface broadband sensors and 100 geophones installed by the Institute of Seismology, University of Helsinki, as well as Finnish National Seismic Network stations. The local magnitudes (ML) of the recorded earthquakes are estimated using a Finnish local magnitude scale and the local magnitude of the largest induced event was 1.8. We apply three different approaches for estimation of moment magnitudes (MW) to a data base of ~400 induced seismic events from the 2018 stimulation to explore the variability and sensitivity of the magnitude estimates. This is important for real-time monitoring and decision making when the induced event magnitudes approach the pre-defined magnitude limit, and to assess which trends can be robustly associated to earthquake source physics. (1) We employ a time-domain calculation of source parameters based on the application of Parseval's theorem to the integrals of the squared spectral displacement and velocity for the horizontal S-wave trains. The time window between the S-wave arrival time and twice the length of the S-wave travel time is considered for the S-wave train isolation. (2) We obtain moment magnitude estimates from an inversion of 50 s long three-component envelopes based on radiative transfer. (3) We apply a moment tensor inversion to 0.71 s long P and 0.81 s long S-wave signals. We fit a linear ML-MW conversion model to the values obtained from the different approaches. Considering the available local magnitude range between –0.5 and 1.8, a comparison of the linear conversion models shows that the moment magnitudes form the envelope inversion are systematically larger by ~0.2 units compared to those obtained from the moment tensor inversion. While the moment magnitudes determined by the time-domain calculation consistently exceed those of the envelope inversion for small local magnitudes (by ~0.2 units), they tend to yield similar estimates towards the larger local magnitudes. Other source parameter systematics include that the smallest seismic moment is obtained with the moment tensor inversion, and the largest with the time-domain equivalent of the spectral integrals. An initial extension of the analysis to 2020 data yields ML-MW as well as corner frequency-MW scaling relations that are, interestingly, different compared to the 2018 results; we will present updated results that inform about the reliability of these trends

Reassessing evidence of Moon–Earth dynamics from tidal bundles at 3.2 Ga (Moodies Group, Barberton Greenstone Belt, South Africa)

Past orbital parameters of the Moon are difficult to reconstruct from geological records because relevant data sets of tidal strata are scarce or incomplete. The sole Archean data point is from the Moodies Group (ca 3.22 Ga) of the Barberton Greenstone Belt, South Africa. From the time-series analysis of tidal bundles from a well-exposed subaqueous sand wave of this unit, Eriksson and Simpson (Geology, 28, 831) suggested that the Moon’s anomalistic month at 3.2 Ga was closer to 20 days than the present 27.5 days. This is in apparent accordance with models of orbital mechanics which place the Archean Moon in a closer orbit with a shorter period, resulting in stronger tidal action. Although this study’s detailed geological mapping and section measuring of the site confirmed that the sandstone bed in question is likely a migrating dune, the presence of angular mud clasts, channel-margin slumps, laterally aggrading channel fills and bidirectional paleocurrents in overlying and underlying beds suggests that this bedform was likely located in a nearshore channel near lower-intertidal flats and subtidal estuarine bars; it thus carries risk of incomplete preservation. Repeated measurements of foreset thicknesses along the published traverse, measured perpendicular to bedding, failed to show consistent spectral peaks. Larger data sets acquired along traverses measured parallel to bedding along the 20.5 m wide exposure are affected by minor faulting, uneven outcrop weathering, changing illumination, weather, observer bias and show a low reproducibility. The most robust measurements herein confirm the periodicity peak of approximately 14 in the original data of Eriksson and Simpson (Geology, 28, 831). Because laminae may have been eroded, the measurements may represent a lower bound of about 28 lunar days per synodic month. This estimate agrees well with Earth–Moon dynamic models which consider the conservation of angular momentum and place the Archaean Moon in a lower orbit around a faster-spinning Earth

Reassessing evidence of Moon–Earth dynamics from tidal bundles at 3.2 Ga (Moodies Group, Barberton Greenstone Belt, South Africa)

Past orbital parameters of the Moon are difficult to reconstruct from geological records because relevant data sets of tidal strata are scarce or incomplete. The sole Archean data point is from the Moodies Group (ca 3.22 Ga) of the Barberton Greenstone Belt, South Africa. From the time-series analysis of tidal bundles from a well-exposed subaqueous sand wave of this unit, Eriksson and Simpson (Geology, 28, 831) suggested that the Moon’s anomalistic month at 3.2 Ga was closer to 20 days than the present 27.5 days. This is in apparent accordance with models of orbital mechanics which place the Archean Moon in a closer orbit with a shorter period, resulting in stronger tidal action. Although this study’s detailed geological mapping and section measuring of the site confirmed that the sandstone bed in question is likely a migrating dune, the presence of angular mud clasts, channel-margin slumps, laterally aggrading channel fills and bidirectional paleocurrents in overlying and underlying beds suggests that this bedform was likely located in a nearshore channel near lower-intertidal flats and subtidal estuarine bars; it thus carries risk of incomplete preservation. Repeated measurements of foreset thicknesses along the published traverse, measured perpendicular to bedding, failed to show consistent spectral peaks. Larger data sets acquired along traverses measured parallel to bedding along the 20.5 m wide exposure are affected by minor faulting, uneven outcrop weathering, changing illumination, weather, observer bias and show a low reproducibility. The most robust measurements herein confirm the periodicity peak of approximately 14 in the original data of Eriksson and Simpson (Geology, 28, 831). Because laminae may have been eroded, the measurements may represent a lower bound of about 28 lunar days per synodic month. This estimate agrees well with Earth–Moon dynamic models which consider the conservation of angular momentum and place the Archaean Moon in a lower orbit around a faster-spinning Earth

Comparison of multiple lapse time window analysis and qopen to determine intrinsic and scattering attenuation

This study compares the results of Multiple Lapse Time Windows Analysis (MLTWA) and full envelope inversion (Qopen) to determine intrinsic and scattering attenuation of the crust using the region around the central part of the Leipzig–Regensburg fault zone in Germany as an example. We use 18 of the region’s strongest earthquakes from 2008 to 2019 with a magnitude between 1.4 and 3.0 in the frequency band range between 3 and 34 Hz. The determined attenuation values of both methods are similar within their error bars. The inverse quality factors of the shear wave are relatively low compared to other regions, with values of 3.2 × 10−4 to 8.7 × 10−4 for Q−1i and 1.4 × 10−4 to 2.8 × 10−4 for Q−1sc⁠, respectively. As a by-product of Qopen, we also obtain the energy site amplification of the stations used in the inversion as well as source displacement spectra and moment magnitudes of the inverted earthquakes. Several combinations of inversion parameters were tested for MLTWA, with Q−1i and Q−1sc providing the lowest trade-off. Likewise, we investigated the influence of window length on the results of Qopen. We found a dependency of the results on the length, if the windows are shorter than 30 s. For longer time windows, the dependence disappears, and the result becomes independent of window length