Finite-source Effects Research Articles

How Rare Are TESS Free-floating Planets?

Recently, Kunimoto et al. claimed that a short-lived signal in the Transiting Exoplanet Survey Satellite (TESS) Sector 61 database was possibly caused by a microlensing event with a terrestrial-mass free-floating planet (FFP) lens. In this study, we investigate TESS’s ability to detect microlensing FFPs by considering the detailed source information (e.g., distance and radius), the TESS photometric accuracy, and finite-source effects. Using the FFP mass function from microlensing surveys toward the Galactic bulge, we find that only 0.0018 microlensing events are expected to be detected in TESS Sector 61 for the entire planetary mass range. The reported signal is unlikely to be a real microlensing event, which is consistent with the evidence from the long-term Optical Gravitational Lensing Experiment data that the signal was likely due to a stellar flare. By extrapolating our result to fainter stars until T = 16 mag and adopting a possible optimized search algorithm, we find that only ∼1 FFP event can be detected in the entire TESS mission within the first 7 yr. Significant improvements in our understanding of FFPs still require future satellite missions, such as Roman and Earth 2.0, which can detect thousands of FFPs.

Spectral Variance in a Stochastic Gravitational-wave Background from a Binary Population

A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational-wave signal. While the expected spectrum over population realizations is well known from Phinney, its higher-order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations due to finite source effects. If the time derivative of the binary orbital frequency can be expressed as a power law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns.

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.

Gaia21blx: Complete resolution of a binary microlensing event in the Galactic disk

Gravitational microlensing is a method that is used to discover planet-hosting systems at distances of several kiloparsec in the Galactic disk and bulge. We present the analysis of a microlensing event reported by the Gaia photometric alert team that might have a bright lens. In order to infer the mass and distance to the lensing system, the parallax measurement at the position of Gaia21blx was used. In this particular case, the source and the lens have comparable magnitudes and we cannot attribute the parallax measured by Gaia to the lens or source alone. Since the blending flux is important, we assumed that the Gaia parallax is the flux-weighted average of the parallaxes of the lens and source. Combining this assumption with the information from the microlensing models and the finite source effects we were able to resolve all degeneracies and thus obtained the mass, distance, luminosities and projected kinematics of the binary lens and the source. According to the best model, the lens is a binary system at $2.18 0.07$ kpc from Earth. It is composed of a G star with $0.95 odot $ and a K star with $0.53 odot $. The source is likely to be an F subgiant star at $2.38 1.71$ kpc with a mass of $1.10 odot $. Both lenses and the source follow the kinematics of the thin-disk population. We also discuss alternative models, that are disfavored by the data or by prior expectations, however.

Radio imaging of gravitationally lensed radio-quiet quasars

Abstract We present 6-GHz Very Large Array radio images of 70 gravitational lens systems at 300-mas resolution, in which the source is an optically-selected quasar, and nearly all of which have two lensed images. We find that about in half of the systems (40/70, with 33/70 secure), one or more lensed images are detected down to our detection limit of 20 $\mu$Jy beam−1, similar to previous investigations and reinforcing the conclusion that typical optically-selected quasars have intrinsic GHz radio flux densities of a few $\mu$Jy (∼1023 W Hz−1) at redshifts of 1–2. In addition, for ten cases it is likely that the lensing galaxies are detected in the radio. Available detections of, and limits on the far-infrared luminosities from the literature, suggest that nearly all of the sample lie on the radio-FIR correlation typical of star-forming galaxies, and that their radio luminosities are at least compatible with the radio emission being produced by star formation processes. One object, WISE2329−1258, has an extra radio component that is not present in optical images, and is difficult to explain using simple lens models. In-band spectral indices, where these can be determined, are generally moderately steep and consistent with synchrotron processes either from star-formation/supernovae or AGN. Comparison of the A/B image flux ratios at radio and optical wavelengths suggests a 10 per cent level contribution from finite source effects or optical extinction to the optical flux ratios, together with sporadic larger discrepancies that are likely to be due to optical microlensing.

Terrestrial- and Neptune-mass Free-Floating Planet Candidates from the MOA-II 9 yr Galactic Bulge Survey

We report the discoveries of low-mass free-floating planet (FFP) candidates from the analysis of 2006–2014 MOA-II Galactic bulge survey data. In this data set, we found 6111 microlensing candidates and identified a statistical sample consisting of 3535 high-quality single-lens events with Einstein radius crossing times in the range 0.057 < t E/days < 757, including 13 events that show clear finite-source effects with angular Einstein radii of 0.90 < θ E/μas < 332.54. Two of the 12 events with t E < 1 day have significant finite-source effects, and one event, MOA-9y-5919, with t E = 0.057 ± 0.016 days and θ E = 0.90 ± 0.14 μas, is the second terrestrial-mass FFP candidate to date. A Bayesian analysis indicates a lens mass of M ⊕ for this event. The low detection efficiency for short-duration events implies a large population of low-mass FFPs. The microlensing detection efficiency for low-mass planet events depends on both the Einstein radius crossing times and the angular Einstein radii, so we have used image-level simulations to determine the detection efficiency dependence on both t E and θ E. This allows us to use a Galactic model to simulate the t E and θ E distribution of events produced by the known stellar populations and models of the FFP distribution that are fit to the data. Methods like this will be needed for the more precise FFP demographics determinations from Nancy Grace Roman Space Telescope data.

Numerically studying the degeneracy problem in extreme finite-source microlensing events

ABSTRACT Most transit microlensing events due to very low mass lens objects suffer from extreme finite-source effects. While modelling their light curves, there is a known continuous degeneracy between their relevant lensing parameters, i.e. the source angular radius normalized to the angular Einstein radius ρ⋆, the Einstein crossing time tE, the lens impact parameter u0, the blending parameter, and the stellar apparent magnitude. In this work, I numerically study the origin of this degeneracy. I find that these light curves have five observational parameters (i.e. the baseline magnitude, the maximum deviation in the magnification factor, the full width at half-maximum $\rm {FWHM}=2 \mathit{ t}_{\rm {HM}}$, the deviation from a top-hat model, and the time of the maximum time derivative of microlensing light curves $T_{\rm {max}}=t_{\rm E}\sqrt{\rho _{\star }^{2}-u_{0}^{2}}$). For extreme finite-source microlensing events due to uniform source stars, we get tHM ≃ Tmax and the deviation from the top-hat model tends to zero, which both cause the known continuous degeneracy. When either ρ⋆ ≲ 10 or the limb-darkening effect is considerable, tHM and Tmax are two independent observational parameters. I use a numerical approach, i.e. random forests containing 100–120 decision trees, to study how these observational parameters are efficient in yielding the lensing parameters. These machine learning models find the mentioned five lensing parameters for finite-source microlensing events from uniform and limb-darkened source stars with the average R2-scores of 0.87 and 0.84, respectively. R2-score for evaluating the lens impact parameter gets worse on adding limb darkening, and for extracting the limb-darkening coefficient itself this score falls as low as 0.67.

Mechanical formation damage management in oil wells with finite extent hydraulic fractures and source effects using an asymptotic-perturbation method

The petroleum industry has used hydraulic fracturing technology to solve various problems and provide an understanding of many complex issues. This work presents a new analytical model to evaluate the effective permeability response during the oil’s production through a vertical well fully penetrating a pressure-sensitive reservoir with a finite extent hydraulic fracture. The nonlinear hydraulic diffusivity equation (NHDE) is solved analytically through an integro-differential model coupled with Green’s function (GF) related to an oil source plan representing a finite extent hydraulic fracture. A new effective hydraulic diffusivity deviator factor is also derived to represent the permeability loss as a function of the pore pressure throughout the well-reservoir life cycle. For this oil flow modeling, the general solution is expressed by the sum of the linear solution (constant permeability) plus a corrective term given by the combination of the exponential function Ei(xD,yD,tD) and the complementary error function erfc(xD,yD,tD). The proposed model is implemented in Matlab software to evaluate the effect of the effective deviator factor in the permeability response over the oil’s production period. The model calibration is performed through a numerical oil flow simulator, widely used in the petroleum industry, and the results were accurate.

Microlensing due to free-floating moon-planet systems

ABSTRACT Gravitational microlensing is a powerful method for detecting and characterizing free-floating planetary-mass objects (FFPs). FFPs could have exomoons rotating them. In this work, we study the probability of realizing these systems (i.e. free-floating moon-planet ones) through microlensing observations. These systems make mostly close caustic configurations with a considerable finite-source effect. We investigate finite-source microlensing light curves owing to free-floating moon-planet systems. We conclude that crossing planetary caustics causes an extensive extra peak at light curves’ wing that only changes its width if the source star does not cross the central caustic. If the source trajectory is normal to the moon-planet axis, the moon-induced perturbation has a symmetric shape with respect to the magnification peak, and its light curve is similar to a single-lens one with a higher finite-source effect. We evaluate the Roman efficiency for realizing moon-induced perturbations, which is $\left[0.002-0.094\right]\ \mathrm{ per\, cent}$ by assuming a log-uniform distribution for moon-planet mass ratio in the range ∈ [ −9, −2]. The highest detection efficiency (i.e. $\simeq 0.094~{{\ \rm per\ cent}}$) happens for Saturn-mass planets when moon-planet distance is ∼43Rp, where Rp is the Saturn radius. Enhancing planetary mass extends the event’s time-scale and decreases the finite-source effect, but it reduces the projected moon-planet distance normalized to the Einstein radius s(RE) which in turn decreases the size of planetary caustics and takes them away from the host planet’s position in close caustic configurations.

MOA-2019-BLG-008Lb: A New Microlensing Detection of an Object at the Planet/Brown Dwarf Boundary

We report on the observations, analysis and interpretation of the microlensing event MOA-2019-BLG-008. The observed anomaly in the photometric light curve is best described through a binary lens model. In this model, the source did not cross caustics and no finite-source effects were observed. Therefore, the angular Einstein ring radius θ E cannot be measured from the light curve alone. However, the large event duration, t E ∼ 80 days, allows a precise measurement of the microlensing parallax π E. In addition to the constraints on the angular radius θ * and the apparent brightness I s of the source, we employ the Besançon and GalMod galactic models to estimate the physical properties of the lens. We find excellent agreement between the predictions of the two galactic models: the companion is likely a resident of the brown dwarf desert with a mass M p ∼ 30 M Jup, and the host is a main-sequence dwarf star. The lens lies along the line of sight to the Galactic bulge, at a distance of ≤4 kpc. We estimate that in about 10 yr the lens and source will be separated by ∼55 mas, and it will be possible to confirm the exact nature of the lensing system by using high-resolution imaging from ground- or space-based observatories.

OGLE-2016-BLG-1093Lb: A Sub-Jupiter-mass Spitzer Planet Located in the Galactic Bulge

OGLE-2016-BLG-1093 is a planetary microlensing event that is part of the statistical Spitzer microlens parallax sample. The precise measurement of the microlens parallax effect for this event, combined with the measurement of finite-source effects, leads to a direct measurement of the lens masses and system distance, M host =0.38–0.57 M ⊙ and m p = 0.59–0.87 M Jup, and the system is located at the Galactic bulge (D L ∼ 8.1 kpc). Because this was a high-magnification event, we are also able to empirically show that the “cheap-space parallax” concept produces well-constrained (and consistent) results for ∣π E∣. This demonstrates that this concept can be extended to many two-body lenses. Finally, we briefly explore systematics in the Spitzer light curve in this event and show that their potential impact is strongly mitigated by the color constraint.

Seismic Waveform‐Coherence Controlled by Earthquake Source Dimensions

Rupture size is a fundamental earthquake source parameter that is challenging to infer independently from far-field seismological observations. Here, we develop a novel observational constraint on source size based on the decay rate of wavefield coherence across a seismic array. For a given earthquake, waveform coherence decays with increasing interstation distance or, more precisely, with increasing projection difference defined as the difference between the takeoff vectors associated to the two stations projected along the rupture direction. We find that coherence generally falls off with projection difference faster for earthquakes of larger magnitudes. The magnitude dependence of the coherence decay rate can be explained by a finite source effect: larger source sizes cause larger differences of phase delays between waves arriving from different parts of the rupture at different stations, hence a stronger spatial variability of the wavefield, resulting in a breakdown of waveform coherence. Assuming a 1-D Haskell's source model, the rupture size can be estimated from the coherence decay rate. We apply this method to USArray data of earthquakes in three subduction zones, the Sea of Okhotsk, South America and Japan. The source sizes inferred from the coherence decay patterns are consistent with scaling relations intermediate between width-saturated L-models and quasi equi-dimensional rupture models. Our observation captures a unique pattern of array waveform coherence and demonstrates the potential of utilizing waveform coherence to study earthquake source parameters.

Evaluation and Updates for the USGS San Francisco Bay Region 3D Seismic Velocity Model in the East and North Bay Portions

ABSTRACTWe update the eastern and the northern portions of the detailed domain of the U.S. Geological Survey San Francisco Bay region 3D seismic velocity model (SFVM) based on comparisons of recorded and synthetic ground motions from 20 moderate (Mw 3.7–4.6) earthquakes. We modify the current SFVM (v.08.3.0) by assigning alternate property-versus-depth relations to the existing 3D geologic model. In some places, changes correspond to reassigning correct relations in which geologic units appear to be mislabeled, and in other places we subdivide geologic units where mapped geologic boundaries are missing from the 3D models so that we can implement a velocity contrast across a boundary. We also make ad hoc adjustments to velocity rules near the surface in some areas to better fit arrival times (specifically, in the Livermore basin). The updates reduce misfits in waveform correlation, travel time, cumulative absolute displacement, and peak ground velocity and are included in v.21.1 of the model. The selected earthquakes are small enough so that we neglect finite-source effects and model them as point sources. This allows us to assume that observed waveform characteristics are the result of path effects, and discrepancies between synthetic and recorded motions arise from misrepresentation of the elastic properties. Our analysis suggests refining the 3D geologic model, and adjusting the rules assigning properties to the geologic units will further improve the accuracy of the SFVM for simulating earthquake ground motions.

A Multiparameter Degeneracy in Microlensing Events with Extreme Finite Source Effects

Abstract For microlenses with sufficiently low mass, the angular radius of the source star can be much larger than the angular Einstein ring radius of the lens. For such extreme finite source effect (EFSE) events, finite source effects dominate throughout the duration of the event. Here, we demonstrate and explore a continuous degeneracy between multiple parameters of such EFSE events. The first component in the degeneracy arises from the fact that the directly observable peak change of the flux depends on both the ratio of the angular source radius to the angular Einstein ring radius and the fraction of the baseline flux that is attributable to the lensed source star. The second component arises because the directly observable duration of the event depends on both the impact parameter of the event and the relative lens-source proper motion. These two pairwise degeneracies become coupled when the detailed morphology of the light curve is considered, especially when including a limb-darkening profile of the source star. We derive these degeneracies mathematically through analytic approximations and investigate them further numerically with no approximations. We explore the likely physical situations in which these mathematical degeneracies may be realized and potentially broken. As more and more low-mass lensing events (with ever decreasing Einstein ring radii) are detected with improving precision and increasing cadence from microlensing surveys, one can expect that more of these EFSE events will be discovered. In particular, the detection of EFSE microlensing events could increase dramatically with the Roman Space Telescope Galactic Bulge Time Domain Survey.

Single-lens mass measurement in the high-magnification microlensing event Gaia19bld located in the Galactic disc

Context. Microlensing provides a unique opportunity to detect non-luminous objects. In the rare cases that the Einstein radius θE and microlensing parallax πE can be measured, it is possible to determine the mass of the lens. With technological advances in both ground- and space-based observatories, astrometric and interferometric measurements are becoming viable, which can lead to the more routine determination of θE and, if the microlensing parallax is also measured, the mass of the lens. Aims. We present the photometric analysis of Gaia19bld, a high-magnification (A ≈ 60) microlensing event located in the southern Galactic plane, which exhibited finite source and microlensing parallax effects. Due to a prompt detection by the Gaia satellite and the very high brightness of I = 9.05 mag at the peak, it was possible to collect a complete and unique set of multi-channel follow-up observations, which allowed us to determine all parameters vital for the characterisation of the lens and the source in the microlensing event. Methods. Gaia19bld was discovered by the Gaia satellite and was subsequently intensively followed up with a network of ground-based observatories and the Spitzer Space Telescope. We collected multiple high-resolution spectra with Very Large Telescope (VLT)/X-shooter to characterise the source star. The event was also observed with VLT Interferometer (VLTI)/PIONIER during the peak. Here we focus on the photometric observations and model the light curve composed of data from Gaia, Spitzer, and multiple optical, ground-based observatories. We find the best-fitting solution with parallax and finite source effects. We derived the limit on the luminosity of the lens based on the blended light model and spectroscopic distance. Results. We compute the mass of the lens to be 1.13 ± 0.03 M⊙ and derive its distance to be 5.52−0.64+0.35 kpc. The lens is likely a main sequence star, however its true nature has yet to be verified by future high-resolution observations. Our results are consistent with interferometric measurements of the angular Einstein radius, emphasising that interferometry can be a new channel for determining the masses of objects that would otherwise remain undetectable, including stellar-mass black holes.

OGLE-2019-BLG-0960 Lb: the Smallest Microlensing Planet

Abstract We report the analysis of OGLE-2019-BLG-0960, which contains the smallest mass-ratio microlensing planet found to date (q = 1.2–1.6 × 10−5 at 1σ). Although there is substantial uncertainty in the satellite parallax measured by Spitzer, the measurement of the annual parallax effect combined with the finite source effect allows us to determine the mass of the host star (M L = 0.3–0.6 M ⊙), the mass of its planet (m p = 1.4–3.1 M ⊕), the projected separation between the host and planet (a ⊥ = 1.2–2.3 au), and the distance to the lens system (D L = 0.6–1.2 kpc). The lens is plausibly the blend, which could be checked with adaptive optics observations. As the smallest planet clearly below the break in the mass-ratio function, it demonstrates that current experiments are powerful enough to robustly measure the slope of the mass-ratio function below that break. We find that the cross-section for detecting small planets is maximized for planets with separations just outside of the boundary for resonant caustics and that sensitivity to such planets can be maximized by intensively monitoring events whenever they are magnified by a factor A &gt; 5. Finally, an empirical investigation demonstrates that most planets showing a degeneracy between (s &gt; 1) and (s &lt; 1) solutions are not in the regime ( ∣ log s ∣ ≫ 0 ) for which the “close”/“wide” degeneracy was derived. This investigation suggests that there is a link between the “close”/“wide” and “inner/outer” degeneracies and also that the symmetry in the lens equation goes much deeper than symmetries uncovered for the limiting cases.

On the detection of free-floating planets through microlensing towards the Magellanic Clouds

ABSTRACT In this work, we study detecting free-floating planets (FFPs) by microlensing observations towards the Magellanic Clouds (MCs). In comparison to similar events towards the Galactic bulge, an FFP in the Galactic halo produces on average longer microlensing events with smaller projected source radii towards these clouds. For these microlensing events, the relative lens-source velocities are on average smaller. The MC self-lensing events due to FFPs suffer from severe finite-source effects. We first simulate microlensing events due to FFPs towards MCs and assume a log-uniform step function for their mass. The efficiencies for capturing their lensing signatures (with signal-to-noise greater than 50) are found to be 0.1–0.6 per cent and 3–6 per cent through ground-based optical surveys and space-based near-infrared surveys, respectively. We then promote these simulations and assume the Roman telescope continuously observes each MC during one 72-d season with the 15 min observing cadence. From simulated microlensing events with the resolvable source stars at the baseline due to FFPs with the masses ∼0.01–104M⊕, Roman discovers their lensing effects with the efficiencies $\sim 10\!-\!80{{\ \rm per\ cent}}$, respectively. By adopting $5{{\ \rm per\ cent}}$ as haloes fraction from FFPs, we estimate the expected number of events. The highest number of detectable FFPs which is ∼1700–2200 per season per square degree happens for ones with masses ∼0.01M⊕. Our simulations show that Roman potentially extends the mass range of detectable FFPs in haloes down to 5.9 × 10−7M⊕ with continuous observations during one observing season from the Large Magellanic Cloud.

KMT-2019-BLG-2073: Fourth Free-floating Planet Candidate with θ E &lt; 10 μas

Abstract We analyze the very short Einstein timescale (t E ≃ 7 hr) event KMT-2019-BLG-2073. Making use of the pronounced finite-source effects generated by the clump giant source, we measure the Einstein radius θ E ≃ 4.8 μas and so infer a mass M = 59 M ⊕ ( π rel / 16 μ as ) − 1 , where π rel is the lens-source relative parallax. We find no significant evidence for a host of this planetary-mass object, though one could be present at sufficiently wide separation. If so, it would be detectable after about 10 yr. This is the fourth isolated microlens with a measured Einstein radius θ E &lt; 10 μas, which we argue is a useful threshold for a “likely free-floating planet (FFP)” candidate. We outline a new approach to constructing a homogeneous sample of giant-star finite-source/point-lens (FSPL) events, within which the subsample of FFP candidates can be statistically analyzed. We illustrate this approach using 2019 KMTNet data and show that there appears to be a large θ E gap between the two FFP candidates and the 11 other FSPL events. We argue that such sharp features are more identifiable in a sample selected on θ E compared to the traditional approach of identifying candidates based on short t E.

OGLE-2018-BLG-1428Lb: a Jupiter-mass planet beyond the snow line of a dwarf star

ABSTRACT We present the analysis of the microlensing event OGLE-2018-BLG-1428, which has a short-duration (∼1 d) caustic-crossing anomaly. The event was caused by a planetary lens system with planet/host mass ratio q = 1.7 × 10−3. Because of the detection of the caustic-crossing anomaly, the finite source effect was well measured, but the microlens parallax was not constrained due to the relatively short time-scale (tE = 24 d). From a Bayesian analysis, we find that the host star is a dwarf star $M_{\rm host}=0.43^{+0.33}_{-0.22} \ \mathrm{M}_{\odot }$ at a distance $D_{\rm L}=6.22^{+1.03}_{-1.51}\ {\rm kpc}$ and the planet is a Jovian-mass planet $M_{\rm p}=0.77^{+0.77}_{-0.53} \ M_{\rm J}$ with a projected separation $a_{\perp }=3.30^{+0.59}_{-0.83}\ {\rm au}$. The planet orbits beyond the snow line of the host star. Considering the relative lens-source proper motion of $\mu _{\rm rel} = 5.58 \pm 0.38\ \rm mas\ yr^{-1}$, the lens can be resolved by adaptive optics with a 30 m telescope in the future.

Regional broad-band ground-shaking modelling over extended and thick sedimentary basins: an example from the Lower Rhine Embayment (Germany)

The simulation of broad-band (0.1 to 10 + Hz) ground-shaking over deep and spatially extended sedimentary basins at regional scales is challenging. We evaluate the ground-shaking of a potential M 6.5 earthquake in the southern Lower Rhine Embayment, one of the most important areas of earthquake recurrence north of the Alps, close to the city of Cologne in Germany. In a first step, information from geological investigations, seismic experiments and boreholes is combined for deriving a harmonized 3D velocity and attenuation model of the sedimentary layers. Three alternative approaches are then applied and compared to evaluate the impact of the sedimentary cover on ground-motion amplification. The first approach builds on existing response spectra ground-motion models whose amplification factors empirically take into account the influence of the sedimentary layers through a standard parameterization. In the second approach, site-specific 1D amplification functions are computed from the 3D basin model. Using a random vibration theory approach, we adjust the empirical response spectra predicted for soft rock conditions by local site amplification factors: amplifications and associated ground-motions are predicted both in the Fourier and in the response spectra domain. In the third approach, hybrid physics-based ground-motion simulations are used to predict time histories for soft rock conditions which are subsequently modified using the 1D site-specific amplification functions computed in method 2. For large distances and at short periods, the differences between the three approaches become less notable due to the significant attenuation of the sedimentary layers. At intermediate and long periods, generic empirical ground-motion models provide lower levels of amplification from sedimentary soils compared to methods taking into account site-specific 1D amplification functions. In the near-source region, hybrid physics-based ground-motions models illustrate the potentially large variability of ground-motion due to finite source effects.