Correlation‐based reflection waveform inversion by one‐way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two‐way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation‐based reflection waveform inversion using one‐way wave equations to retrieve the background velocity. In this method, one‐way wave equations are used for the seismic wave forward modelling, migration/de‐migration and the gradient computation of objective function in frequency domain. Compared with the method using two‐way wave equation, the proposed method benefits from the lower computational cost of one‐way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two‐way wave equation both for two‐ and three‐dimensional situations. Through numerical analysis, we also find that one‐way wave equations can better construct the low wavenumber reflection wavepath without producing high‐amplitude short‐wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.     

Probabilistic assessment of one‐step‐ahead rainfall variation by Split Markov Process

In this paper, Split Markov Process (SMP) is developed to assess one‐step‐ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first‐order Markov chain to simulate daily rainfall variation at a point through state/sub‐state transitional probability matrix (TPM). The state/sub‐state TPM is based on the historical transitions from a particular state to a particular sub‐state, which is the basic difference between SMP and general Markov Process. The cumulative state/sub‐state TPM is represented in a contour plot at different probability levels. The developed cumulative state/sub‐state TPM is used to assess the possible range of rainfall in next time step, in a probabilistic sense. Application of SMP is investigated for daily rainfall at four rain gauge stations – Khandwa, Jabalpur, Sambalpur, and Puri, located at various parts in India. There are 99 years of record available out of which approximately 80% of data are used for calibration, and 20% of data are used to assess the performance. Thus, 80 years of daily monsoon rainfall is used to develop the state/sub‐state TPM, and 19 years data are used to investigate its performance. Model performance is assessed in terms of hit rate (HR), false alarm rate (FAR), and percentage captured. It is found that percentage captured is maximum for Khandwa (70%) and minimum for Sambalpur (44%) whereas hit rate is maximum for Sambalpur and minimum for Khandwa (73%). FAR is around 30% or below for Jabalpur, Sambalpur, and Puri. FAR is maximum for Khandwa (37%). Overall, the assessed range, particularly the upper limit, provides a quantification possible extreme value in the next time step, which is a very useful information to tackle the extreme events, such as flooding, water logging and so on. Copyright © 2011 John Wiley & Sons, Ltd.     

Simplified seismic analysis of one‐way asymmetric elastic systems with supplemental damping

This study investigates the effectiveness of the modal analysis using two‐degree‐of‐freedom (2DOF) modal stick to deal with the seismic analysis of one‐way asymmetric elastic systems with supplemental damping. The 2DOF modal stick possessing the non‐proportional damping property enables the modal translation and rotation to not be proportional even at elastic state. The analytical results of one‐storey and three‐storey buildings obtained by the proposed method are compared with those obtained by direct integration of the equation of motion and conventional approximate method, which neglects the off‐diagonal elements in the transformed damping matrix. It is found that the proposed simplified method, compared to conventional approximate methods, can significantly improve the accuracy of the analytical results and, at the same time, without obviously increasing computational efforts. Copyright © 2006 John Wiley & Sons, Ltd.     

Lithology-dependent seismic anisotropic amplitude variation with offset correction in transversely isotropic media

Analysis of amplitude variation with offset is an essential step for reservoir characterization. For an accurate reservoir characterization, the amplitude obtained with an isotropic assumption of the reservoir must be corrected for the anisotropic effects. The objective is seismic anisotropic amplitude correction in an effective medium, and, to this end, values and signs of anisotropic parameter differences (Δδ and Δε) across the reflection interfaces are needed. These parameters can be identified by seismic and well log data. A new technique for anisotropic amplitude correction was developed to modify amplitude changes in seismic data in transversely isotropic media with a vertical axis of symmetry. The results show that characteristics of pre-stack seismic data, that is, amplitude variation with offset gradient, can be potentially related to the sign of anisotropic parameter differences (Δδ and Δε) between two layers of the reflection boundary. The proposed methodology is designed to attain a proper fit between modelled and observed amplitude variation with offset responses, after anisotropic correction, for all possible lithofacies at the reservoir boundary. We first estimate anisotropic parameters, that is, δ and ε, away from the wells through Backus averaging of elastic properties resulted from the first pass of isotropic pre-stack seismic inversion, on input data with no amplitude correction. Next, we estimate the anisotropic parameter differences at reflection interfaces (values and signs of Δδ and Δε). We then generate seismic angle gather data after anisotropic amplitude correction using Rüger's equation for the P-P reflection coefficient. The second pass of isotropic pre-stack seismic inversion is then performed on the amplitude-corrected data, and elastic properties are estimated. Final outcome demonstrates how introduced methodology helps to reduce the uncertainty of elastic property prediction. Pre-stack seismic inversion on amplitude-corrected seismic data results in more accurate elastic property prediction than what can be obtained from non-corrected data. Moreover, a new anisotropy attribute (ν) is presented for improvement of lithology identification.     

Probabilistic evaluation of seismic performance of 3‐story 3D one‐ and two‐way steel moment‐frame structures

This paper presents the results of a probabilistic evaluation of the seismic performance of 3D steel moment‐frame structures. Two types of framing system are considered: one‐way frames typical of construction in the United States and two‐way frames typical of construction in Japan. For each framing system, four types of beam–column connections are considered: pre‐Northridge welded‐flange bolted‐web, post‐Northridge welded‐flange welded‐web, reduced‐beam‐section, and bolted‐flange‐plate connections. A suite of earthquake ground motions is used to compute the annual probability of exceedence (APE) for a series of drift demand levels and for member plastic‐rotation capacity. Results are compared for the different framing systems and connection details. It is found that the two‐way frames, which have a larger initial stiffness and strength than the one‐way frames for the same beam and column volumes, have a smaller APE for small drift demands for which members exhibit no or minimal yielding, but have a larger APE for large drift demands for which members exhibit large plastic rotations. However, the one‐way frames, which typically comprise a few seismic frames with large‐sized members that have relatively small rotation capacities, may have a larger APE for member failure. The probabilistic approach presented in this study may be used to determine the most appropriate frame configuration to meet an owner's performance objectives. Copyright © 2008 John Wiley & Sons, Ltd.     

Vp‐Vs relationship and amplitude variation with offset modelling of glauconitic greensand‡

The relationship between V_p and V_s may be used to predict V_s where only V_p is known. V_p/V_s is also used to identify pore fluids from seismic data and amplitude variation with offset analysis. Theoretical, physical, as well as statistical empirical V_p‐V_s relationships have been proposed for reservoir characterization when shear‐wave data are not available. In published work, the focus is primarily on the V_p‐V_s relationship of quartzitic sandstone. In order to broaden the picture we present V_p‐V_s relationships of greensand composed of quartz and glauconite by using data from the Paleocene greensand Nini oil field in the North Sea. A V_p‐V_s relationship derived from modelling is compared with empirical V_p‐V_s regressions from laboratory data as well as from log data. The accuracy of V_s prediction is quantified in terms of root‐mean‐square error. We find that the V_p‐V_s relationship derived from modelling works well for greensand shear‐wave velocity prediction. We model the seismic response of glauconitic greensand by using laboratory data from the Nini field. Our studies here reveal that brine‐saturated glauconitic greensand can have a similar seismic response to that from oil‐saturated quartzitic sandstone and that oil‐saturated strongly cemented greensand can have a similar amplitude variation with offset response to that from brine‐saturated weakly cemented greensand.     

Scaling and self‐similarity in one‐dimensional unsteady open channel flow

The conditions under which the Saint Venant equations system for unsteady open channel flow, as an initial–boundary value problem, becomes self‐similar are investigated by utilizing one‐parameter Lie group of point scaling transformations. One of the advantages of this methodology is that the self‐similarity conditions due to the initial and boundary conditions can also be investigated thoroughly in addition to the conditions due to the governing equation. The obtained self‐similarity conditions are compared with the scaling relationships that are derived through the Froude similitude. It is shown that the initial–boundary value problem of a one‐dimensional unsteady open channel flow process in a prototype domain can be self‐similar with that of several different scaled domains. However, the values of all the flow variables (at specified time and space) under different scaled domains can be upscaled to the same values in the prototype domain (at the corresponding time and space), as shown in this study. Distortion in scales of different space dimensions has been implemented extensively in physical hydraulic modelling, mainly because of cost, space and time limitations. Unlike the traditional approach, the distinction is made between the longitudinal–horizontal and transverse–horizontal length scales in this study. The scaled domain obtained by the proposed approach, when scaling ratios of channel width and water depth are equal, is particularly important for the similarity of flow characteristics in a cross‐section because the width‐to‐depth ratio and the inclination angles of the banks are conserved in a cross‐section. It is also shown that the scaling ratio of the roughness coefficient under distorted channel conditions depends on that of hydraulic radius and longitudinal length. The proposed scaling relations obtained by the Lie group scaling approach may provide additional spatial, temporal and economical flexibility in setting up physical hydraulic models. Copyright © 2013 John Wiley & Sons, Ltd.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Natural and accidental torsion in one‐storey structures on elastic foundation under non‐vertically incident SH‐waves

Factors α and β used in equivalent static analysis to account for natural and accidental torsion are evaluated with consideration of soil–structure interaction. The combined torsional effects of structural asymmetry and foundation rotation are examined with reference to a single monosymmetric structure placed on a rigid foundation that is embedded into an elastic half‐space, under to the action of non‐vertically incident SH waves. Dynamic and accidental eccentricities are developed such that when used together with the code‐specified base shear, the resulting static displacement at the flexible edge of the building is identical to that computed from dynamic analysis. It is shown that these eccentricities do not have a unique definition because they depend on both the selection of the design base shear and the criterion used for separation of the torsional effects of foundation rotation from those of structural asymmetry. Selected numerical results are presented in terms of dimensionless parameters for their general application, using a set of appropriate earthquake motions for ensuring generality of conclusions. The practical significance of this information for code‐designed buildings is elucidated. Copyright © 2006 John Wiley & Sons, Ltd.     

Spatial variation in sap flow velocity in semiarid region trees: its impact on stand‐scale transpiration estimates

In this study, we aimed to clarify spatial variations in xylem sap flow, and to determine the impacts of these variations on stand‐scale transpiration (E) estimates. We examined circumferential and radial variations in sap flow velocity (F_d) measured at several directions and depths in tree trunks of black locust (Robinia pseudoacacia) and native oak (Quercus liaotungensis), both of which have ring‐porous wood anatomy, in forest stands on the Loess Plateau, China. We evaluated the impacts of circumferential variations in F_d on stand‐scale transpiration estimates using a simple scaling exercise. We found significant circumferential variations in F_d in the outermost xylem in both species (coefficients of variation = 20–45%). For both species, F_d measured at the inner xylem was smaller than that of the outermost xylem and the F_d at the depth of > 10 mm was almost zero. The simple exercises showed that omitting circumferential variations in F_d affected the E estimate by 16–21%, which was less than the effects of omitting within‐tree radial and tree‐to‐tree variations in F_d in both species. These results suggest that circumferential variations in F_d can be a minor source of error for E estimates compared with within‐tree radial and tree‐to‐tree variations in F_d, regardless of the significant circumferential variations. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of out‐of‐plane seismic performance of column‐to‐column precast concrete cladding panels in one‐storey industrial buildings

Recent earthquakes in Italy (L'Aquila 2009 and Emilia 2012) highlighted the vulnerability of precast cladding panels, typically associated with a connection system not designed to account for displacement and rotation compatibility between the panels and the supporting structure. Experimental investigations were performed in the past to investigate the in‐plane performance of cladding panels and design recommendations have been made accordingly; however, in the case of out‐of‐plane seismic loads, the load demand is commonly evaluated in the design practice by means of formulations for nonstructural components. This paper summarizes the results obtained from parametric analyses conducted to estimate the out‐of‐plane load demand in column‐to‐column cladding panels typical of one‐storey commercial and industrial buildings. Empirical equations suitable for both new and existing panels are proposed and compared with the design equations given in Eurocode 8 and ASCE 7. The paper also considers the effects of the development of plastic hinges at the column base and of the roof flexibility on the load demand in panel‐to‐column connections. The roof flexibility may generate the torsion of the panels; consequently, an analytical procedure to account for such effects is proposed. Finally, general design recommendations are made.     

Surveyed and modelled one‐year morphodynamics in the braided lower Tana River

Field measurements and morphodynamic simulations were carried out along a 5‐km reach of the sandy, braided, lower Tana River in order to detect temporal and spatial variations in river bed modifications and to determine the relative importance of different magnitude discharges on river bed and braid channel evolution during a time span of one year, i.e. 2008–2009. Fulfilling these aims required testing the morphodynamic model's capability to simulate changes in the braided reach. We performed the simulations using a 2‐D morphodynamic model and different transport equations. The survey showed that more deposition than erosion occurred during 2008–2009. Continuous bed‐load transport and bed elevation changes of ±1 m, and a 70–188‐m downstream migration of the thalweg occurred. Simulation results indicated that, during low water periods, modifications occurred in both the main channel and in other braid channels. Thus, unlike some gravel‐bed rivers, the sandy lower Tana River does not behave like a single‐thread channel at low discharge. However, at higher discharge, i.e. exceeding 497 m³/s, the river channel resembled a single‐thread channel when channel banks confined the flow. Although the spring discharge peaks caused more rapid modifications than slower flows, the cumulative volumetric changes of the low water period were greater. The importance of low water period flows for channel modifications is emphasized. Although the 2‐D model requires further improvements, the results were nevertheless promising for the future use of this approach in braided rivers. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessing the dye‐tracer correction factor for documenting the mean velocity of sheet flow over smooth and grassed surfaces

In the investigation of overland flow hydraulics, mean flow velocity (V) is frequently estimated using the measured surface flow velocity (Vs) multiplied by a correction factor, α. In total, 291 tests were performed in a flume with three beds [smooth glass (GL), sandpaper (SD), and plastic grass (GR)] to investigate α under submerged and non‐submerged flows, and Vs was observed using dye‐tracer method whilst V was calculated by the measured water depth and flow rate. For GL with 5.2% slope and 100 < Re < 5000 [Reynolds number (Re)], α ranged from 0.35 to 0.79, with an average of 0.54. For SD with slopes ranging from 2.6% to 25.9% and 300 < Re < 1200, α varied from 0.18 to 0.48 with an average of 0.32. Raindrop impacts decreased α for GL at 5.2% slope, but the effect diminished for SD as the slope increased. The α‐values less than the theoretical value of 0.67 in laminar flows may be attributed to the greater spatial variability in overland flow compared with channel flow. For GR with non‐submerged flows and Re < 4200, α varied inversely with sediment concentration (SC) at 5.2% slope but was only slightly related to SC at steep slopes of 15.6% and 25.9%. The α‐values were approximately 0.8 for turbulent flows and even greater than 1.0 under high flow discharges. This finding may relate to sheet flow disturbance and retarded surface velocity due to the protruding scattered grass stems. For each surface, α varied positively with Re; α was inversely related to slope for SD but positively related to slope for GR. There was a positive relation between h and α for GL and SD but a negative relation for GR, which highlights the importance of flow inundation status to α. The inundation ratio (h/Δ) is a promising indicator for predicting α; thus, further investigations using different submerged and non‐submerged surfaces are required to predict α effectively based on (h/Δ). Copyright © 2015 John Wiley & Sons, Ltd.     

Micro X‐Ray computed tomography imaging and ultrasonic velocity measurements in tetrahydrofuran‐hydrate‐bearing sediments

Naturally occurring gas hydrates contain significant amounts of natural gas that might be produced as an energy resource in the foreseeable future. Thus, it is necessary to understand the pore‐space characteristics of hydrate reservoirs, particularly the pore‐scale distribution of the hydrate and its interaction with the sediment. Four end‐member models for hydrate distribution in the pore space are pore filling, sediment‐frame component, envelope cementing, and contact cementing. The goal of this study is to compare the models with pore‐scale hydrate distributions obtained in laboratory‐formed hydrates. Our results verify hydrate pore‐scale distributions by direct, visual observations that were previously implied by indirect, elastic property measurements. Laboratory measurements were conducted using tetrahydrofuran as a guest molecule since tetrahydrofuran hydrate can be used as a proxy for naturally occurring hydrates. We performed micro X‐ray computed tomography to obtain information about the distribution of hydrate in the pore space of synthetic sediment (glass beads). We also made ultrasonic velocity measurements on the same samples. Micro X‐ray computed tomography images and ultrasonic velocity measurements both indicate that the tetrahydrofuran hydrate forms in the pore space with a part of the hydrate bridging the grains without touching the grain surfaces. These hydrate‐bearing sediments appear to follow a pore‐filling model with a portion of the hydrate becoming a load‐bearing part of the sediment frame.     

Effects of helical flow in one‐dimensional modelling of sediment distribution at river bifurcations

Complex flow processes at river bifurcations and the influence of the layout of a bifurcation make it difficult to predict sediment distribution over the downstream branches in case bedload transport dominates. In one‐dimensional models we need a nodal point relationship that prescribes the distribution of sediment over the downstream branches. We have identified which factors need to be included in such a relationship for the division of bedload transport at bifurcations. Next, irrotational flow theory for idealized geometries has been used to derive a simple physics‐based nodal point relationship that accounts for the effects of helical flow in the situation that a channel takes off under an angle from a straight main channel. This first step towards a complete nodal point relationship is applicable to bedload transport situations if the flow is clearly curved and if there is no pronounced bed topography. The relationship has been tested against data from a unique set of laboratory measurements, numerical data and data from a scale model of the Rhine bifurcation at Pannerden in the Netherlands. We find that the derived model yields a reasonable prediction of the sediment division over the downstream branches, and yields better predictions than the Wang et al. model for the situation considered. Considering the relative complexity and limited accuracy of the nodal point relationship for the effect of helical flow alone, however, we conclude thatderiving a practical physics‐based 1‐D relationship including all relevant processes is not feasible. We therefore recommend 2‐D or 3‐D modelling for all cases in general where morphological evolution depends on the division of bedload transport at bifurcations. Copyright © 2012 John Wiley & Sons, Ltd.     

Contaminant transport in one‐dimensional single fractured media: semi‐analytical solution for three‐member decay chain with pulse and Heaviside input sources

A semi‐analytical solution of the one‐dimensional transport for considering a three‐member decay chain in a single fracture with pulse and Heaviside input sources has been studied using the Laplace transform and its numerical inversion. The results reveal that breakthrough curves of dimensionless concentration for the decay chain of Np‐237, U‐233, and Th‐229 in the fracture can be well demonstrated in the temporal and spatial domains. The conditions with and without retardation effects are also compared. During the preliminary screening phase the solutions are suitable for performance assessment on radioactive waste disposal sites under a one‐dimensional single fracture condition. Copyright © 2007 John Wiley & Sons, Ltd.     

Cyclic testing of unreinforced masonry walls in two‐way bending

An experimental programme was conducted in which eight full‐scale unreinforced masonry walls were subjected to cyclic face loading using a system of airbags. Of the eight walls, six contained a window opening and four were subjected to vertical pre‐compression. Combined supports at the vertical and horizontal edges ensured that under face loading the walls underwent two‐way bending. The test walls were found to possess good post‐peak strength and displacement capacity as well as reasonable energy dissipation characteristics. Significant strength and stiffness degradation and non‐symmetry of strength in the positive and negative displacement directions were also evident. Discussion of the causes of the aforementioned trends and their implications towards the seismic response of masonry walls is provided. Copyright © 2006 John Wiley & Sons, Ltd.     

A robust approach to time‐to‐depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations

The problem of conversion from time‐migration velocity to an interval velocity in depth in the presence of lateral velocity variations can be reduced to solving a system of partial differential equations. In this paper, we formulate the problem as a non‐linear least‐squares optimization for seismic interval velocity and seek its solution iteratively. The input for the inversion is the Dix velocity, which also serves as an initial guess. The inversion gradually updates the interval velocity in order to account for lateral velocity variations that are neglected in the Dix inversion. The algorithm has a moderate cost thanks to regularization that speeds up convergence while ensuring a smooth output. The proposed method should be numerically robust compared to the previous approaches, which amount to extrapolation in depth monotonically. For a successful time‐to‐depth conversion, image‐ray caustics should be either nonexistent or excluded from the computational domain. The resulting velocity can be used in subsequent depth‐imaging model building. Both synthetic and field data examples demonstrate the applicability of the proposed approach.     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.