Attractor reconstruction from the time series of information entropy of seismic kinetics process

The attractor is reconstructed from the time series of the information entropy of the seismic kinetics process. It is shown that the seismic kinetics process is governed by three order parameters and is characterized by a strange attractor in the three-dimensional phase space. The D_q-spectrum of the multifractal measure induced by the attractor, which describes the topological structure of the latter, is obtained. The monofractal dimension of the attractor is D_q(0) = 2.31…, and the correlation dimension is D_q(2) = 2.16…. The estimate of the largest Lyapunov exponent of the attractor λ1 = 0.331…. The positive signature of the largest Lyapunov exponent suggests that the attractor is chaotic and the behavior of the phase trajectory is unpredictable.     

Nuclear magnetic resonance <Emphasis Type="Italic">T</Emphasis><Subscript>2</Subscript> spectrum: multifractal characteristics and pore structure evaluation

Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance (NMR), we studied the pore structure of low-permeability sandstone rocks from the 4th Member (E_S4) of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T₂ spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters α (intensity of singularity) and f (α) (density of distribution) were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with α and f (α). The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.     

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.     

Testing the reference Moon model in respect of the thermal regime and chemical composition of the mantle: Thermodynamics versus seismology

The VPREMOON seismic reference Moon model (Garcia et al., 2011) has been tested with respect to the thermal regime and chemical composition of the mantle. Based on a self-consistent thermodynamic approach and petrological models of the lunar mantle covering a wide range of concentrations of CaO, Al₂O₃, and FeO, we convert the P- and S-wave velocity profiles to the temperature–depth profiles. The solution procedure relies on the method of the Gibbs free energy minimization and the equations of state for the mantle material which take into account the effects of phase transformations, anharmonicity, and anelasticity. We find that regardless of the chemical composition, the positive P- and S-wave velocity gradient in the lunar mantle leads to a negative temperature gradient, which has no physical basis. For adequate mantle temperatures, the P- and S-wave velocities should remain almost constant or slightly decrease with depth (especially V_S) as a result of the effects of the temperature, which grows faster than pressure. These findings underscore the importance of the relationship of the thermodynamics and physics of minerals with seismology.     

Prestack migration velocity analysis based on simplified two-parameter moveout equation

Stacking velocity V _C2, vertical velocity ratio γ ₀, effective velocity ratio γ _eff, and anisotropic parameter χ _eff are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity V _C2 and anisotropic parameter k _eff) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocity V _C2, vertical velocity ratio γ ₀, effective velocity ratio γ _eff, and anisotropic parameter k _eff) PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratio γ ₀ of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratio γ _eff is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratio γ _eff is obtained by percentage scanning migration. This method simplifies the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice.     

Upper mantle structure beneath central Western Europe from data on phase velocities of surface waves

The deep structure of the upper mantle is determined from data on phase velocities of Love and Rayleigh waves measured by a differential method on traces between two stations in central Western Europe. One-dimensional velocity structures are first constructed from data of each pair of stations, after which two-dimensional distributions of SH and SV velocities are calculated by the method of two-dimensional tomography from S wave velocities at fixed depths. The results are presented in the form of 2-D vertical structures of the average S wave velocity (S = (SV + SH)/2) constructed along profiles crossing the region in directions of the best resolution. The main structural features are a higher velocity zone at depths of 60–80 km in the area (48°–50°N, 9°–11°E) and a lower velocity zone in the western part of the region at depths of 100–150 km, probably extending farther beyond the studied area.     

Limits of transversely isotropic elastic parameters for the existence of classical Rayleigh waves

Solutions of P-SV equations of motion in a homogeneous transversely isotropic elastic layer contain a factor exp(±ν _j z), where z is the vertical coordinate and j?=?1, 2. For computing Rayleigh wave dispersion in a multi-layered half space, ν _j is computed at each layer. For a given phase velocity (c), ν _j becomes complex depending on the transversely isotropic parameters. When ν _j is complex, classical Rayleigh waves do not exist and generalised Rayleigh waves propagate along a path inclined to the interface. We use transversely isotropic parameters as α _H , β _V , ξ, ? and η and find their limits beyond which ν _j becomes complex. It is seen that ν _j depends on ? and η, but does not depend on ξ. The complex ν _j occurs when ? is small and η is large. For a given c/β _V , the region of complex ν _j in a ? -η plane increases with the increase of α _H /β _V . Further, for a given α _H /β _V , the complex region of ν _j increases significantly with the decrease of c/β _V . This study is useful to compute dispersion parameters of Rayleigh waves in a layered medium.     

Peculiarities of Rayleigh wave displacement in a transversely isotropic half space

We consider a transversely isotropic medium with vertical axis of symmetry (VTI). Rayleigh wave displacement components in a homogeneous VTI medium contain exp(±kr_jz), where z is the vertical coordinate, k is the wave number, and j?=?1, 2; r_j may be considered as depth-decay factor. In a VTI medium, r_j can be a real or imaginary as in an isotropic medium, or it can be a complex depending on the elastic parameters of the VTI medium; if complex, r₁ and r₂ are complex conjugates. In a homogeneous VTI half space, Rayleigh wave displacement is significantly modified with a phase shift when r_j changes from real to complex with variation of VTI parameters; at the transition, the displacement becomes zero when r₁?=?r₂. In a liquid layer over a VTI half space, Rayleigh waves are dispersive. Here, also Rayleigh wave displacement significantly modified with a phase shift when r_j changes from real to complex with a decrease of period. At very low period, phase velocity of Rayleigh waves becomes less than P-wave velocity in the liquid layer giving rise to Scholte waves (interface waves). The amplitudes of Scholte waves with a VTI half space are found to be significantly larger than those with an isotropic half space.     

Shear Wave Velocity Estimates through Combined Use of Passive Techniques in a Tectonically Active Area

We made an attempt to assess the shear wave velocity values V _S and, to a lesser extent, the V _P values from ambient noise recordings in an array configuration. Five array sites were situated in the close proximity to borehole sites. Shear wave velocity profiles were modeled at these five array sites with the aid of two computational techniques, viz. spatial autocorrelation (SPAC) and H/V ellipticity. Out of these five array sites, velocity estimates could be reliably inferred at three locations. The shear wave velocities estimated by these methods are found to be quite consistent with each other. The computed V _S values up to 30 m depth are in the range from 275 to 375 m/s in most of the sites, which implies prevalence of a low velocity zone at some pocket areas. The results were corroborated by evidence of site geology as well as geotechnical information.     

Hysteretic energy prediction method for mainshock-aftershock sequences

Structures located in seismically active regions may be subjected to mainshock-aftershock (MSAS) sequences. Strong aftershocks significantly affect the hysteretic energy demand of structures. The hysteretic energy, E_H,seq, is normalized by mass m and expressed in terms of the equivalent velocity, V_D,seq, to quantitatively investigate aftershock effects on the hysteretic energy of structures. The equivalent velocity, V_D,seq, is computed by analyzing the response time-history of an inelastic single-degree-of-freedom (SDOF) system with a varying vibration period subjected to 309 MSAS sequences. The present study selected two kinds of MSAS sequences, with one aftershock and two aftershocks, respectively. The aftershocks are scaled to maintain different relative intensities. The variation of the equivalent velocity, V_D,seq, is studied for consideration of the ductility values, site conditions, relative intensities, number of aftershocks, hysteretic models, and damping ratios. The MSAS sequence with one aftershock exhibited a 10% to 30% hysteretic energy increase, whereas the MSAS sequence with two aftershocks presented a 20% to 40% hysteretic energy increase. Finally, a hysteretic energy prediction equation is proposed as a function of the vibration period, ductility value, and damping ratio to estimate hysteretic energy for mainshock-aftershock sequences.     

Magnetic field variations in the umbra of single sunspots during their passage across the solar disk

Temporal variations of the maximum (B _max) and average (〈B〉) magnetic inductions, minimum (α _min) and average (〈α〉) inclination angles of the field lines to the radial direction from the center of the Sun, and areas of the sunspot umbra S in the umbra of single sunspots during their passage across the solar disk are investigated. The variation of the properties of single sunspots has been considered at different stages of their existence, i.e., during formation, the “quiet” period, and the disappearance stage. It has been found that, for the majority of the selected single sunspots, there is a positive correlation between B _max and S and between 〈B〉 and S defined at different times during the passage of sunspots across the solar disk. It is shown in this case that the nature of the dependence between the parameters α _min and B _max, α _min and S, as well as between 〈α〉 and 〈B〉, 〈α〉 and S, can vary from sunspot to sunspot, but for many sunspots the inclination angle of the field lines decreases on average with the growth of the sunspot umbra area and the field strength.     

Characterisation of ground motion recording stations in the Groningen gas field

The seismic hazard and risk analysis for the onshore Groningen gas field requires information about local soil properties, in particular shear-wave velocity (V_S). A fieldwork campaign was conducted at 18 surface accelerograph stations of the monitoring network. The subsurface in the region consists of unconsolidated sediments and is heterogeneous in composition and properties. A range of different methods was applied to acquire in situ V_S values to a target depth of at least 30 m. The techniques include seismic cone penetration tests (SCPT) with varying source offsets, multichannel analysis of surface waves (MASW) on Rayleigh waves with different processing approaches, microtremor array, cross-hole tomography and suspension P-S logging. The offset SCPT, cross-hole tomography and common midpoint cross-correlation (CMPcc) processing of MASW data all revealed lateral variations on length scales of several to tens of metres in this geological setting. SCPTs resulted in very detailed V_S profiles with depth, but represent point measurements in a heterogeneous environment. The MASW results represent V_S information on a larger spatial scale and smooth some of the heterogeneity encountered at the sites. The combination of MASW and SCPT proved to be a powerful and cost-effective approach in determining representative V_S profiles at the accelerograph station sites. The measured V_S profiles correspond well with the modelled profiles and they significantly enhance the ground motion model derivation. The similarity between the theoretical transfer function from the V_S profile and the observed amplification from vertical array stations is also excellent.     

Effects of chemical,mineralogical, and temperature variations on the density and bulk sound velocity of the bottom lower mantle

In this study, we have modeled the density(ρ) and bulk sound velocity(VΦ) profiles of the bottom lower mantle using the experimental thermal equation of state(EoS) parameters of lower-mantle minerals, including bridgmanite, ferropericlase,CaSiO3-perovskite, and post-perovskite. We re-evaluated the literature pressure-volume-temperature relationships of these minerals using a self-consistent pressure scale in order to avoid the long-standing pressure scale problem and to provide more reliable constraints on the thermal EoS parameters. With the obtained thermal EoS parameters, we have constructed the ρ and VΦ profiles of the bottom lower mantle in different composition, mineralogy, and temperature models. Our modelling results show that the variations of chemistry, mineralogy, and temperature have different seismic signatures from each other. The Fe and Al enrichment at the bottom lower mantle can cause an increase in ρ but greatly lower VΦ. A change in mineralogy needs to be considered with the lateral variation in temperature. The cold slabs will be shown as denser regions compared to the normal mantle because of the combined effect of a lower temperature and the presence of a denser post-perovskite at a shallower depth,whereas the hot regions will have a 1–2% lower ρ than the normal mantle. VΦ of both cold slabs and hot regions will be lower than the normal mantle when bridgmanite is the dominant phase in the normal mantle, yet they will be greater once bridgmanite transforms into post-perovskite in the normal mantle. Our modeling also shows that the presence of a(Fe, Al)-enriched bridgmanite thermal pile above the core-mantle boundary will exhibit a seismic signature of enhanced ρ and VΦ, but a reduced VS,which is consistent with the observed seismic anomalies in the large-low-shear-velocity-provinces(LLSVPs). The existence of such a(Fe, Al)-enriched bridgmanite thermal pile thus can help to understand the origin of the LLSVPs. These results provide new insights for the chemical and structure of the deepest lower mantle.     

<Emphasis Type="Italic">Q</Emphasis><Subscript>c</Subscript> and <Emphasis Type="Italic">Q</Emphasis><Subscript>S</Subscript> wave attenuation of South African earthquakes

Quality factor Q, which describes the attenuation of seismic waves with distance, was determined for South Africa using data recorded by the South African National Seismograph Network. Because of an objective paucity of seismicity in South Africa and modernisation of the seismograph network only in 2007, I carried out a coda wave decay analysis on only 13 tectonic earthquakes and 7 mine-related events for the magnitude range 3.6?≤?M _L ?≤?4.4. Up to five seismograph stations were utilised to determine Q _c for frequencies at 2, 4, 8 and 16 Hz resulting in 84 individual measurements. The constants Q ₀ and α were determined for the attenuation relation Q _c(f)?=?Q ₀ f ^α . The result was Q ₀?=?396?±?29 and α?=?0.72?±?0.04 for a lapse time of 1.9*(t _s???t ₀) (time from origin time t ₀ to the start of coda analysis window is 1.9 times the S-travel time, t _s) and a coda window length of 80 s. This lapse time and coda window length were found to fit the most individual frequencies for a signal-to-noise ratio of at least 3 and a minimum absolute correlation coefficient for the envelope of 0.5. For a positive correlation coefficient, the envelope amplitude increases with time and Q _c was not calculated. The derived Q _c was verified using the spectral ratio method on a smaller data set consisting of nine earthquakes and one mine-related event recorded by up to four seismograph stations. Since the spectral ratio method requires absolute amplitudes in its calculations, site response tests were performed to select four appropriate stations without soil amplification and/or signal distortion. The result obtained for Q _S was Q ₀?=?391?±?130 and α?=?0.60?±?0.16, which agrees well with the coda Q _c result.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Shape and position of Earth’s bow shock near-lunar orbit based on ARTEMIS data

Earth’s bow shock is the result of interaction between the supersonic solar wind and Earth’s magnetopause. However, data limitations mean the model of the shape and position of the bow shock are based largely on near-Earth satellite data. The model of the bow shock in the distant magnetotail and other factors that affect the bow shock, such as the interplanetary magnetic field (IMF) B_y, remain unclear. Here, based on the bow shock crossings of ARTEMIS from January 2011 to January 2015, new coefficients of the tail-flaring angle α of the Chao model (one of the most accurate models currently available) were obtained by fitting data from the middle-distance magnetotail (near-lunar orbit, geocentric distance -20R_E>X>-50R_E). In addition, the effects of the IMF B_y on the flaring angle α were analyzed. Our results showed that: (1) the new fitting coefficients of the Chao model in the middle-distance magnetotail are more consistent with the observed results; (2) the tail-flaring angle α of the bow shock increases as the absolute value of the IMF B_y increases. Moreover, positive IMF B_y has a greater effect than negative IMF B_y on flaring angle. These results provide a reference for bow shock modeling that includes the IMF B_y.     

Crustal and upper mantle velocity model along the DOBRE-4 profile from North Dobruja to the central region of the Ukrainian Shield: 1. seismic data

For studying the structure of the lithosphere in southern Ukraine, wide-angle seismic studies that recorded the reflected and refracted waves were carried out under the DOBRE-4 project. The field works were conducted in October 2009. Thirteen chemical shot points spaced 35–50 km apart from each other were implemented with a charge weight varying from 600 to 1000 kg. Overall 230 recording stations with an interval of 2.5 km between them were used. The high quality of the obtained data allowed us to model the velocity section along the profile for P- and S-waves. Seismic modeling was carried out by two methods. Initially, trial-and-error ray tracing using the arrival times of the main reflected and refracted P- and S-phases was conducted. Next, the amplitudes of the recorded phases were analyzed by the finite-difference full waveform method. The resulting velocity model demonstrates a fairly homogeneous structure from the middle to lower crust both in the vertical and horizontal directions. A drastically different situation is observed in the upper crust, where the V _p velocities decrease upwards along the section from 6.35 km/s at a depth of 15–20 km to 5.9–5.8 km/s on the surface of the crystalline basement; in the Neoproterozoic and Paleozoic deposits, it diminishes from 5.15 to 3.80 km/s, and in the Mesozoic layers, it decreases from 2.70 to 2.30 km/s. The subcrustal V _p gradually increases downwards from 6.50 to 6.7–6.8 km/s at the crustal base, which complicates the problem of separating the middle and lower crust. The V _p velocities above 6.80 km/s have not been revealed even in the lowermost part of the crust, in contrast to the similar profiles in the East European Platform. The Moho is clearly delineated by the velocity contrast of 1.3–1.7 km/s. The alternating pattern of the changes in the Moho depths corresponding to Moho undulations with a wavelength of about 150 km and the amplitude reaching 8 to 17 km is a peculiarity of the velocity model.     

Experimental Study on Velocity Profiles with Different Roughness Elements in a Flume

The classical log law for velocity profile is applied to engineering practice. Field observations indicate that the composition of the bed materials obviously influences the shape of vertical velocity distribution. To clearly understand the roughness effect, six types of materials were laid separately at various depths for the investigation of the effects of roughness elements on the vertical velocity distribution. A down-looking 3D acoustic Doppler velocimeter was used to measure the velocity profiles. The experimental results showed that the curve characteristics of velocity profiles are strongly dependent on the roughness scale and related flow parameters. If d/R, Fr, and Re are larger than 0.15, 0.47, and 60 000, respectively, the velocity distribution may resemble an S-shape profile. The inflexion position Z*/H for a given S-shape profile was empirically deduced as Z*/H = ?0.4481d/R + 0.3225. Otherwise, the velocity profile agrees well with the logarithmic law. The findings of this study are useful in engineering practice (i.e., depth-averaged velocity and flow rate estimate). Key words: velocity profiles, acoustic Doppler velocimeter, roughness elements, logarithmic law, S-shape curve.     

Estimation of site effects using strong motion data of BYTNet array in Turkey

Simultaneous estimation of effects of source, propagation path, and local site amplification was carried out using observed strong motion records in a frequency range from 0.8 to 20 Hz for the purpose of empirical evaluation of the local site effects in different geological conditions in the northwestern part of Turkey. The analyzed data are S-wave portions of 162 accelerograms from 39 shallow events observed at 14 sites of BYTNet array. A spectral separation method was applied to the observed S-wave spectra. The solutions for source spectra, inelasticity factor of propagation path for S-waves (Q _s-value), and factor of site amplification at each site were obtained in a least squares sense. In the analysis, we assumed that the factor of the site amplification at a reference site is the same as that of theoretical amplification of S-waves to the soil model whose bottom layer has an S-wave velocity around 2.15 km/s. The estimated Q _s-value of the propagation path is modeled as Q _s(f)?=?87.4f^0.78. The estimated site amplifications are characterized into three groups. The sites in the first group belong to rock site with no dominant peaks at a frequency range of 2 to 10 Hz. The second group of hard soil sites is characterized with moderately dominant peaks at a frequency of 5 Hz. The last group for soft soil sites has common peaks at a frequency of 4 Hz with larger amplitudes than those in the hard soil group. We, then, compare the amplifications with average S-wave velocity in top 30 m of the shallow S-wave profiles and proposed linear empirical formula between them at each frequency. We, furthermore, inverted the observed amplification factors into S-wave velocity and Q _s-value profiles of the deep soil over the basement.     

Site Specific Ground Motion Modeling and Seismic Response Analysis for Microzonation of Baku,Azerbaijan

We investigated ground response for Baku (Azerbaijan) from two earthquakes of magnitude M6.3 occurred in Caspian Sea (characterized as a near event) and M7.5 in Shamakhi (characterized as a remote extreme event). S-wave velocity with the average shear wave velocity over the topmost 30 m of soil is obtained by experimental method from the V _P values measured for the soils. The downtown part of Baku city is characterized by low V_S30 values (< 250 m/s), related to sand, water-saturated sand, gravel-pebble, and limestone with clay. High surface PGA of 240 gal for the M7.5 event and of about 190 gal for the M6.3 event, and hence a high ground motion amplification, is observed in the shoreline area, through downtown, in the north-west, and in the east parts of Baku city with soft clays, loamy sands, gravel, sediments.