A different method for interpretation of magnetic anomalies due to 2-D dipping dikes

In this study a new method is presented to determine model parameters from magnetic anomalies caused by dipping dikes. The proposed method is applied by employing only the even component of the anomaly. First, the maximum of the even component is divided to its value at any distance x in order to obtain S1. Then, theoretical even component values are computed for the minimal depth (h) and half-width (b) values. S2 is obtained by dividing their maximum to the value computed for the same distance x. A set of S2 values is calculated by slowly increasing the half-width, and h and b for the S2 closest to S1 are determined. The same procedure is repeated by increasing the depth. The determined b values are plotted against the corresponding values of h. After repeating the process and plotting curves for different distances, it is possible to determine the actual depth and half-width values.     

Seismic analysis of nailed vertical excavation using pseudo-dynamic approach

An attempt has been made to study the behavior of nailed vertical excavations in medium dense to dense cohesionless soil under seismic conditions using a pseudo-dynamic approach. The effect of several parameters such as angle of internal friction of soil(Φ), horizontal(k_h) and vertical(k_v) earthquake acceleration coefficients, amplification factor(f_a), length of nails(L), angle of nail inclination(α) and vertical spacing of nails(S_v) on the stability of nailed vertical excavations has been explored. The limit equilibrium method along with a planar failure surface is used to derive the formulation involved with the pseudo-dynamic approach, considering axial pullout of the installed nails. A comparison of the pseudo-static and pseudo-dynamic approaches has been established in order to explore the effectiveness of the pseudo-dynamic approach over pseudo-static analysis, since most of the seismic stability studies on nailed vertical excavations are based on the latter. The results are expressed in terms of the global factor of safety(FOS). Seismic stability, i.e., the FOS of nailed vertical excavations is found to decrease with increase in the horizontal and vertical earthquake forces. The present values of FOS are compared with those available in the literature.     

Improved random noise attenuation using <Emphasis Type="Italic">f</Emphasis>−<Emphasis Type="Italic">x</Emphasis> empirical mode decomposition and local similarity

Conventional f?x empirical mode decomposition (EMD) is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events. However, when a seismic event is not horizontal, the use of f?x EMD is harmful to most useful signals. Based on the framework of f?x EMD, this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals. Compared with conventional f?x EMD, f?x predictive filtering, and f?x empirical mode decomposition predictive filtering, the new approach can preserve more useful signals and obtain a relatively cleaner denoised image. Synthetic and field data examples are shown as test performances of the proposed approach, thereby verifying the effectiveness of this method.     

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in <Emphasis Type="Italic">E</Emphasis>-polarization induction problems

To improve the accuracy of the numerical evaluation through the 3-D finite difference method, the surface boundary conditions are added to modify the old program. The author has tested the new program by making calculations for the model constructed by Wanamaker, et al (1984). The comparison between the numerical results obtained from this paper and those by Wannamaker, et al (1984) indicates that a pronounced improvement is realized in the evaluation of the horizontal magnetic components. Moreover, better calculations for the vertical magnetic components are also obtainable by using the new program.     

Splitter plate as a flow-altering pier scour countermeasure

Results of an experimental study on the countermeasure of scour depth at circular piers are presented. Experiments were conducted for pier scour with and without a splitter plate under a steady, uniform clear-water flow condition. The results of pier scour without splitter plate were used as a reference. Different combinations of lengths and thicknesses of splitter plates were tested attaching each of them to a pier at the upstream vertical plane of symmetry. Two different median sediment sizes (d ₅₀ = 0.96 and 1.8 mm) were considered as bed sediment. The experimental results show that the scour depth consistently decreases with an increase in splitter plate length, while the scour depth remains independent of splitter plate thickness. In addition, temporal evolution of scour depth at piers with and without a splitter plate is observed. The best combination is found to be with a splitter plate thickness of b/5 and a length of 2b. Here, b denotes the pier diameter. An empirical formula for the estimation of equilibrium scour depth at piers with splitter plates is obtained from a multiple linear regression analysis of the experimental data. The flow fields for various combinations of circular piers with and without splitter plate including plain bed and equilibrium scour conditions were measured by using an acoustic Doppler velocimeter. The turbulent flow fields for various configurations are investigated by plotting the velocity vectors and the turbulent kinetic energy contours on vertical and horizontal planes. The splitter plate attached to the pier deflects the approach flow and thus weakens the strength of the downflow and the horseshoe vortex, being instrumental in reducing the equilibrium scour depth at piers. The proposed method of pier scour countermeasure is easy to install and cost effective as well.     

Gravity Anomalies of Arbitrary 3D Polyhedral Bodies with Horizontal and Vertical Mass Contrasts

During the last 15 years, more attention has been paid to derive analytic formulae for the gravitational potential and field of polyhedral mass bodies with complicated polynomial density contrasts, because such formulae can be more suitable to approximate the true mass density variations of the earth (e.g., sedimentary basins and bedrock topography) than methods that use finer volume discretization and constant density contrasts. In this study, we derive analytic formulae for gravity anomalies of arbitrary polyhedral bodies with complicated polynomial density contrasts in 3D space. The anomalous mass density is allowed to vary in both horizontal and vertical directions in a polynomial form of \(\lambda =ax^m+by^n+cz^t\), where m, n, t are nonnegative integers and a, b, c are coefficients of mass density. First, the singular volume integrals of the gravity anomalies are transformed to regular or weakly singular surface integrals over each polygon of the polyhedral body. Then, in terms of the derived singularity-free analytic formulae of these surface integrals, singularity-free analytic formulae for gravity anomalies of arbitrary polyhedral bodies with horizontal and vertical polynomial density contrasts are obtained. For an arbitrary polyhedron, we successfully derived analytic formulae of the gravity potential and the gravity field in the case of \(m\le 1\), \(n\le 1\), \(t\le 1\), and an analytic formula of the gravity potential in the case of \(m=n=t=2\). For a rectangular prism, we derive an analytic formula of the gravity potential for \(m\le 3\), \(n\le 3\) and \(t\le 3\) and closed forms of the gravity field are presented for \(m\le 1\), \(n\le 1\) and \(t\le 4\). Besides generalizing previously published closed-form solutions for cases of constant and linear mass density contrasts to higher polynomial order, to our best knowledge, this is the first time that closed-form solutions are presented for the gravitational potential of a general polyhedral body with quadratic density contrast in all spatial directions and for the vertical gravitational field of a prismatic body with quartic density contrast along the vertical direction. To verify our new analytic formulae, a prismatic model with depth-dependent polynomial density contrast and a polyhedral body in the form of a triangular prism with constant contrast are tested. Excellent agreements between results of published analytic formulae and our results are achieved. Our new analytic formulae are useful tools to compute gravity anomalies of complicated mass density contrasts in the earth, when the observation sites are close to the surface or within mass bodies.     

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.     

A Least-squares Minimization Approach to Depth Determination from Magnetic Data

—We have developed a least-squares minimization approach to depth determination from magnetic data. By defining the anomaly value T(0) at the origin and the anomaly value T(N) at any other distance (N) on the profile, the problem of depth determination from magnetic data has been transformed into finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for a sphere, horizontal cylinder, dike, and for a geologic contact. Procedures are also formulated to estimate the effective magnetization intensity and the effective magnetization inclination. A scheme for analyzing the magnetic data has been formulated for determining the model parameters of the causative sources. The method is applied to synthetic data with and without random errors. Finally, the method is applied to two field examples from Canada and Arizona. In all cases examined, the estimated depths are found to be in goodagreement with actual values.     

Gravity anomaly and crustal density structure in Jilantai rift zone and its adjacent region

This paper deals with the interpretation of Bouguer gravity anomalies measured along a 250 km long Suhaitu-Etuokeqi gravity profile located at the transitional zone of the Alxa and Ordos blocks where geophysical characteristics are very complex. The analysis is carried out in terms of the ratio of elevation and Bouguer gravity anomaly, the normalized full gradient of a section of the Bouguer gravity anomaly (G ^h ) and the crustal density structure reveal that (1) the ratio of highs and lows of elevation and Bouguer gravity anomaly is large between Zhengyiguan fault (F4) and Helandonglu fault (F6), which can be explained due to crustal inhomogeneities related to the uplift of the Qinghai-Tibet block in the northeast; (2) the main active faults correspond to the G ^h contour strip or cut the local region, and generally show strong deformation characteristics, for example the Bayanwulashan mountain front fault (F1) or the southeast boundary of Alxa block is in accord with the western change belt of G ^h , a belt about 10 km wide that extends to about 30 km; (3) Yinchuan-Pingluo fault (F8) is the seismogenic structure of the Pingluo M earthquake, and its focal depth is about 15 km; (4) the Moho depth trend and Bouguer gravity anomaly variation indicates that the regional gravity field is strongly correlated with the Moho discontinuity.     

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.     

New relationship between fundamental site frequency and thickness of soft sediments from seismic ambient noise

In this contribution, new relationship between the fundamental site frequency and the thickness of soft sediments is obtained for many sites in Egypt. The Horizontal-to-Vertical Spectral Ratio (“H/V”) technique (known as Nakamura technique) can be used as a robust tool to determine the thickness of soft sediments layers overlaying bedrock from observations and measurements of seismic ambient noise data. In Egypt, numerous seismic ambient noise measurements have been conducted in several areas to determine the dynamic properties of soft soil for engineering purposes. At each site in each studied area, the fundamental site frequency was accurately estimated from the main peak in the spectral ratio between the horizontal and vertical component. Consequently, an extensive database of microtremor measurements, well logging data, and shallow seismic refraction data have been configured and assembled for the studied areas. New formula between fundamental site frequency (f₀) and thickness of soft sediments (h) is established. The new formula has been validated and compared with other formulas of earlier scientists, and the results indicate that the calculated depth and geometry of the bedrock surface using new formula are in a good agreement with well logs data and previously published seismic refraction surveys in the investigated sites.     

Comparison of ionospheric parameters calculated with UAM and measured at Voeykovo observatory

The measurements of the critical frequencies of the ionospheric F2 layer based on vertical radiosounding, which was performed with a CADI digital ionosonde at the Voeykovo magnetic–ionospheric observatory in February 2013, have been considered. The observations have been compared with the upper atmosphere numerical model (UAM) data for three days that differ in the amplitude and the character of solar and magnetic activity and correspond to quiet and moderately disturbed states of the ionosphere. The work was performed in order to improve the methods for determining the ionospheric state by vertical sounding ionograms. The time variations in the F2 layer critical frequency, electric field vector zonal component, and thermospheric wind velocity meridional component have been analyzed. Calculations were performed with three UAM variants. The UAM version providing the best agreement with the CADI ionosonde data was the version in which the neutral temperature, neutral composition, and pressure gradients are calculated according to the MSIS empirical model and the horizontal neutral wind velocity is determined by the equation of motion with pressure gradients from MSIS. The calculated values corresponded to the measurements, except those for the evening, because the electron density at the ionospheric F2 layer maximum depends more strongly on electric fields and thermospheric wind velocities during this period. Thus, the indicated UAM version with the above limitations can be used to determine the state of the subauroral ionosphere.     

Regression between earthquake magnitudes having errors with known variances

Recent publications on the regression between earthquake magnitudes assume that both magnitudes are affected by error and that only the ratio of error variances is known. If X and Y represent observed magnitudes, and x and y represent the corresponding theoretical values, the problem is to find the a and b of the best-fit line \(y = a x + b\). This problem has a closed solution only for homoscedastic errors (their variances are all equal for each of the two variables). The published solution was derived using a method that cannot provide a sum of squares of residuals. Therefore, it is not possible to compare the goodness of fit for different pairs of magnitudes. Furthermore, the method does not provide expressions for the x and y. The least-squares method introduced here does not have these drawbacks. The two methods of solution result in the same equations for a and b. General properties of a discussed in the literature but not proved, or proved for particular cases, are derived here. A comparison of different expressions for the variances of a and b is provided. The paper also considers the statistical aspects of the ongoing debate regarding the prediction of y given X. Analysis of actual data from the literature shows that a new approach produces an average improvement of less than 0.1 magnitude units over the standard approach when applied to \(M_{w}\) vs. \(m_{b}\) and \(M_{w}\) vs. \(M_{S}\) regressions. This improvement is minor, within the typical error of \(M_{w}\). Moreover, a test subset of 100 predicted magnitudes shows that the new approach results in magnitudes closer to the theoretically true magnitudes for only 65 % of them. For the remaining 35 %, the standard approach produces closer values. Therefore, the new approach does not always give the most accurate magnitude estimates.     

Прерывистое освещение поля зрения при методе соответствуюших высот и относительные уклонения отвеса в высоких татрах

To determine the relative deflections of the vertical from geodetic data and from astronomical measurements we used the method of equal altitudes, determining the time of passage by means of interrupted illumination of the field of view. The field of view of the telescope used (Zeiss Theo 010 and an astrolabe having an angle of 60°) was therefore supplied with five groups of seven horizontal fibres and during the passage of the two images the field of view was illuminated by a neon tube for a period of about 0·15 s every three seconds. The neon tube was connected either directly to an OMA 50 time signal by means of a transistor receiver or to a chronometer. The calculation was performed by means of relations (1) and (2). Apart from the corrections usually introduced, the personal-instrumental error (containing also a correction from the decimal equation) of the longitudeo _λ and the correctiona _η of the component η were also determined from the measurements. The correctionso _λ=?0·069s ando _η=?0·66″ also contain a correction from the decimal equation. Its value iso _λ ^′ =?0·030s for the longitude. The lago _λ?o _λ ^′ in reading the interpolation was ?0·039 s. The valueo _η=?0·66″ was introduced into the calculation of the vertical components η obtained from measurements in the High Tatras. The values of the corrections are given in Tab. 1. The method permits measurement of the passages of stars through the almucantar in the meridian. No conclusive proof was found for the impersonality (Tab. 1). The method was verified practically when determining the relative deflections of the vertical in the High Tatras for refining altitude measurements. The results are given in Tab. 2 and Fig. 2. The course of the quasigeoid profile in the Kriváňmeridian was also found (Fig. 3).     

Spatiotemporal parameters of anomalous reflections from the ionosphere

Analysis of vertical sounding data obtained on the network of domestic stations equipped with Parus-A ionosondes has shown that anomalous reflections from the ionosphere previously detected in Moscow are observed throughout the whole mid-latitude region. It is shown that the longitudinal effect impacts the probability of the appearance of anomalous reflections. Their spatiotemporal scales are determined. The horizontal dimensions of the anomalies, as a rule, range from several tens to several hundred, possibly a thousand, kilometers. The region of altitudes at which anomalous reflections are observed extends from the E region to F2 layer. The frequency range in which they are most often recorded is from 2 to 14 MHz. The time of their existence ranges from a fraction of minutes to many hours.     

Large-scale aseismic creep in the areas of the strong earthquakes revealed from the GRACE data on the time variations of the Earth’s gravity field

The refinement of the accuracy and resolution of the monthly global gravity field models from the GRACE satellite mission, together with the accumulation of more than a decade-long series of these models, enabled us to reveal the processes that occur in the regions of large (M_w≥8) earthquakes that have not been studied previously. The previous research into the time variations of the gravity field in the regions of the giant earthquakes, such as the seismic catastrophes in Sumatra (2004) and Chile (2010), and the Tohoku mega earthquake in Japan (2011), covered the coseismic gravity jump followed by the long postseismic changes reaching almost the same amplitude. The coseismic gravity jumps resulting from the lower-magnitude events are almost unnoticeable. However, we have established a long steady growth of gravity anomalies after a number of such earthquakes. For instance, in the regions of the subduction earthquakes, the growth of the positive gravity anomaly above the oceanic trench was revealed after two events with magnitudes M_w=8.5 in the Sumatra region (the Nias earthquake of March 2005 and the Bengkulu event of September 2007 near the southern termination of Sumatra Island), after the earthquake with M_w=8.5 on Hokkaido in September 2007, a doublet Simushir earthquake with the magnitudes M_w = 8.3 and 8.1 in the Kuriles in November 2006 and January 2007, and after the earthquake off the Samoa Island in September 2009 (M_w=8.1). The steady changes in the gravity field have also been recorded after the earthquake in the Sichuan region (May 2008, M_w = 8.0) and after the doublet event with magnitudes 8.6 and 8.2, which occurred in the Wharton Basin of the Indian Ocean on April 11, 2012. The detailed analysis of the growth of the positive anomaly in gravity after the Simushir earthquake of November 2006 is presented. The growth started a few months after the event synchronously with the seismic activation on the downdip extension of the coseismically ruptured fault plane zone. The data demonstrating the increasing depth of the aftershocks since March 2007 and the approximately simultaneous change in the direction and average velocity of the horizontal surface displacements at the sites of the regional GPS network indicate that this earthquake induced postseismic displacements in a huge area extending to depths below 100 km. The total displacement since the beginning of the growth of the gravity anomaly up to July 2012 is estimated at 3.0 m in the upper part of the plate’s contact and 1.5 m in the lower part up to a depth of 100 km. With allowance for the size of the region captured by the deformations, the released total energy is equivalent to the earthquake with the magnitude M_w = 8.5. In our opinion, the growth of the gravity anomaly in these regions indicates a large-scale aseismic creep over the areas much more extensive than the source zone of the earthquake. These processes have not been previously revealed by the ground-based techniques. Hence, the time series of the GRACE gravity models are an important source of the new data about the locations and evolution of the locked segments of the subduction zones and their seismic potential.     

On the stability of Maxwell distribution for a system of thermals in turbulent convective layers of fresh and salt water bodies

An ensemble of cold thermals in a convective layer of a fresh or salt water body is considered. The probability distribution density of the vertical velocities of thermals is assumed to satisfy the K-form of Fokker?Planck equation. The K-form of the Fokker?Planck equation is shown to have a steady-state solution in the form of a generalized Maxwell distribution. Natural and numerical experiments were carried out to demonstrate the existence of such distribution. Lyapunov functional in the form of Kullback relationship was used to establish the nonlinear instability of this distribution with respect to small perturbations in the Hilbert space norm.     

Comparative analysis of atmospheric and ionospheric variability by measurements of temperature in the mesopause region and peak electron density <Emphasis Type="Italic">NmF</Emphasis>2

The results of studying the atmospheric and ionospheric variability in the region of Eastern Siberia are presented. The analysis involved data on the atmosphere temperature at mesopause heights (Tm) and vertical sounding data on the peak electron density (NmF2). The data on temperature were obtained by spectrometric observations of the hydroxyl molecule emission (band ОН (6-2), 834.0 nm, maximum emission height ~87 km). The analysis covers the period from 2008 to 2015. Seasonal and year-to-year variations in the variability of Tm and NmF2 were studied and compared in different time periods: day-to-day variations (T > 24 h), tidal variations (8 h ≤ T ≤ 24 h), and variations with periods of internal gravity waves (T < 8 h). Both common features and distinctions in the behavior of the analyzed parameters have been found, and their possible physical causes are analyzed.     

Ground motion prediction equations for horizontal and vertical components of acceleration in Northern Iran

Recent studies have shown that the vertical component of ground motion can be quite destructive on a variety of structural systems. Development of response spectrum for design of buildings subjected to vertical component of earthquake needs ground motion prediction equations (GMPEs). The existing GMPEs for northern Iranian plateau are proposed for the horizontal component of earthquake, and there is not any specified GMPE for the vertical component of earthquake in this region. Determination of GMPEs is mostly based on regression analyses on earthquake parameters such as magnitude, site class, distance, and spectral amplitudes. In this study, 325 three-component records of 55 earthquakes with magnitude ranging from M _w 4.1 to M _w 7.3 are used for estimation on the regression coefficients. Records with distances less than 300 km are selected for analyses in the database. The regression analyses on earthquake parameters results in determination of GMPEs for peak ground acceleration and spectral acceleration for both horizontal and vertical components of the ground motion. The correlation between the models for vertical and horizontal GMPEs is studied in details. These models are later compared with some other available GMPEs. According to the result of this investigation, the proposed GMPEs are in agreement with the other relationships that were developed based on the local and regional data.     

Region-specific <Emphasis Type="Italic">S</Emphasis>-wave attenuation for earthquakes in northwestern Iran

In this study, continuous wavelet transform is applied to estimate the frequency-dependent quality factor of shear waves, Q _S , in northwestern Iran. The dataset used in this study includes velocigrams of more than 50 events with magnitudes between 4.0 and 6.5, which have occurred in the study area. The CWT-based method shows a high-resolution technique for the estimation of S-wave frequency-dependent attenuation. The quality factor values are determined in the form of a power law as Q _S (f)?=?(147?±?16)f ^0.71?±?0.02 and (126?±?12)f ^0.73?±?0.02 for vertical and horizontal components, respectively, where f is between 0.9 and 12 Hz. Furthermore, in order to verify the reliability of the suggested Q _S estimator method, an additional test is performed by using accelerograms of Ahar-Varzaghan dual earthquakes on August 11, 2012, of moment magnitudes 6.4 and 6.3 and their aftershocks. Results indicate that the estimated Q _S values from CWT-based method are not very sensitive to the numbers and types of waveforms used (velocity or acceleration).