Empirical Scaling Relations Research Articles

Revisiting empirical solar energetic particle scaling relations

Aims. The space radiation environment conditions and the maximum expected coronal mass ejection (CME) speed are assessed by investigating scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the speed of the CMEs. Methods. We used a complete catalog of SEP events, covering the last ∼25 years of CME observations (i.e., 1997–2017). We calculated the peak proton fluxes and integrated event fluences for events that reached an integral energy of up to E > 100 MeV. For a sample of 38 strong SEP events, we first investigated the statistical relations between the recorded peak proton fluxes (IP) and fluences (FP) at a set of integral energies of E > 10 MeV, E > 30 MeV, E > 60 MeV, and E > 100 MeV versus the projected CME speed near the Sun (VCME) obtained by the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph (SOHO/LASCO). Based on the inferred relations, we further calculated the integrated energy dependence of both IP and FP, assuming that they follow an inverse power law with respect to energy. By making use of simple physical assumptions, we combined our derived scaling laws to estimate the upper limits for VCME, IP, and FP by focusing on two cases of known extreme SEP events that occurred on 23 February 1956, (GLE05) and in AD774/775, respectively. Based on the physical constraints and assumptions, several options for the upper limit VCME associated with these events were investigated. Results. A scaling law relating IP and FP to the CME speed as VCME5 for CMEs ranging between ∼3400–5400 km/s is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775. At the same time, the upper CME speed that the current Sun can provide possibly falls within an upper limit of VCME ≤ 5500 km/s.

Counting the Unseen. I. Nuclear Density Scaling Relations for Nucleated Galaxies

The volumetric rate of tidal disruption events (TDEs) encodes information on the still-unknown demographics of central massive black holes (MBHs) in low-mass galaxies (≲109 M ⊙). Theoretical TDE rates from model galaxy samples can extract this information, but this requires accurately defining the nuclear stellar density structures. This region is typically dominated by nuclear star clusters (NSCs), which have been shown to increase TDE rates by orders of magnitude. Thus, we assemble the largest available sample of parsec-scale 3D density profiles that include NSC components. We deproject the point-spread-function-deconvolved surface-brightness profiles of 91 nearby galaxies of varying morphology and combine these with nuclear mass-to-light ratios estimated from measured colors or spectral synthesis to create 3D mass density profiles. We fit the inner 3D density profile to find the best-fit power-law density profile in each galaxy. We compile this information as a function of galaxy stellar mass to fit new empirical density scaling relations. These fits reveal positive correlations between galaxy stellar mass and central stellar density in both early- and late-type galaxies. We find that early-type galaxies have somewhat higher densities and shallower profiles relative to late-type galaxies at the same mass. We also use the density profiles to estimate the influence radius of each galaxy’s MBH and find that the sphere of influence was likely resolved in most cases. These new relations will be used in future works to build mock galaxy samples for dynamical TDE rate calculations, with the aim of constraining MBH demographics in low-mass galaxies.

An estimate of the impact rate on Mars from statistics of very-high-frequency marsquakes

The number density of impact craters on a planetary surface is used to determine its age, which requires a model for the production rate of craters of different sizes. On Mars, however, estimates of the production rate of small craters (<60 m) from orbital imagery and from extrapolation of lunar impact data do not match. Here we provide a new independent estimate of the impact rate by analysing the seismic events recorded by the seismometer onboard NASA’s InSight lander. Some previously confirmed seismically detected impacts are part of a larger class of marsquakes (very high frequency, VF). Although a non-impact origin cannot be definitively excluded for each VF event, we show that the VF class as a whole is plausibly caused by meteorite impacts. We use an empirical scaling relationship to convert between seismic moment and crater diameter. Applying area and time corrections to derive a global impact rate, we find that 280–360 craters >8 m diameter are formed globally per year, consistent with previously published chronology model rates and above the rates derived from freshly imaged craters. Our work shows that seismology is an effective tool for determining meteoroid impact rates and complements other methods such as orbital imaging.

DTM resolution controls the accuracy of estimating surface runoff indicators in flat, lowland landscapes

AbstractSurface runoff plays an important role in contaminant transport, nutrient loss, soil erosion and peak discharges in streams and rivers. Because it is the result of a variety of complex hydrological processes, estimating surface runoff using physically based hydrological models is challenging. Upscaling of physical soil properties is necessary to cope with the limits of computational power in surface runoff modelling. In flat landscapes, the (micro)topographic surface controls the onset and progression of surface runoff on saturated soils during rain events. Therefore, its proper representation is crucial when attempting to model and predict surface runoff. In this study, the influence of microtopography (centimetre scale) on estimations of maximum depression storage (MDS), random roughness (RR) and the connectivity threshold (CT) is explored. These properties are selected because they often serve as surface runoff indicators in hydrological modelling. To characterize microtopography, a terrestrial laser scanner (TLS) is used to generate a digital terrain model (DTM) of the study site with a horizontal spatial resolution of 5 cm. MDS, RR and CT are then calculated and compared to the values generated from the publicly available Dutch national DTM dataset with a resolution of 50 cm. Our results show considerable differences in MDS, RR and CT when calculated for the different input resolution datasets. Using DTMs that do not sufficiently capture microtopography leads to underestimation of MDS and RR, and to overestimation of CT. Our findings indicate that surface runoff indicators, and thereby the surface runoff response of a saturated surface to rainfall events, are defined at scales smaller than the scales of typically available DTMs. Understanding surface runoff through modelling studies therefore requires a framework that accounts for this lack of information arising from using coarser resolution DTMs. We demonstrate a linear relationship between MDS values generated from the different resolution DTMs. This opens the possibility of using empirical scaling relationships between high‐ and lower‐resolution DTMs to account for microtopography. Repetition of our measurements on similar surfaces would contribute to establishing such empirical scaling relationships. Our results should be seen as indicative of flat landscapes and surfaces where centimetre scale microtopography is relevant.

Galactic Magnetic Fields. I. Theoretical Model and Scaling Relations

Galactic dynamo models have generally relied on input parameters that are very challenging to constrain. We address this problem by developing a model that uses observable quantities as input: the galaxy rotation curve, the surface densities of the gas, stars and star formation rate, and the gas temperature. The model can be used to estimate parameters of the random and mean components of the magnetic field, as well as the gas scale height, root-mean-square velocity and the correlation length and time of the interstellar turbulence, in terms of the observables. We use our model to derive theoretical scaling relations for the quantities of interest, finding reasonable agreement with empirical scaling relations inferred from observation. We assess the dependence of the results on different assumptions about turbulence driving, finding that agreement with observations is improved by explicitly modeling the expansion and energetics of supernova remnants. The model is flexible enough to include alternative prescriptions for the physical processes involved, and we provide links to two open-source python programs that implement it.

Analyzing urban scaling laws in the United States over 115 years

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is difficult due to the challenge of defining city boundaries and a lack of historical data to study city dynamics over time and space. To address this issue, we analyze scaling between city infrastructure and population across 857 metropolitan areas in the conterminous United States over an unprecedented 115 years (1900–2015) using dasymetrically refined historical population estimates, historical urban road network models, and multi-temporal settlement data to define dynamic city boundaries. We demonstrate that urban scaling exponents closely match theoretical models over a century. Despite some close quantitative agreement with theory, the empirical scaling relations unexpectedly vary across regions. Our analysis of scaling coefficients, meanwhile, reveals that contemporary cities use more developed land and kilometers of road than cities of similar population in 1900, which has serious implications for urban development and impacts on the local environment. Overall, our results provide a new way to study urban systems based on novel, geohistorical data.

Optimization of InSAR based coseismic slip modeling for moderate earthquakes accounting for fore–aftershock sequence

Determination of coseismic slip distribution for moderate (moment magnitude, Mw≤ 6.5) earthquakes is challenging as the commonly-used interferometric synthetic aperture radar (InSAR) technique is unable to separate mainshock and fore–aftershocks due to its limited temporal resolution. In this study, we propose a new method of optimizing coseismic slip modeling by removing fore–aftershock contributions using earthquake relocation data and empirical earthquake source scaling relationships. The method is tested with a series of synthetic fore–main–aftershock sequences, through which we demonstrate that our method can largely recover the real slip distribution of the mainshock. The synthetic tests show that if the moment release by fore–aftershocks is ≥10% of the mainshock moment release, fore–aftershock corrections are necessary to improve the accuracy of coseismic slip model. We also test the proposed method with the 2021 Mw 6.3 northern Thessaly, Greece earthquake sequence, in which case we have independent InSAR measurements for both the mainshock and aftershocks. We successfully obtain the slip distribution of the mainshock from the main–aftershock-mixed InSAR measurements, and the result is highly consistent with that derived from the mainshock-only InSAR data. We also evaluate the robustness of the method using the northern Thessaly sequence through a series of tests, showing that the proposed method makes significant improvements even if the earthquake relocation error reaches 5 km. In the end, we apply the method to re-investigate the 2021 Mw 6.0 Yangbi earthquake sequence and find that previous studies may have overestimated the coseismic slip by 25% and the total seismic moment by 18%.

Empirical Earthquake Source Scaling Relations for Maximum Magnitudes Estimations in Central America

ABSTRACT Central America is a seismically active region where six tectonic plates (North America, Caribbean, Cocos, Nazca, Panama, and South America) interact in a subduction zone with transform faults and two triple points. This complex tectonic setting makes the maximum magnitude—Mmax—estimation a challenging task, with the crustal fault earthquakes being the most damaging in the seismic history of Central America. The empirical source scaling relations (ESSR) allow the Mmax of faults to be determined from rupture parameters. In this study, we use a dataset of well-characterized earthquakes in the region, comprising 64 events from 1972 to 2021 with magnitudes between Mw 4.1 and 7.7. The dataset incorporates records of rupture parameters (length, width, area, slip, and magnitude) and information on the faults and aftershocks associated. This database is an important product in itself, and through its use we determine which global relations fit best to our data via a residual analysis. Moreover, based on the best-quality records, we develop scaling relations for Central America (CA-ESSR) for rupture length, width, and area. These new relations were tested and compared with recent earthquakes, and logic trees are proposed to combine the CA-ESSR and the best-fit global relations. Therefore, we estimate the Mmax for 30 faults using the logic tree for rupture length, considering a total rupture of the fault and multifault scenarios. Our results suggest that in Central America rupture areas larger than other regions are required to generate the same magnitudes. We associate this with the shear modulus (μ), which seems to be lower (∼30% less) than the global mean values for crustal rocks. Furthermore, considering multifault ruptures, we found several fault systems with potential Mmax≥Mw 7.0. These findings contribute to a better understanding of regional seismotectonics and to the efficient characterization of fault rupture models for seismic hazards.

Reconstructing the Zama (Mexico) discovery source to sink palaeogeography, Part II: Sediment routing from the Late Miocene shelf‐margin to deepwater basin

AbstractThe Late Miocene source terrane tectonic history in the southern Gulf of Mexico Basin, as informed by detrital zircon geothermochronology data, supports a detailed regional palaeogeographic reconstruction from palaeoshoreline to the deepwater Zama minibasin of the Sureste salt basin. Seismic mapping points to a trio of pathways that converge upon two entry points into the Zama minibasin, illuminating how sediment gravity flows transit a complex seascape defined by shallow salt bodies. Consideration of empirical scaling relationships within and between segments of this sediment dispersal system allows for testable predictions of Upper Miocene submarine fan‐runout lengths over basin exploration areas. Distances from the reconstructed shelf‐margin to the Zama wells vary around 100 km, an increase of 20% over a straight‐line distance as flows likely navigated around extant salt stocks, walls and sheets. This 100‐km fan length is about 40% of the reconstructed minimum palaeo‐river length, within predicted ranges for smaller source‐to‐sink systems in tectonically active areas (25 to 50%). The estimated fan‐runout distance can be extended even further basinwards, considering the contemporaneous passage of the mobile Chortis block along the Tonala shear zone, expanding the Palaeo‐Rio Grijalva drainage network during the Tortonian. These Late Miocene deepwater systems linked to the Palaeo‐Rio Grijalva differ substantially from onshore Mexico‐sourced turbidity flows feeding into the axis of the north‐trending Veracruz Trough. Textural data from wells here suggests these systems were less effective at larger grain transport and sorting. Local (intrabasinal) variations are also evident within the Zama minibasin, as well data (image logs and cores) indicate that axially oriented sediment gravity flows involved fewer high‐density turbidities, depositing lower net‐to‐gross sandstones and thicker shales than those flowing transverse to the basin axis from a southeastern basin entry point. These interpretations will guide both local exploitation of these economic resources and could also support future exploration for analogous salt‐influenced deepwater reservoir systems in the Sureste basin and globally.

Design displacement for lifelines at fault crossings: the code-based approach for Europe

The earthquake-resistant design of lifelines, such as pipelines, tunnels and bridges, is based on the reliable representation and estimation of the seismic loading. In the case of lifeline–fault crossings, the design fault displacement is typically derived from estimates based on fault dimensions via empirical fault scaling relations for a given “design” scenario event. This approach comes with an unknown level of safety because the fault productivity and the actual distribution of earthquake events are essentially disregarded. To overcome this challenge, a simplified approach is proposed by statistically analyzing the outcome of probabilistic fault displacement hazard analyses (PFDHAs). A selection of faults from the 2020 European Fault-Source Model is used to build the logic tree and to set the range of parameters considered in the PFDHAs. The methodology allows the (mostly conservative) approximation of the fault displacement corresponding to any given return period based on readily available data, namely fault productivity, fault mechanism, fault length, and lifeline crossing location on the fault. The proposed methodology has been proposed and adopted as an informative Annex in prEN 1998-4:2022.

Fault displacement hazard estimation at lifeline–fault crossings: A simplified approach for engineering applications

Lifelines, such as pipelines, roads, and tunnels, are critical infrastructure and when crossing active tectonic faults, a reliable estimation of the fault displacement in case of an earthquake is required. The first and simplest approach is to use empirical fault scaling relations to compute the design fault displacement, but this may result in an unknown level of safety. Thus, the probabilistic fault displacement hazard analysis (PFDHA) is the appropriate tool to assess the fault displacement hazard within a performance-based framework. Based upon an established PFDHA model, we present a simplified approach for engineering applications focusing on the lifeline–fault crossing along with appropriate simplifications and assumptions to extend its applicability to numerous faults. The aim is to provide a structure-independent approach of PFDHA that can be used when a site-specific study is not required, not possible (e.g., absence of recent sediments for dating past events), or too cumbersome, e.g., for lifeline route selection. Additionally, an in-depth investigation is presented on the key parameters, such as maximum earthquake magnitude, fault length, recurrence rate of all earthquakes above a minimum magnitude, and lifeline-fault crossing site, and how they affect the hazard level. This approach will be the basis for deriving hazard-consistent expressions to approximate fault displacement for use within the Eurocodes. The latter is intended to serve as a compromise between hazard-agnostic fault scaling relations and a comprehensive PFDHA, which requires detailed calculations and site-specific seismological data.

JWST/NIRSpec Measurements of the Relationships between Nebular Emission-line Ratios and Stellar Mass at z ∼ 3–6

We analyze the rest-optical emission-line ratios of star-forming galaxies at 2.7 ≤ z < 6.5 drawn from the Cosmic Evolution Early Release Science (CEERS) Survey and their relationships with stellar mass (M *). Our analysis includes both line ratios based on the [N ii] λ6583 feature ([N ii] λ6583/Hα, ([O iii] λ5007/Hβ)/([N ii] λ6583/Hα) (O3N2), and [N ii] λ6583/[O ii] λ3727) and those featuring α-elements ([O iii] λ5007/Hβ, [O iii] λ5007/[O ii] λ3727 (O32), ([O iii] λλ4959, 5007 + [O ii] λ3727)/Hβ (R23), and [Ne iii] λ3869/[O ii] λ3727). Given the typical flux levels of [N ii] λ6583 and [Ne iii] λ3869, which are undetected in the majority of individual CEERS galaxies at 2.7 ≤ z < 6.5, we construct composite spectra in bins of M * and redshift. Using these composite spectra, we compare the relationships between emission-line ratios and M * at 2.7 ≤ z < 6.5 with those observed at lower redshift. While there is significant evolution toward higher excitation (e.g., higher [O iii] λ5007/Hβ, O32, O3N2) and weaker nitrogen emission (e.g., lower [N ii] λ6583/Hα and [N ii] λ6583/[O ii] λ3727) between z ∼ 0 and z ∼ 3, we find in most cases that there is no significant evolution in the relationship between line ratio and M * beyond z ∼ 3. The [Ne iii] λ3869/[O ii] λ3727 ratio is anomalous in showing evidence for significant elevation at 4.0 ≤ z < 6.5 at fixed mass, relative to z ∼ 3.3. Collectively, however, our empirical results suggest no significant evolution in the mass–metallicity relationship at 2.7 ≤ z < 6.5. Representative galaxy samples and metallicity calibrations based on existing and upcoming JWST/NIRSpec observations will be required to translate these empirical scaling relations into ones tracing chemical enrichment and gas cycling and to distinguish among descriptions of feedback in galaxy formation simulations at z > 3.

A New Wide-field Infrared Survey Explorer Calibration of Stellar Mass

We derive new empirical scaling relations between Wide-field Infrared Survey Explorer (WISE) mid-IR (MIR) galaxy photometry and well-determined stellar masses from spectral energy distribution modeling of a suite of optical–infrared photometry provided by the Data Release 4 (DR4) Catalog of the GAMA-KiDS-VIKING survey of the southern G23 field. The MIR source extraction and characterization are drawn from the WISE Extended Source Catalogue and the archival ALLWISE catalog, combining both resolved and compact galaxies in the G23 sample to a redshift of 0.15. Three scaling relations are derived: W1 3.4 μm luminosity versus stellar mass, and WISE W1–W2, W1–W3 colors versus mass-to-light ratio (M/L, sensitive to a variety of galaxy types from passive to star-forming). For each galaxy in the sample, we then derive the combined stellar mass from these scaling relations, producing M ⋆ estimates with better than ∼25%–30% accuracy for galaxies with >109 M ⊙ and <40%–50% for lower-luminosity dwarf galaxies. We also provide simple prescriptions for rest-frame corrections and estimating stellar masses using only the W1 flux and the W1–W2 color, making stellar masses more accessible to users of the WISE data. Given a redshift or distance, these new scaling relations will enable stellar mass estimates for any galaxy in the sky detected by WISE with high fidelity across a range of M/L ratios.

Revisiting empirical solar energetic particle scaling relations

Aims. The possible influence of solar superflares on the near-Earth space radiation environment are assessed through the investigation of scaling laws between the peak proton flux and fluence of solar energetic particle (SEP) events with the solar flare soft X-ray peak photon flux. Methods. We compiled a catalog of 65 well-connected (W20-90) SEP events during the last three solar cycles covering a period of ∼34 yr (1984–2020) that were associated with flares of class ≥C6.0, and investigated the statistical relations between the recorded peak proton fluxes (IP) and the fluences (FP) at a set of integral energies from E &gt; 10, &gt; 30, and &gt; 60 to &gt; 100 MeV versus the associated solar flare peak soft X-ray flux in the 1–8 Å band (FSXR). Based on the inferred relations, we calculated the integrated energy dependence of the peak proton flux (IP) and fluence (FP) of the SEP events, assuming that they follow an inverse power law with respect to energy. Finally, we made use of simple physical assumptions, combining our derived scaling laws, and estimated the upper limits for IP and FP focusing on the flare associated with the strongest ground level enhancement (GLE) directly observed to date (GLE 05 on 23 February 1956), and that inferred for the cosmogenic radionuclide-based SEP event of AD774/775. Results. A scaling law relating IP and FP to the solar soft X-ray peak intensity (FSXR) as ∝ $ {F}_{\mathrm{SXR}}^{5/6} $ for a flare with a FSXR = X600 (in the revised scale) is consistent with values of FP inferred for the cosmogenic nuclide event of AD774/775.

Analyzing the engineering feasibility of the direct fusion drive

The Direct Fusion Drive (DFD) and its terrestrial counterpart, the Princeton Field Reversed Configuration (PFRC) reactor, have seen significant developments in the past decade. Various groups conducted detailed research on the required specifications of the engine and associated technology for power delivery to onboard avionics and payloads. Multiple studies have also addressed the thrust generation mechanism using empirical specific power scaling relations and plasma flow simulations. Recent studies have designed spacecraft for missions to Earth’s second Lagrange point, Mars, transneptunian bodies like Pluto, and the neighboring star systems Alpha Centauri A and B. However, significant work is needed to design the engine components in detail using scientific scaling relations and ab inito calculations to develop the physical systems for prototyping and testing. After critically analyzing the reference design of the DFD and the underlying fusion reactor, this paper addresses the technological gaps and suggests avenues to improve specifications toward targets outlined in previous studies while considering costs. Further, the authors present a prototype engine and magnetohydrodynamic power conversion system design to study the engineering hurdles relevant to the practical implementation of the DFD.

NuSTAR Observations of a Heavily X-Ray-obscured AGN in the Dwarf Galaxy J144013+024744

We present a multiwavelength analysis of the dwarf Seyfert 2 galaxy J144013+024744, a candidate obscured active galactic nucleus (AGN) thought to be powered by an intermediate-mass black hole (IMBH, M • ≈ 104−106 M ⊙) of mass M • ∼ 105.2 M ⊙. To study its X-ray properties, we targeted J144013+024744 with NuSTAR for ≈100 ks. The X-ray spectrum was fitted with an absorbed power law, Pexmon, and a physical model (RXTorus). A Bayesian X-ray analysis was performed to estimate the posteriors. The phenomenological and the physical models suggest the AGN to be heavily obscured by a column density of N H = (3.4–7.0) × 1023 cm−2. In particular, the RXTorus model with a subsolar metallicity suggests the obscuring column to be almost Compton-thick. We compared the 2–10 keV intrinsic X-ray luminosity with the inferred X-ray luminosities based on empirical scaling relations for unobscured AGNs using L [Oiv] 25.89 μm, L [Oiii] λ5007, and L 6μm and found that the high-excitation [Oiv] line provides a better estimate of the intrinsic 2–10 keV X-ray luminosity ( erg s−1). Our results suggest that J144013+024744 is the first type 2 dwarf galaxy that shows X-ray spectroscopic evidence for obscuration. The column density that we estimated is among the highest measured to date for IMBH-powered AGNs, implying that a typical AGN torus geometry might extend to the low-mass end. This work has implications for constraining the BH occupation fraction in dwarf galaxies using X-ray observations.

Seismo-Lineaments in Egypt: Analysis and Implications for Active Tectonic Structures and Earthquake Magnitudes

Quiescent faults may be capable of creating catastrophic earthquakes in locations with moderate and/or low seismic activity, such as Egypt. This study combines structural, remote sensing (RS), geophysical, and seismic activity data to examine and analyze the relationship between tectonic structures and seismotectonic activity in Egypt. In a new seismo-lineaments map of Egypt, tectonic lineaments of the Egyptian mainland were delineated and classified. The database contains 8000 lineaments that were divided into distinct geographical zones using statistical analysis and general features. Delineated lineaments were integrated with digitized geological and geophysical surface and subsurface faults and geographic information systems (GIS) processing techniques were applied to produce 4249 faults. The spatial distribution of seismic activity was determined to extract 1968 competent faults out of 4249 capable faults (i.e., greater than 10 km and suitably orientated concerning the existing stress field). Maximum expected magnitudes (Mmax) were calculated for distinct seismogenic locations in Egypt, taking into account the nature of the regional rupture. At the national scale, empirical scaling relations between fault lengths and earthquake magnitude were employed for all mapped faults in Egypt. The findings concerning the faults were highly consistent with traditional geological information. The results suggest that our technique for estimating the highest predicted magnitudes produces similar values and might be used to evaluate Egypt’s possible future seismic hazard. The results were compared to seismic databases. The similarity of our results with those reported in the catalogs lends confidence to the proposed scheme.

Geologic and geodetic constraints on the magnitude and frequency of earthquakes along Malawi's active faults: the Malawi Seismogenic Source Model (MSSM)

Abstract. Active fault data are commonly used in seismic hazard assessments, but there are challenges in deriving the slip rate, geometry, and frequency of earthquakes along active faults. Herein, we present the open-access geospatial Malawi Seismogenic Source Model (MSSM; https://doi.org/10.5281/zenodo.5599616), which describes the seismogenic properties of faults that formed during ongoing east African rifting in Malawi. We first use empirically derived constraints to geometrically classify active faults into section, fault, and multifault seismogenic sources. For sources in the North Basin of Lake Malawi, slip rates can be derived from the vertical offset of a seismic reflector that dated lake cores indicate is 75 ka. Elsewhere, slip rates are constrained from advancing a systems-based approach that partitions geodetically derived rift extension rates in Malawi between seismogenic sources using a priori constraints on a regional strain distribution and a hanging wall flexural extension in magma-poor continental rifts. Slip rates are then combined with source geometry and empirical scaling relationships to estimate earthquake magnitudes and recurrence intervals, and their uncertainty is described from the variability in logic tree outcomes used in these calculations. Sources in the MSSM are 5–269 km long, which implies that large-magnitude (Mw 7–8) earthquakes may occur in Malawi. However, low slip rates (0.05–2 mm yr−1) mean that the frequency of such events will be low (recurrence intervals of ∼103–104 years). We also find that, for 9 out of 11 faults in Lake Malawi's North Basin, differences in the slip rates, when estimated independently from the geodetic data and the offset seismic reflector, are not statistically significant. The MSSM represents an important resource for investigating Malawi's increasing seismic risk and provides a framework for incorporating active fault data into seismic hazard assessment elsewhere in the East African Rift and other tectonically active regions.

Estimating the depth of gaps opened by planets in eccentric orbit

ABSTRACT Planets can carve gaps in the surface density of protoplanetary discs. The formation of these gaps can reduce the corotation torques acting on the planets. In addition, gaps can halt the accretion of solids on to the planets as dust and pebbles can be trapped at the edge of the gap. This accumulation of dust could explain the origin of the ring-like dust structures observed using high-resolution interferometry. In this work, we provide an empirical scaling relation for the depth of the gap cleared by a planet on an eccentric orbit as a function of the planet-to-star mass ratio q, the disc aspect ratio h, Shakura–Sunyaev viscosity parameter α, and planetary eccentricity e. We construct the scaling relation using a heuristic approach: we calibrate a toy model based on the impulse approximation with 2D hydrodynamical simulations. The scaling reproduces the gap depth for moderate eccentricities (e ≤ 4h) and when the surface density contrast outside and inside the gap is ≤102. Our framework can be used as the basis of more sophisticated models aiming to predict the radial gap profile for eccentric planets.

Spatio-temporal clustering of successive earthquakes as inferred from analyses of global CMT and NIED F-net catalogs

Investigation of the characteristic behavior of successive earthquakes that closely occur in space and time is important to understand the generation mechanism of earthquakes and useful to assess a triggered earthquake, especially around the area, where a first large earthquake took place. Here, we analyzed the Global Centroid Moment Tensor catalog from 1976 to 2016 for shallow earthquakes with a moment magnitude, {M}_{w}, of at least 5.5, and the F-net catalog, Japan, for 4le {M}_{w}<5.5, to clarify the spatio-temporal characteristics of the successive earthquakes. We first sorted all of the earthquakes in time and removed the aftershocks that occurred in and around the faults of earthquakes with {M}_{w} larger than the target magnitude range we investigated. Then, we selected source events from the beginning and searched for earthquakes that occurred within a horizontal distance (D) and a lapsed time ({T}_{a}) from the source event to group them in clusters. Then, the source event was selected from the catalog in order, and the same procedure was repeated. We counted the number of clusters, each of which consisted of successive earthquakes, for different D and {T}_{a}. To examine whether successive earthquakes were explained by random occurrences, we compared the results with simulations in which earthquakes occurred randomly in time but at the same locations matching the centroids in the real data. The comparison showed that the number of clusters for the simulation rapidly increased with D and merged with that for real data at a short distance, which is defined here as the triggering distance. We find that triggering distance is proportional to about 1/5 to 1/4 of the seismic moment {(M}_{0}) of the source event, and exponentially decreases with increasing {T}_{a}. Relating the derived empirical scaling relations between {M}_{0} and triggering distance from the equations in the ETAS model, we show that the observed exponents of 1/5 to 1/4 were well predicted from the estimated ETAS parameters in various regions around the world. These consistencies first show that successive occurrence of earthquakes is well explained by the ETAS model.Graphical abstract