Classical Scaling Relations Research Articles

Planar random-cluster model: scaling relations

Abstract This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in [1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the critical exponents $\beta $ , $\gamma $ , $\delta $ , $\eta $ , $\nu $ , $\zeta $ as well as $\alpha $ (when $\alpha \ge 0$ ). As a key input, we show the stability of crossing probabilities in the near-critical regime using new interpretations of the notion of the influence of an edge in terms of the rate of mixing. As a byproduct, we derive a generalisation of Kesten’s classical scaling relation for Bernoulli percolation involving the ‘mixing rate’ critical exponent $\iota $ replacing the four-arm event exponent $\xi _4$ .

Initial solidification dynamics of spreading droplets

An experimental study is performed to investigate the influence of crystal growth on the contact line behavior of a droplet on an undercooled surface. We show the effect that the growing nucleus has on the arrest of the contact line and the underlying dependence on nucleation rate. Finally, based on classical nucleation theory and scaling relations for droplet spreading, we calculate the temporal evolution of the solidifying area.

Automatic identification model of micro-earthquakes and blasting events in Laohutai coal mine based on the measurement of source parameter difference

The micro-seismic signal of coal mine is obviously affected by blasting signal, which seriously affects the identification accuracy of micro-seismic signal. For this purpose, automated identification and discrimination methods exist to monitor seismicity occurrence. In this study, seismic source properties of blasting events and micro-earthquakes in the Laohutai coal mine are quantified to more accurately distinguish between these two types of events and to investigate potential physical differences between them. Besides examining the space–time evolution of micro-earthquakes in the Laohutai coal mine, source parameters of blasting events and micro-earthquakes (corner frequency f0; spectral level Ω0; seismic moment M0; moment magnitude Mw; source radius R; stress drop △σ; apparent stress σa, radiated seismic energy E) are determined and scaling relationships between them are investigated. Our results show that the number of micro-earthquakes is closely related to the mining activity. Source-spectral characteristics of blasting events are well described by the Brune omega-square model and follow in general the classical scaling relations (i.e. increasing seismic moment with decreasing corner frequency), like the source-spectral characteristics of micro-earthquakes. Importantly, for events of same magnitude, corner frequency and stress drop of blasting events are larger than for micro-earthquakes. This observation helps to improve automatic identification and discrimination of micro-seismic and blast events, thereby providing important information for (real-time) seismic hazard monitoring and risk management.

The 2019 Mw 5.9 Torkaman chay earthquake in Bozgush mountain, NW Iran: A buried strike-slip event related to the sinistral Shalgun-Yelimsi fault revealed by InSAR

On 7 November 2019, an Mw 5.9 earthquake with a left-lateral strike-slip mechanism struck the Bozgush mountain in NW Iran, marking the largest event in the mountain area in the past 44 years. Because no surface rupture associated with the earthquake has been reported, the causative fault of the earthquake is unknown. This event provides an opportunity to gain insight into the active tectonics of the region. Here, we acquire the coseismic deformation associated with this earthquake through Sentinel-1A interferometric synthetic aperture radar (InSAR) data and further invert the fault geometry and the detailed coseismic slip of this event based on the planar fault model. By a joint analysis of the inversion results, aftershocks sequence and local tectonics, we propose that the buried branch fault splaying from the Shalgun-Yelimsi fault (SYF) at depth may be responsible for this earthquake. Both the uniform and distributed slip models infer a smaller fault rupture size than predicted by classical fault scaling relation. We suggest that the subsurface fault geometry of the SYF may stop the rupture propagation further down to southeast at depth, thus resulting in high slip and stress drop at such a small fault plane. Considering the proximity of the epicenter to the SYF, we also invert for the distributed slip model on an anti-listric fault with the purpose to explore the possible complexity of rupture fault. However, due to the lack of obvious improvement to fit the observed data and the limited slip in the deep fault segment, the planar fault model is still regarded as the optimal one. According to the calculated coseismic Coulomb stress changes, we find that 55 % of aftershocks are triggered by the statics stress and that the northern segment of SYF and the eastern segment of SBF have a potential rupture risk. The occurrence of this earthquake, together with the prominent offset feature and slip style of surrounding active fault, indicates an active conjugate fault system, which may accommodate the small-scale northeastward lateral extrusion.

First detection of oscillations in the Halo giant HD 122563: Validation of seismic scaling relations and new parameters

Aims. The nearby metal-poor giant HD 122563 is an important astrophysical laboratory in which to test stellar atmospheric and interior physics. It is also a benchmark star for which to calibrate methods to apply to large scale surveys. Recently it has been remeasured using various methodologies given the new high precision instruments at our disposal. However, inconsistencies in the observations and models have been found. Methods. In order to better characterise this star using complementary techniques we have been measuring its radial velocities since 2016 using the Hertzsprung telescope (SONG network node) in order to detect oscillations. Results. In this work we report the first detections of sun-like oscillations in this star, and to our knowledge, a detection in the most metal-poor giant to date. We applied the classical seismic scaling relation to derive a new surface gravity for HD 122563 of log gν = 1.39 ± 0.01. Reasonable constraints on the mass imposed by its PopII giant classification then yields a radius of 30.8 ± 1.0 ℛ⊙. By coupling this new radius with recent interferometric measurements we infer a distance to the star of 306 ± 9 pc. This result places it further away than was previously thought and is inconsistent with the HIPPARCOS parallax. Independent data from the Gaia mission corroborate the distance hypothesis (dGDR2 = 290 ± 5 pc), and thus the updated fundamental parameters. Conclusions. We confirm the validity of the classical seismic scaling relation for surface gravity in metal-poor and evolved star regimes. The remaining discrepancy of 0.04 dex between log gGDR2 (= 1.43 ± 0.03) reduces to 0.02 dex by applying corrections to the scaling relations based on the mean molecular weight and adiabatic exponent. The new constraints on the Hertzsprung–Russell diagram (L⋆ν = 381 ± 26 ℒ⊙) significantly reduce the disagreement between the stellar parameters and evolution models, however, a discrepancy of the order of 150 K still exists. Fine-tuned stellar evolution calculations show that this discrepancy can be reconciled by changing the mixing-length parameter by an amount (−0.35) that is in agreement with predictions from recent 3D simulations and empirical results. Asteroseismic measurements are continuing, and analysis of the full frequency data complemented by a distance estimate promises to bring important constraints on our understanding of this star and of the accurate calibration of the seismic scaling relations in this regime.

Stellar masses from granulation and oscillations of 23 bright red giants observed by BRITE-Constellation

Context. The study of stellar structure and evolution depends crucially on accurate stellar parameters. The photometry from space telescopes has provided superb data that enabled the asteroseismic characterisation of thousands of stars. However, typical targets of space telescopes are rather faint and complementary measurements are difficult to obtain. On the other hand, the brightest, otherwise well-studied stars, are lacking seismic characterization. Aims. Our goal is to use the granulation and/or oscillation timescales measured from photometric time series of bright red giants (1.6 ≤ V mag ≤ 5.3) observed with BRITE-Constellation to determine stellar surface gravities and masses. Methods. We used probabilistic methods to characterise the granulation and/or oscillation signal in the power density spectra and the autocorrelation function of the BRITE-Constellation time series. Results. We detect a clear granulation and/or oscillation signal in 23 red giant stars and extract the corresponding timescales from the power density spectra as well as the autocorrelation function of the BRITE-Constellation time series. To account for the recently discovered non-linearity of the classical seismic scaling relations, we used parameters from a large sample of Kepler stars to re-calibrate the scalings of the high- and low-frequency components of the granulation signal. We developed a method to identify which component is measured if only one granulation component is statistically significant in the data. We then used the new scalings to determine the surface gravity of our sample stars, finding them to be consistent with those determined from the autocorrelation signal of the time series. We further used radius estimates from the literature to determine the stellar masses of our sample stars from the measured surface gravities. We also defined a statistical measure for the evolutionary stage of the stars. Conclusions. Our sample of stars covers low-mass stars on the lower giant branch to evolved massive supergiants and even though we cannot verify our mass estimates with independent measurements from the literature, they appear to be at least good enough to separate high-mass from low-mass stars. Given the large known but usually not considered systematic uncertainties in the previous model-based mass estimates, we prefer our model-independent measurements.

A seismic scaling relation for stellar age

A simple solar scaling relation for estimating the ages of main-sequence stars from asteroseismic and spectroscopic data is developed. New seismic scaling relations for estimating mass and radius are presented as well, including a purely seismic radius scaling relation (i.e., no dependence on temperature). The relations show substantial improvement over the classical scaling relations and perform similarly well to grid-based modeling.

Deep and wide gaps by super Earths in low-viscosity discs

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple one-dimensional scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet's to star's mass ratio $\mu$, the gas disc's aspect ratio $h$, and its Shakura & Sunyaev viscosity parameter $\alpha$. Specifically, we focus on low-mass planets ($\mu<\mu_{\rm th}\equiv h^3$) and identify a new low-viscosity regime, $\alpha<h(\mu/\mu_{\rm th})^5$, in which the classical analytical scaling relations are invalid. Equivalently, this low-viscosity regime applies to every gap that is depleted by more than a factor of $(\mu_{\rm th}/\mu)^3$ relative to the unperturbed density. We show that such gaps are significantly deeper and wider than previously thought, and consequently take a longer time to reach equilibrium.

Anomalous Hall effect in CoxSi1−x granular films deposited by magnetron co-sputtering

In this research, CoxSi1−x granular films with Co volume fraction (x) varying from 0.36 to 1 were prepared by using a magnetron co-sputtering method. The influence of x on the temperature-dependent longitudinal resistivity ($${\rho _{xx}}$$) and anomalous Hall effect (AHE) in CoxSi1−x granular films were systematically studied. The dependence of $${\rho _{xx}}$$ on measuring temperature could be explained by the superposition of fluctuation-induced tunneling (FIT) process and temperature-dependent scattering. Interestingly, the contribution from scattering and FIT can be distinguished. The saturated Hall resistivity ($$\rho _{{xy}}^{A}$$) increased monotonically with decreasing x. In addition, the $$\rho _{{xy}}^{A}$$ amplified nearly 26-fold as x decreased from 1 to 0.4. For the pure Co film (x = 1), the intrinsic and side jump mechanisms dominated the Hall transport. However, the deviation of classical scaling relation was observed in other samples, which was mainly ascribed to the influence of interfacial scattering.

Impact velocity dependence of transient cratering growth

AbstractThe present paper describes observations of crater growth for various impact velocities up to ∼6 km s−1. Spherical polycarbonate projectiles (4.76 mm) were impacted vertically into dry sand targets at impact velocities vi ranging from 0.7 to ∼6 km s−1, and the temporal change (diameter growth) in diameter of crater cavities was measured by a high‐speed profilometer with 2000 frames per second. Our data show that the diameter growth follows a power law relation at the early stages, but the data at the later stages deviate from the power law relation. It is also shown that the power law exponent at the early stages decreases with increasing vi, indicating a possibility that the growth rate of the transient crater cavity decreases with increasing vi. On the other hand, the power law relation for final crater sizes in our data is consistent with the classical scaling relation for final crater sizes, which is thought to be independent of vi. Thus, our data may suggest that there is a difference in the power law behavior between the crater growth and the final crater sizes.

Hydrodynamic Analysis Resolves the Pharmaceutically-Relevant Absolute Molar Mass and Solution Properties of Synthetic Poly(ethylene glycol)s Created by Varying Initiation Sites.

The solution behavior originating from molecular characteristics of synthetic macromolecules plays a pivotal role in many areas, in particular the life sciences. This situation necessitates the use of complementary hydrodynamic analytical methods as the only means for a complete structural understanding of any macromolecule in solution. To this end, we present a combined hydrodynamic approach for studying in-house prepared, low dispersity poly(ethylene glycols)s (PEGs), also known as poly(ethylene oxide)s (PEOs) depending on the classification used, synthesized from varying initiation sites by the living anionic ring opening polymerization. The series of linear PEGs in the molar mass range of only a few thousand to 50 000 g mol-1 have been studied in detail via viscometry and sedimentation-diffusion analysis by analytical ultracentrifugation. The obtained estimations for intrinsic viscosity, diffusion coefficients, and sedimentation coefficients of the macromolecules in the solution-based analysis clearly showed self-consistency of the followed hydrodynamic approach. This self-consistency is underpinned by appropriate and physically sound values of hydrodynamic invariants, indicating adequate values of derived absolute molar masses. The classical scaling relations of Kuhn-Mark-Houwink-Sakurada of all molar-mass dependent hydrodynamic estimates show linear trends, allowing for interrelation of all parametric macromolecular characteristics. Differences among these are ascribed to the observation of α-end and chain-length dependent solvation of the macromolecules, identified from viscometric studies. This important information allows for analytical tracing of variations of scaling relationships and a physically sound estimation of hydrodynamic characteristics. The demonstrated self-sufficient methodology paves an important way for a complete structural understanding and potential replacement of pharmaceutically relevant PEGs by alternative macromolecules offering a suite of similar or tractably distinct physicochemical properties.

Landau-like theory for universality of critical exponents in quasistationary states of isolated mean-field systems.

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

Spectral analogues of the law of the wall, the defect law and the log law

AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defect law and the log law. By design, each spectral analogue applies in the same spatial domain as the attendant scaling relation for the mean-velocity profiles: the spectral analogue of the law of the wall in the inner layer, the spectral analogue of the defect law in the outer layer and the spectral analogue of the log law in the overlap layer. In addition, as we are able to show without invoking any model of wall turbulence, each spectral analogue applies in a specific spectral domain (the spectral analogue of the law of the wall in the high-wavenumber spectral domain, where viscosity is active, the spectral analogue of the defect law in the low-wavenumber spectral domain, where viscosity is negligible, and the spectral analogue of the log law in a transitional intermediate-wavenumber spectral domain, which may become sizable only at ultra-high$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Re}_{\tau }$), with the implication that there exist model-independent one-to-one links between the spatial domains and the spectral domains. We test the spectral analogues using experimental and computational data on pipe flow and channel flow.

FUNDAMENTAL MASS-SPIN-MORPHOLOGY RELATION OF SPIRAL GALAXIES

This work present high-precision measurements of the specific baryon angular momentum jb, contained in stars, atomic gas, and molecular gas, out to ~10 scale radii, in 16 nearby spiral galaxies of the THINGS sample. The accuracy of these measurements improves on existing studies by an order of magnitude, leading to the discovery of a strong correlation between the baryon mass Mb, jb, and the bulge mass fraction B/T, fitted by B/T=-(0.34+-0.03)*log(jb/Mb/[1e-7 kpc km/s/Msun])-(0.04+-0.01) on the full sample range of B/T=0.00-0.32 and Mb/Msun=1e9-1e11. The corresponding relation for the stellar quantities Ms and js is identical within the uncertainties. These M-j-B/T relations likely originate from the proportionality between j/M and the surface density of the disk that dictates its stability against (pseudo-)bulge formation. Using a CDM model, we can approximately explain classical scaling relations, such as the fundamental plane of spiral galaxies, the Tully-Fisher relation, and the mass-size relation, in terms of the M-j-B/T relation. These results advocate the use of mass and angular momentum as the most fundamental quantities of spiral galaxies.

A continuum mechanical theory for turbulence: a generalized Navier–Stokes-α equation with boundary conditions

We develop a continuum-mechanical formulation and generalization of the Navier–Stokes-α equation based on a recently developed framework for fluid-dynamical theories involving higher-order gradient dependencies. Our flow equation involves two length scales α and β. The first of these enters the theory through the specific free-energy α2|D|2, where D is the symmetric part of the gradient of the filtered velocity, and contributes a dispersive term to the flow equation. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity and which contributes a viscous term, with coefficient proportional to β2, to the flow equation. In contrast to Lagrangian averaging, our formulation delivers boundary conditions and a complete structure based on thermodynamics applied to an isothermal system. For a fixed surface without slip, the standard no-slip condition is augmented by a wall-eddy condition involving another length scale l characteristic of eddies shed at the boundary and referred to as the wall-eddy length. As an application, we consider the classical problem of turbulent flow in a plane, rectangular channel of gap 2h with fixed, impermeable, slip-free walls and make comparisons with results obtained from direct numerical simulations. We find that α/β ~ Re0.470 and l/h ~ Re−0.772, where Re is the Reynolds number. The first result, which arises as a consequence of identifying the specific free-energy with the specific turbulent kinetic energy, indicates that the choice β = α required to reduce our flow equation to the Navier–Stokes-α equation is likely to be problematic. The second result evinces the classical scaling relation η/L ~ Re−3/4 for the ratio of the Kolmogorov microscale η to the integral length scale L.

Turbulent kinetic energy and a possible hierarchy of length scales in a generalization of the Navier-Stokesαtheory

We present a continuum-mechanical formulation and generalization of the Navier-Stokes alpha theory based on a general framework for fluid-dynamical theories with gradient dependencies. Our flow equation involves two additional problem-dependent length scales alpha and beta. The first of these scales enters the theory through the internal kinetic energy, per unit mass, alpha2|D|2, where D is the symmetric part of the gradient of the filtered velocity. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity. When alpha and beta are equal, our flow equation reduces to the Navier-Stokes alpha equation. In contrast to the original derivation of the Navier-Stokes alpha equation, which relies on Lagrangian averaging, our formulation delivers boundary conditions. For a confined flow, our boundary conditions involve an additional length scale l characteristic of the eddies found near walls. Based on a comparison with direct numerical simulations for fully developed turbulent flow in a rectangular channel of height 2h, we find that alphabeta approximately Re(0.470) and lh approximately Re(-0.772), where Re is the Reynolds number. The first result, which arises as a consequence of identifying the internal kinetic energy with the turbulent kinetic energy, indicates that the choice alpha=beta required to reduce our flow equation to the Navier-Stokes alpha equation is likely to be problematic. The second result evinces the classical scaling relation eta/L approximately Re(-3/4) for the ratio of the Kolmogorov microscale eta to the integral length scale L . The numerical data also suggests that l < or = beta . We are therefore led to conjecture a tentative hierarchy, l < or = beta < alpha , involving the three length scales entering our theory.

Structure and Swelling of Grafted Polyelectrolytes: Predictions from a Nonlocal Density Functional Theory

The properties of polyelectrolytes anchored on surfaces depend on a broad range of parameters including the characteristics of the polyions, salt concentration, ion valence, and solvent conditions. While these systems have been subjected to extensive theoretical and experimental investigations in particular in the brush limit, a number of important questions remain to be addressed concerning the electrostatic correlations and excluded-volume effects beyond typical mean-field approximations. In this work, we applied a nonlocal density functional theory (DFT) to tethered polyelectrolytes within a primitive model and examined the effects of salt concentration, polymer grafting density, and chain length on the polyion configurations, the mean electrostatic potential, and the distributions of both counterions and co-ions. Whereas the theoretical framework is directly applicable to arbitrary solution conditions, this work is focused on systems containing only monovalent ions so that the comparison can be made with the established results. Given the polyion chain length and grafting density, we predicted a smooth transition from the osmotic brush to the salted brush in response to the increase of the salt concentration. In the osmotic regime, the brush thickness is invariant with the salt concentration but grows with the grafting density. In the salted regime, the brush thickness follows the classical scaling relation H ∝ Cs-1/3 for long polyelectrolytes but noticeably, the magnitude of the fractional exponent declines as the polyion chain length falls. Linear relations between the polyelectrolyte chain length and the brush thickness were identified for both osmotic and salted brushes. Qualitatively, all these predictions were found in good agreement with experiments or with simulations.

Tracing the X-ray emitting intra-cluster medium of clusters of galaxies beyondr$\mathsf{_{200}}$

(Abridged) We present in this paper a sample of 14 nearby clusters of galaxies observed with the ROSAT/PSPC. We only select clusters with low galactic nH in order to trace the X-ray emitting intra-cluster medium (ICM) out to large radii. We convert the X-ray surface brightness profiles of the clusters into emission measure profiles scaled to the classical scaling relations based on the spherical collapse model. We sort the clusters into different temperature bins and stack the scaled emission measure (ScEM) profiles of clusters together. The stacked profiles allow us to observe out to radii r>r_200. In the center we find that the ScEM profiles deviate from predicted scaling laws. This result is in very good agreement with current studies on the L_X-T relation and the entropy - temperature relation (S \propto T^0.65) found recently. At radii r>0.4r_200 we find that the ScEM profiles agree well within the error bars, suggesting self-similarity. Fitting beta-models to the overall ScEM profiles we find for the different sub samples r_c=0.15-0.18 r_200 and beta=0.8, which is higher than beta=2/3 often found. The beta-model is generally a better representation for hotter than for cooler clusters. We see indications for continuous steepening of the profiles with increasing radius: at radii r>0.8r_200 the profiles are systematically below the beta-model curve with beta=0.8. We discuss our results with respect to the observed X-ray luminosity L_X-T relation, the gas mass M_gas-T relation and the total mass M-T relation. We also address implications on the origin of the observed S-T relation. Furthermore we discuss the observed steepness of the X-ray profiles, which falls off more rapidly than predicted from the NFW-profile for cold dark matter halos.

Decomposition and reconstruction of multidimensional signals using polyharmonic pre-wavelets

In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines. The pre-wavelets are polyharmonic splines and so not tensor products of univariate wavelets. Explicit construction of the filters specified by the classical dyadic scaling relations is given and the decay of the functions and the filters is shown. We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products.

An integrated magnetotelluric and aeromagnetic investigation of the Serra da Cangalha impact crater, Brazil

The research is aimed at delineating the post-impact structural characteristics across the Serra da Cangalha impact crater in Brazil using a combination of magnetotelluric (MT) and aeromagnetic data. The MT survey was carried out along three radial MT profiles trending NW–SE, ENE–WSW and NNE–SSW across the crater. For MT sites located further away from the centre of the crater, isotropic MT responses were observed, suggesting a 1D conductivity distribution in the subsurface in the frequency range of 100–10 Hz. For sites located in the vicinity of the inner ring of the crater, anisotropic responses were observed for the same frequency range. We believe that this zone probably represents the areas of structural disturbance. A 2D resistivity inversion of these data reveals a four-layer model, representing a thin resistive layer underlain by a conductive layer, a weathered basement and a resistive crystalline basement. The depth to the top of the basement is estimated to be about 1.2 km. This is in good agreement with the estimation of depth to the basement of about 1.1 km, calculated using the aeromagnetic data. However, in view of the circular geometry of the crater, we have carried out a 3D forward modeling computation to supplement the derived 2D model. The 3D resistivity forward model, fitting the MT responses by trial-by-error revealed a five-layer model, showing a significant reduction in the basement resistivity. This, perhaps, could be due to the structural disturbances that have been caused by the impact on the crater, resulting in brecciation, fracturing, alteration and shocked zone filled with weak-magnetic materials and fluids. We have calculated the effect of the impact on the overall structural deformation beneath the Serra da Cangalha crater, following the classical crater scaling relation of Holsapple and Schmidt [Holsapple, K.A., Schmidt, R.M., 1982. On the scaling of crater dimensions. II. Impact processes. J. Geophys. Res. 87, 1849–1870] and found to be about 2 km.