Search results for: full wave inversion

Authors: Sheryl Avendaño, Miguel Ospina, Hebert Montegranario

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Full Wave Inversion (FWI) is a variant of seismic tomography for obtaining velocity profiles by an optimization process that combine forward modelling (or solution of wave equation) with the misfit between synthetic and observed data. In this research we are modelling wave propagation in a visco-acoustic medium in the frequency domain. We apply finite differences for the numerical solution of the wave equation with a mix between usual and rotated grids, where density depends on velocity and there exists a damping function associated to a linear dissipative medium. The velocity profiles are obtained from an initial one and the data have been modeled for a frequency range 0-120 Hz. By an iterative procedure we obtain an estimated velocity profile in which are detailed the remarkable features of the velocity profile from which synthetic data were generated showing promising results for our method.

Keywords: seismic inversion, full wave inversion, visco acoustic wave equation, finite diffrence methods

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Ying Zhang

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Surface waves provide critical constraints about the earth's structure in the crust and upper mantle. However, different modes of Love waves with close group velocities often arrive at a similar time and interfere with each other. This problem is typical for Love waves at intermediate periods that travel through the oceanic lithosphere. Therefore, we developed a two-step inversion approach to separate the waveforms of the fundamental and first higher mode of Love waves. We first solve the phase velocities of the two modes and their amplitude ratios. The misfit function is based on the sum of phase differences among the station pairs. We then solve the absolute amplitudes of the two modes and their initial phases using obtained phase velocities and amplitude ratio. The separated waveforms of each mode from the two-step inversion method can be further used in surface wave tomography to improve model resolution.

Keywords: surface wave inversion, waveform separation, love waves, higher-mode interference

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: Nastaran Moosavi, Mohammad Mokhtari

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Seismic inversion is a technique which has been in use for years and its main goal is to estimate and to model physical characteristics of rocks and fluids. Generally, it is a combination of seismic and well-log data. Seismic inversion can be carried out through different methods; we have conducted and compared post-stack and pre- stack seismic inversion methods on real data in one of the fields in the Persian Gulf. Pre-stack seismic inversion can transform seismic data to rock physics such as P-impedance, S-impedance and density. While post- stack seismic inversion can just estimate P-impedance. Then these parameters can be used in reservoir identification. Based on the results of inverting seismic data, a gas reservoir was detected in one of Hydrocarbon oil fields in south of Iran (Persian Gulf). By comparing post stack and pre-stack seismic inversion it can be concluded that the pre-stack seismic inversion provides a more reliable and detailed information for identification and prediction of hydrocarbon reservoirs.

Keywords: density, p-impedance, s-impedance, post-stack seismic inversion, pre-stack seismic inversion

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Authors: E. N. Masri, E. Takács

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Amplitude Versus Offset (AVO) and simultaneous model-based impedance inversion techniques have not been utilized for geothermal exploration commonly; however, some recent publications called the attention that they can be very useful in the geothermal investigations. In this study, we present rock physical attributes obtained from 3D pre-stack seismic data and well logs collected in a study area of the NW part of Pannonian Basin where the geothermal reservoir is located in the fractured zones of Triassic basement and it was hit by three productive-injection well pairs. The holes were planned very successfully based on the conventional 3D migrated stack volume prior to this study. Subsequently, the available geophysical-geological datasets provided a great opportunity to test modern inversion procedures in the same area. In this presentation, we provide a summary of the theory and application of the most promising seismic inversion techniques from the viewpoint of geothermal exploration. We demonstrate P- and S-wave impedance, as well as the velocity (Vp and Vs), the density, and the Vp/Vs ratio attribute volumes calculated from the seismic and well-logging data sets. After a detailed discussion, we conclude that P-wave impedance and Vp/Vp ratio are the most helpful parameters for lithology discrimination in the study area. They detect the hot water saturated fracture zone very well thus they can be very useful in mapping the investigated reservoir. Integrated interpretation of all the obtained rock-physical parameters is essential. We are extending the above discussed pre-stack seismic tools by studying the possibilities of Elastic Impedance Inversion (EII) for geothermal exploration. That procedure provides two other useful rock-physical properties, the compressibility and the rigidity (Lamé parameters). Results of those newly created elastic parameters will also be demonstrated in the presentation. Geothermal extraction is of great interest nowadays; and we can adopt several methods have been successfully applied in the hydrocarbon exploration for decades to discover new reservoirs and reduce drilling risk and cost.

Keywords: fractured zone, seismic, well-logging, inversion

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Authors: Sheng-Po Tseng, Che-Hua Yang

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Motivation and Objective: Ultrasonic guided waves become an important tool for nondestructive evaluation of structures and components. Guided waves are used for the purpose of identifying defects or evaluating material properties in a nondestructive way. While guided waves are applied for evaluating material properties, instead of knowing the properties directly, preliminary signals such as time domain signals or frequency domain spectra are first revealed. With the measured ultrasound data, inversion calculation can be further employed to obtain the desired mechanical properties. Methods: This research is development of high speed inversion calculation technique for obtaining full-field mechanical properties from the quantitative laser ultrasound visualization system (QLUVS). The quantitative laser ultrasound visualization system (QLUVS) employs a mirror-controlled scanning pulsed laser to generate guided acoustic waves traveling in a two-dimensional target. Guided waves are detected with a piezoelectric transducer located at a fixed location. With a gyro-scanning of the generation source, the QLUVS has the advantage of fast, full-field, and quantitative inspection. Results and Discussions: This research introduces two important tools to improve the computation efficiency. Firstly, graphic procession unit (GPU) with large amount of cores are introduced. Furthermore, combining the CPU and GPU cores, parallel procession scheme is developed for the inversion of full-field mechanical properties based on the QLUVS data. The newly developed inversion scheme is applied to investigate the computation efficiency for single-layered and double-layered plate-like samples. The computation efficiency is shown to be 80 times faster than unparalleled computation scheme. Conclusions: This research demonstrates a high-speed inversion technique for the characterization of full-field material properties based on quantitative laser ultrasound visualization system. Significant computation efficiency is shown, however not reaching the limit yet. Further improvement can be reached by improving the parallel computation. Utilizing the development of the full-field mechanical property inspection technology, full-field mechanical property measured by non-destructive, high-speed and high-precision measurements can be obtained in qualitative and quantitative results. The developed high speed computation scheme is ready for applications where full-field mechanical properties are needed in a nondestructive and nearly real-time way.

Keywords: guided waves, material characterization, nondestructive evaluation, parallel processing

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Authors: Shrey Sharma, Gunjan Kumar Verma

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High density electrical prospecting has been widely used in groundwater investigation, civil engineering and environmental survey. For efficient inversion, the forward modeling routine, sensitivity calculation, and inversion algorithm must be efficient. This paper attempts to provide a brief summary of the past and ongoing developments of the method. It includes reviews of the procedures used for data acquisition, processing and inversion of electrical resistivity data based on compilation of academic literature. In recent times there had been a significant evolution in field survey designs and data inversion techniques for the resistivity method. In general 2-D inversion for resistivity data is carried out using the linearized least-square method with the local optimization technique .Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Continued developments in computation technology, as well as fast data inversion techniques and software, have made it possible to use optimization techniques to obtain model parameters to a higher accuracy. A brief discussion on the limitations of the electrical resistivity method has also been presented.

Keywords: inversion, limitations, optimization, resistivity

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Authors: Christopher Hardly Joseph, Nicola Pelagalli, Davide Mencarelli, Luca Pierantoni

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In this contribution, we report the electromagnetic response of a split ring resonator (SRR) based magnetic metamaterial unit cell in free space nature by means of a full-wave electromagnetic simulation. The effective parameters of these designed structures have been analyzed. The structures have been specifically designed to work at high frequency considering the development of many microwave and lower mm-wave devices. In addition to that, the application of the designed metamaterial structures is also proposed, namely metamaterial loaded planar transmission lines, potentially useful to optimize size and quality factor of circuit components and radiating elements.

Keywords: CPW, Microwave Components, Negative Permeability, Split Ring Resonator (SRR)

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

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There exist a wide range of failure modes in composite structures due to the increased usage of the structures especially in aerospace industry. Moreover, temperature dependent wave response of composite and layered structures have been continuously studied, though still limited, in the last decade mainly due to the broad operating temperature range of aerospace structures. A wave finite element (WFE) and finite element (FE) based computational method is presented by which the temperature dependent wave dispersion characteristics and interaction phenomenon in composite structures can be predicted. Initially, the temperature dependent mechanical properties of the panel in the range of -100 ◦C to 150 ◦C are measured experimentally using the Thermal Mechanical Analysis (TMA). Temperature dependent wave dispersion characteristics of each waveguide of the structural system, which is discretized as a system of a number of waveguides coupled by a coupling element, is calculated using the WFE approach. The wave scattering properties, as a function of temperature, is determined by coupling the WFE wave characteristics models of the waveguides with the full FE modelling of the coupling element on which defect is included. Numerical case studies are exhibited for two waveguides coupled through a coupling element.

Keywords: finite element, temperature dependency, wave dispersion characteristics, wave finite element, wave scattering properties

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Authors: Attaullah Khawaja, Amna Shabbir

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Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper regularized channel inversion under equal power constraint in the multiuser multiple input multiple output (MU-MIMO) broadcast channels has been considered. Sum capacity with plain channel inversion also known as Zero Forcing Beam Forming (ZFBF) and optimum sum capacity using Dirty Paper Coding (DPC) has also been investigated. Analysis and simulations show that regularization enhances the system performance and empower linear growth in Sum Capacity and specially work well at low signal to noise ratio (SNRs) regime.

Keywords: broadcast channel, channel inversion, multiple antenna multiple-user wireless, multiple-input multiple-output (MIMO), regularization, dirty paper coding (DPC), sum capacity

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Authors: Stephen Orimoloye, Jose Horrillo-Caraballo, Harshinie Karunarathna, Dominic E. Reeve

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Prediction of wave overtopping is an essential component of coastal seawall designing and management. Not only that excessive overtopping is reported for impermeable seawalls under bimodal waves, but overtopping is also showing a high sensitivity to the peakedness of the random wave propagation patterns. In the present study, we present a comprehensive analysis of the effects of peakedness of bimodal wave patterns of the overtopping of sloping seawalls. An energy-conserved bimodal spectrum with four different spectra peak periods and swell percentages was applied to estimate wave overtopping in both numerical and experimental flumes. Results of incident surface elevations and bimodal spectra were accurately captured across the flume domain using sets of well-positioned resistant-type wave gauges. Peakedness characteristics of the wave patterns were extracted to derive a relationship between the non-dimensional overtopping and the peakedness across the wave groups in the wave series. The full paper will briefly describe the development of the spectrum and present a comprehensive results analysis leading to the derivation of the relationship between dimensionless overtopping and peakedness of bimodal waves.

Keywords: wave overtopping, peakedness, bimodal waves, swell percentages

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Authors: Meng Wu

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Motion planning is a common task required to be fulfilled by robots. A strategy combining Ant Colony Optimization (ACO) and gravity gradient inversion algorithm is proposed for motion planning of mobile robots. In this paper, in order to realize optimal motion planning strategy, the cost function in ACO is designed based on gravity gradient inversion algorithm. The obstacles around mobile robot can cause gravity gradient anomalies; the gradiometer is installed on the mobile robot to detect the gravity gradient anomalies. After obtaining the anomalies, gravity gradient inversion algorithm is employed to calculate relative distance and orientation between mobile robot and obstacles. The relative distance and orientation deduced from gravity gradient inversion algorithm is employed as cost function in ACO algorithm to realize motion planning. The proposed strategy is validated by the simulation and experiment results.

Keywords: motion planning, gravity gradient inversion algorithm, ant colony optimization

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Authors: Olawale Babatunde Olatinsu, Deborah Oluwaseun Olorode

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Industrial rocks were collected from a quarry site at Ewekoro in south-western Nigeria and analysed using Nuclear Magnetic Resonance (NMR) technique. NMR measurement was conducted on the samples in partial water-saturated and full brine-saturated conditions. Raw NMR data were analysed with the aid of T2 curves and T2 spectra generated by inversion of raw NMR data using conventional regularized least-squares inversion routine. Results show that NMR transverse relaxation (T2) signatures fairly adequately distinguish between the rock types. Similar T2 curve trend and rates at partial saturation suggests that the relaxation is mainly due to adsorption of water on micropores of similar sizes while T2 curves at full saturation depict relaxation decay rate as: 1/T2(shale)>1/ T2(glauconite)>1/ T2(limestone) and 1/T2(sandstone). NMR T2 distributions at full brine-saturation show: unimodal distribution in shale; bimodal distribution in sandstone and glauconite; and trimodal distribution in limestone. Full saturation T2 distributions revealed the presence of well-developed and more abundant micropores in all the samples with T2 in the range, 402-504 μs. Mesopores with amplitudes much lower than those of micropores are present in limestone, sandstone and glauconite with T2 range: 8.45-26.10 ms, 6.02-10.55 ms, and 9.45-13.26 ms respectively. Very low amplitude macropores of T2 values, 90.26-312.16 ms, are only recognizable in limestone samples. Samples with multiple peaks showed well-connected pore systems with sandstone having the highest degree of connectivity. The difference in T2 curves and distributions for the rocks at full saturation can be utilised as a potent diagnostic tool for discrimination of these rock types found at Ewekoro.

Keywords: Ewekoro, NMR techniques, industrial rocks, characterization, relaxation

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Authors: Rais Yusoh, Rosli Saad, Mokhtar Saidin, Fauzi Andika, Sabiu Bala Muhammad

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Resistivity and seismic refraction profiling have become a common method in pre-investigations for visualizing subsurface structure. The integration of the methods could reduce an interpretation ambiguity. Both methods have their individual software packages for data inversion, but potential to combine certain geophysical methods are restricted; however, the research algorithms that have this functionality was existed and are evaluated personally. The interpretation of subsurface were improve by combining inversion data from both methods by influence each other models using closure coupling; thus, by implementing both methods to support each other which could improve the subsurface interpretation. These methods were applied on a field dataset from a pre-investigation for archeology in finding the ancient river. There were no major changes in the inverted model by combining data inversion for this archetype which probably due to complex geology. The combine data analysis provides an additional technique for interpretation such as an alluvium, which can have strong influence on the ancient river findings.

Keywords: ancient river, combine inversion, resistivity, seismic refraction

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Authors: Fofie Kokea Ariane Darolle, Gouet Daniel Hervé, Koumetio Fidèle, Yemele David

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The electrical resistivity method is successfully used in this paper in order to have a clearer picture of the subsurface of the North-East ofFiguil in northern Cameroon. It is worth noting that this method is most often used when the objective of the study is to image the shallow subsoils by considering them as a set of stratified ground layers. The problem to be solved is very often environmental, and in this case, it is necessary to perform an inversion of the data in order to have a complete and accurate picture of the parameters of the said layers. In the case of this work, thirty-three (33) Schlumberger VES have been carried out on an irregular grid to investigate the subsurface of the study area. The 1D inversion applied as a preliminary modeling tool and in correlation with the mechanical drillings results indicates a complex subsurface lithology distribution mainly consisting of marbles and schists. Moreover, the quasi-3D inversion with lateral constraint shows that the misfit between the observed field data and the model response is quite good and acceptable with a value low than 10%. The method also reveals existence of two water bearing in the considered area. The first is the schist or weathering aquifer (unsuitable), and the other is the marble or the fracturing aquifer (suitable). The final quasi 3D inversion results and geological models indicate proper sites for groundwaters prospecting and for mining exploitation, thus allowing the economic development of the study area.

Keywords: electrical resistivity method, 1D inversion, quasi 3D inversion, groundwaters, mining

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Authors: B. Bouadjemi, S. Bentata, A. Abbad, W.Benstaali

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The full-potential linearized augmented plane wave method (FP-LAPW) within the Generalized Gradient Approximation (GGA) is used to calculate the magnetic and optical properties of quaternary GaFeMnN. The results show that the compound becomes magnetic and half metallic and there is an apparition of peaks at low frequencies for the optical properties.

Keywords: optical properties, DFT, Spintronic, wave

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: Fernando P. Silva, Valter J. S. Leite, Erivelton G. Nepomuceno

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In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the first is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties.

Keywords: robust multi inversion, omni-directional robot, robocup, nonlinear control

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Authors: Brayden Mi

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Reverse time migration has been widely used in the Petroleum exploration industry to reveal subsurface images and to detect rock and fluid properties since the early 1980s. The seismic technology involves the construction of a velocity model through interpretive model construction, seismic tomography, or full waveform inversion, and the application of the reverse-time propagation of acquired seismic data and the original wavelet used in the acquisition. The methodology has matured from 2D, simple media to present-day to handle full 3D imaging challenges in extremely complex geological conditions. Conventional Ultrasound computed tomography (USCT) utilize travel-time-inversion to reconstruct the velocity structure of an organ. With the velocity structure, USCT data can be migrated with the “bend-ray” method, also known as migration. Its seismic application counterpart is called Kirchhoff depth migration, in which the source of reflective energy is traced by ray-tracing and summed to produce a subsurface image. It is well known that ray-tracing-based migration has severe limitations in strongly heterogeneous media and irregular acquisition geometries. Reverse time migration (RTM), on the other hand, fully accounts for the wave phenomena, including multiple arrives and turning rays due to complex velocity structure. It has the capability to fully reconstruct the image detectable in its acquisition aperture. The RTM algorithms typically require a rather accurate velocity model and demand high computing powers, and may not be applicable to real-time imaging as normally required in day-to-day medical operations. However, with the improvement of computing technology, such a computational bottleneck may not present a challenge in the near future. The present-day (RTM) algorithms are typically implemented from a flat datum for the seismic industry. It can be modified to accommodate any acquisition geometry and aperture, as long as sufficient illumination is provided. Such flexibility of RTM can be conveniently implemented for the application in USCT imaging if the spatial coordinates of the transmitters and receivers are known and enough data is collected to provide full illumination. This paper proposes an implementation of a full 3D RTM algorithm for USCT imaging to produce an accurate 3D acoustic image based on the Phase-shift-plus-interpolation (PSPI) method for wavefield extrapolation. In this method, each acquired data set (shot) is propagated back in time, and a known ultrasound wavelet is propagated forward in time, with PSPI wavefield extrapolation and a piece-wise constant velocity model of the organ (breast). The imaging condition is then applied to produce a partial image. Although each image is subject to the limitation of its own illumination aperture, the stack of multiple partial images will produce a full image of the organ, with a much-reduced noise level if compared with individual partial images.

Keywords: illumination, reverse time migration (RTM), ultrasound computed tomography (USCT), wavefield extrapolation

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Authors: Rezvan Ravanfar Haghighi, S. Chatterjee, Pratik Kumar, V. C. Vani, Priya Jagia, Sanjiv Sharma, Susama Rani Mandal, R. Lakshmy

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The dual energy computed tomography (DECT) aims at noting the HU(V) values for the sample at two different voltages V=V1, V2 and thus obtain the electron densities (ρe) and effective atomic number (Zeff) of the substance. In the present paper, we aim to obtain a numerical algorithm by which (ρe, Zeff) can be obtained from the HU(100) and HU(140) data, where V=100, 140 kVp. The idea is to use this inversion method to characterize and distinguish between the lipid and fibrous coronary artery plaques.With the idea to develop the inversion algorithm for low Zeff materials, as is the case with non calcified coronary artery plaque, we prepare aqueous samples whose calculated values of (ρe, Zeff) lie in the range (2.65×1023≤ ρe≤ 3.64×1023 per cc ) and (6.80≤ Zeff ≤ 8.90). We fill the phantom with these known samples and experimentally determine HU(100) and HU(140) for the same pixels. Knowing that the HU(V) values are related to the attenuation coefficient of the system, we present an algorithm by which the (ρe, Zeff) is calibrated with respect to (HU(100), HU(140)). The calibration is done with a known set of 20 samples; its accuracy is checked with a different set of 23 known samples. We find that the calibration gives the ρe with an accuracy of ± 4% while Zeff is found within ±1% of the actual value, the confidence being 95%.In this inversion method (ρe, Zeff) of the scanned sample can be found by eliminating the effects of the CT machine and also by ensuring that the determination of the two unknowns (ρe, Zeff) does not interfere with each other. It is found that this algorithm can be used for prediction of chemical characteristic (ρe, Zeff) of unknown scanned materials with 95% confidence level, by inversion of the DECT data.

Keywords: chemical composition, dual-energy computed tomography, inversion algorithm

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Rezvan Ravanfar Haghighi, V. C. Vani, Suresh Perumal, Sabyasachi Chatterjee, Pratik Kumar

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X-ray attenuation coefficient [µ(E)] of any substance, for energy (E), is a sum of the contributions from the Compton scattering [ μCom(E)] and photoelectric effect [µPh(E)]. In terms of the, electron density (ρe) and the effective atomic number (Zeff) we have µCom(E) is proportional to [(ρe)fKN(E)] while µPh(E) is proportional to [(ρeZeffx)/Ey] with fKN(E) being the Klein-Nishina formula, with x and y being the exponents for photoelectric effect. By taking the sample's HU at two different excitation voltages (V=V1, V2) of the CT machine, we can solve for X=ρe, Y=ρeZeffx from these two independent equations, as is attempted in DECT inversion. Since µCom(E) and µPh(E) are both energy dependent, the coefficients of inversion are also dependent on (a) the source spectrum S(E,V) and (b) the detector efficiency D(E) of the CT machine. In the present paper we tabulate these coefficients of inversion for different practical manifestations of S(E,V) and D(E). The HU(V) values from the CT follow: <µ(V)>=<µw(V)>[1+HU(V)/1000] where the subscript 'w' refers to water and the averaging process <….> accounts for the source spectrum S(E,V) and the detector efficiency D(E). Linearity of μ(E) with respect to X and Y implies that (a) <µ(V)> is a linear combination of X and Y and (b) for inversion, X and Y can be written as linear combinations of two independent observations <µ(V1)>, <µ(V2)> with V1≠V2. These coefficients of inversion would naturally depend upon S(E, V) and D(E). We numerically investigate this dependence for some practical cases, by taking V = 100 , 140 kVp, as are used for cardiological investigations. The S(E,V) are generated by using the Boone-Seibert source spectrum, being superposed on aluminium filters of different thickness lAl with 7mm≤lAl≤12mm and the D(E) is considered to be that of a typical Si[Li] solid state and GdOS scintilator detector. In the values of X and Y, found by using the calculated inversion coefficients, errors are below 2% for data with solutions of glycerol, sucrose and glucose. For low Zeff materials like propionic acid, Zeffx is overestimated by 20% with X being within1%. For high Zeffx materials like KOH the value of Zeffx is underestimated by 22% while the error in X is + 15%. These imply that the source may have additional filtering than the aluminium filter specified by the manufacturer. Also it is found that the difference in the values of the inversion coefficients for the two types of detectors is negligible. The type of the detector does not affect on the DECT inversion algorithm to find the unknown chemical characteristic of the scanned materials. The effect of the source should be considered as an important factor to calculate the coefficients of inversion.

Keywords: attenuation coefficient, computed tomography, photoelectric effect, source spectrum

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Authors: Tzong-Ying Hao, Mohammad T. Rahmani

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The Torre Central building is a 9-story shear wall structure located in Santiago, Chile, and has been instrumented since 2009. Events of different intensity (ambient vibrations, weak and strong earthquake motions) have been recorded, and thus the building can serve as a full-scale benchmark to evaluate the structural health monitoring method developed. The first part of this article presents an analysis of inter-story drifts, and of changes in the first system frequencies (estimated from the relative displacement response of the 8th-floor with respect to the basement from recorded data) as baseline indicators of the occurrence of damage. During 2010 Chile earthquake the system frequencies were detected decreasing approximately 24% in the EW and 27% in NS motions. Near the end of shaking, an increase of about 17% in the EW motion was detected. The structural health monitoring (SHM) method based on changes in wave traveling time (wave method) within a layered shear beam model of structure is presented in the second part of this article. If structural damage occurs the velocity of wave propagated through the structure changes. The wave method measures the velocities of shear wave propagation from the impulse responses generated by recorded data at various locations inside the building. Our analysis and results show that the detected changes in wave velocities are consistent with the observed damages. On this basis, the wave method is proven for actual implementation in structural health monitoring systems.

Keywords: Chile earthquake, damage detection, earthquake response, impulse response, layered shear beam, structural health monitoring, Torre Central building, wave method, wave travel time

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Authors: Arka Roy, Chandra Prakash Dubey

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Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

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Authors: Bing Li, Tong Lu, Lei Qiang

Abstract:

Stoneley waves are interface waves that propagate at the interface between two solid media. In this study, the dispersion characteristics and wave structures of Stoneley waves in elastic multilayered plates are displayed and investigated. With a perspective of bulk wave, a reasonable assumption of the potential function forms of the expansion wave and shear wave in nth layer medium is adopted, and the characteristic equation of Stoneley waves in a three-layered plate is given in a determinant form. The dispersion curves and wave structures are solved and presented in both numerical and simulation results. It is observed that two Stoneley wave modes exist in a three-layered plate, that conspicuous dispersion occurs on low frequency band, that the velocity of each Stoneley wave mode approaches the corresponding Stoneley wave velocity at interface between two half infinite spaces. The wave structures reveal that the in-plane displacement of Stoneley waves are relatively high at interfaces, which shows great potential for interface defects detection.

Keywords: characteristic equation, interface waves, potential function, Stoneley waves, wave structure

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Authors: Yingchen Yang

Abstract:

Ocean waves are a rich renewable energy source that is nearly untapped to date, even though many wave energy conversion (WEC) technologies are currently under development. The present work discusses a vertical-axis WEC rotor for power generation. The rotor was specially designed to allow easy rearrangement of the same blades to achieve different rotor configurations and result in different wave-rotor interaction behaviors. These rotor configurations were tested in a wave tank under various wave conditions. The testing results indicate that all the rotor configurations perform unidirectional rotation about the vertical axis in waves, but the response characteristics are somewhat different. The rotor's unidirectional rotation about its vertical axis is essential in wave energy harvesting since it makes the rotor respond well in a wide range of the wave frequency and in any wave propagation directions. Result comparison among different configurations leads to a preferred rotor design for further hydrodynamic optimization.

Keywords: unidirectional rotation, vertical axis rotor, wave energy conversion, wave-rotor interaction

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Authors: Swati Sharma, R. P. Sharma

Abstract:

We intend to study the nonlinear evolution of the parallel propagating finite frequency Alfvén wave (also called Dispersive Alfvén wave/Hall MHD wave) propagating in the solar wind regime of the solar region when a perpendicularly propagating magnetosonic wave is present in the background. The finite frequency Alfvén wave behaves differently from the usual non-dispersive behavior of the Alfvén wave. To study the nonlinear processes (such as filamentation) taking place in the solar regions such as solar wind, the dynamical equation of both the waves are derived. Numerical simulation involving finite difference method for the time domain and pseudo spectral method for the spatial domain is then performed to analyze the transient evolution of these waves. The power spectra of the Dispersive Alfvén wave is also investigated. The power spectra shows the distribution of the magnetic field intensity of the Dispersive Alfvén wave over different wave numbers. For DAW the spectra shows a steepening for scales larger than the proton inertial length. This means that the wave energy gets transferred to the solar wind particles as the wave reaches higher wave numbers. This steepening of the power spectra can be explained on account of the finite frequency of the Alfvén wave. The obtained results are consistent with the observations made by CLUSTER spacecraft.

Keywords: solar wind, turbulence, dispersive alfven wave

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Authors: R. K. Apalowo, D. Chronopoulos

Abstract:

A Finite Element (FE) based scheme is presented for quantifying guided wave interaction with Localised Nonlinear Structural Damage (LNSD) within structures of arbitrary layering and geometric complexity. The through-thickness mode-shape of the structure is obtained through a wave and finite element method. This is applied in a time domain FE simulation in order to generate time harmonic excitation for a specific wave mode. Interaction of the wave with LNSD within the system is computed through an element activation and deactivation iteration. The scheme is validated against experimental measurements and a WFE-FE methodology for calculating wave interaction with damage. Case studies for guided wave interaction with crack and delamination are presented to verify the robustness of the proposed method in classifying and identifying damage.

Keywords: layered structures, nonlinear ultrasound, wave interaction with nonlinear damage, wave finite element, finite element

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Authors: Sumit Kumar Vishawakarma, Tapas Ranjan Panihari

Abstract:

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material, where the material properties such as Young's moduli, shear modulus, and density vary as an arbitrary continuous function of depth. In the considered model, Hook's law, strain-displacement relations along with equilibrium equations have been used to derive the governing equation. The mathematical formulation of this physical problem gives rise to an eigenvalue problem with displacement components as fundamental variables. This leads to achieving the closed-form expressions for quasi-wave velocities of SV-wave, SH-wave, and P-wave in the considered framework. These characteristics of wave propagation along with the above-stated variation have been scrutinized based on their numerical results. This parametric study reveals that wave velocity remarkably fluctuates as the magnitude of inhomogeneity parameters increases and decreases. The prominent effect has been shown depicting the dependence of wave velocity on the degree of material anisotropy. The influence of phase angle and depth of the medium has been remarkably established. The present study may facilitate the theoretical foundation and practical application in the field of earthquake source mechanisms.

Keywords: cross-anisotropic, inhomogeneity, P-wave, SH-wave, SV-wave, shear modulus, Young’s modulus

Procedia PDF Downloads 119