Migration velocity analysis using pre‐stack wave fields

Using both image and data domains to perform velocity inversion can help us resolve the long and short wavelength components of the velocity model, usually in that order. This translates to integrating migration velocity analysis into full waveform inversion. The migration velocity analysis part of the inversion often requires computing extended images, which is expensive when using conventional methods. As a result, we use pre‐stack wavefield (the double‐square‐root formulation) extrapolation, which includes the extended information (subsurface offsets) naturally, to make the process far more efficient and stable. The combination of the forward and adjoint pre‐stack wavefields provides us with update options that can be easily conditioned to improve convergence. We specifically use a modified differential semblance operator to split the extended image into a residual part for classic differential semblance operator updates and the image (Born) modelling part, which provides reflections for higher resolution information. In our implementation, we invert for the velocity and the image simultaneously through a dual objective function. Applications to synthetic examples demonstrate the features of the approach.     

Eliminating 3D pre‐stack migration artefacts by 6D filtering

State‐of‐the‐art 3D seismic acquisition geometries have poor sampling along at least one dimension. This results in coherent migration noise that always contaminates pre‐stack migrated data, including high‐fold surveys, if prior‐to‐migration interpolation was not applied. We present a method for effective noise suppression in migrated gathers, competing with data interpolation before pre‐stack migration. The proposed technique is based on a dip decomposition of common‐offset volumes and a semblance‐type measure computation via offset for all constant‐dip gathers. Thus the processing engages six dimensions: offset, inline, crossline, depth, inline dip, and crossline dip. To reduce computational costs, we apply a two‐pass (4D in each pass) noise suppression: inline processing and then crossline processing (or vice versa). Synthetic and real‐data examples verify that the technique preserves signal amplitudes, including amplitude‐versus‐offset dependence, and that faults are not smeared.     

Wave‐equation migration velocity analysis with time‐shift imaging

Wave‐equation migration velocity analysis is a technique designed to extract and update velocity information from migrated images. The velocity model is updated through the process of optimizing the coherence of images migrated with the known background velocity model. The capacity for handling multi‐pathing of the technique makes it appropriate in complex subsurface regions characterized by strong velocity variation. Wave‐equation migration velocity analysis operates by establishing a linear relation between a slowness perturbation and a corresponding image perturbation. The linear relationship and the corresponding linearized operator are derived from conventional extrapolation operators and the linearized operator inherits the main properties of frequency‐domain wavefield extrapolation. A key step in the implementation is to design an appropriate procedure for constructing an image perturbation relative to a reference image that represents the difference between the current image and a true, or more correct image of the subsurface geology. The target of the inversion is to minimize such an image perturbation by optimizing the velocity model. Using time‐shift common‐image gathers, one can characterize the imperfections of migrated images by defining the focusing error as the shift of the focus of reflections along the time‐shift axis. The focusing error is then transformed into an image perturbation by focusing analysis under the linear approximation. As the focusing error is caused by the incorrect velocity model, the resulting image perturbation can be considered as a mapping of the velocity model error in the image space. Such an approach for constructing the image perturbation is computationally efficient and simple to implement. The technique also provides a new alternative for using focusing information in wavefield‐based velocity model building. Synthetic examples demonstrate the successful application of our method to a layered model and a subsalt velocity update problem.     

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.     

双参数展开CRP叠加和速度分析方法研究

椭圆展开共反射点(CRP)方法可以获得比常规倾角时差校正(DMO)方法更近似的零偏移距时间剖面和相应CRP速度场.大量研究和实践证实,在非均质性较弱的地区,该方法取得的成果显著.但由于该方法没有考虑速度的横向变化和转换波等情况,当地下介质存在较强非均质性时,该方法不再准确,需要引进反映速度横向变化的双参数(上行波与下行波的平均速度和速度比)进行改进.本文详细推导了引入双参数后的叠加和速度分析算法,并通过数值模型和地震资料处理证实,修正后的算法可以更好地解决地质复杂地区速度建模和叠加成像问题.     

首都圈上地壳高精度三维P波速度模型——基于石油地震叠加速度和人工地震测深剖面

本文收集了首都圈地区40个测点的石油地震叠加速度资料,经常规处理后得到各测点下方速度随深度变化的曲线;对9条人工地震测深剖面的解释结果进行数字化处理获得各剖面下方离散的速度数据;应用上述资料和专业地质建模软件构建了首都圈地区(115.50°E—117.60°E,38.40°N—40.75°N)范围内上地壳高精度三维P波速度模型.结果表明:华北盆地为隆坳相间区,从东至西依次是黄骅坳陷、沧县隆起和冀中坳陷,上地壳速度结构十分复杂;结晶基底的埋深变化剧烈,冀中坳陷下最深处可达10 km,沿构造走向整体呈西南深、东北浅的趋势,沧县隆起下埋深约2～4 km,黄骅坳陷下最深处则达9 km,剧烈的基底起伏反映出盆地内部不同次级构造单元的差异沉降和中、新生代以来强烈的拉张构造运动.太行山、燕山隆起下的基底埋深较盆地区浅,体现出隆起区新生代以来的抬升构造运动.本文首次将石油地震叠加速度资料用于首都圈地壳速度模型的构建,与以往用人工地震测深资料得到的模型相比,本文结果对华北盆地复杂的上地壳结构刻画得更为细致.     

Exploratory analysis of statistical post‐processing methods for hydrological ensemble forecasts

Despite many recent improvements, ensemble forecast systems for streamflow often produce under‐dispersed predictive distributions. This situation is problematic for their operational use in water resources management. Many options exist for post‐processing of raw forecasts. However, most of these have been developed using meteorological variables such as temperature, which displays characteristics very different from streamflow. In addition, streamflow data series are often very short or contain numerous gaps, thus compromising the estimation of post‐processing statistical parameters. For operational use, a post‐processing method has to be effective while remaining as simple as possible. We compared existing post‐processing methods using normally distributed and gamma‐distributed synthetic datasets. To reflect situations encountered with ensemble forecasts of daily streamflow, four normal distribution parameterizations and six gamma distribution parameterizations were used. Three kernel‐based approaches were tested, namely, the ‘best member’ method and two improvements thereof, and one regression‐based approach. Additional tests were performed to assess the ability of post‐processing methods to cope with short calibration series, missing values or small numbers of ensemble members. We thus found that over‐dispersion is best corrected by the regression method, while under‐dispersion is best corrected by kernel‐based methods. This work also shows key limitations associated with short data series, missing values, asymmetry and bias. One of the improved best member methods required longer series for the estimation of post‐processing parameters, but if provided with adequate information, yielded the best improvement of the continuous ranked probability score. These results suggest guidelines for future studies involving real operational datasets. Copyright © 2014 John Wiley & Sons, Ltd.     

A methodology for regionalizing 3‐D effective porosity at watershed scale in crystalline aquifers

An innovative approach for regionalizing the 3‐D effective porosity field is presented and applied to two large, overexploited, and deeply weathered crystalline aquifers located in southern India. The method derives from earlier work on regionalizing a 2‐D effective porosity field in that part of an aquifer where the water table fluctuates, which is now extended over the entire aquifer using a 3‐D approach. A method based on geological and geophysical surveys has also been developed for mapping the weathering profile layers (saprolite and fractured layers). The method for regionalizing 3‐D effective porosity combines water table fluctuation and groundwater budget techniques at various cell sizes with the use of satellite‐based data (for groundwater abstraction), the structure of the weathering profile, and geostatistical techniques. The approach is presented in detail for the Kudaliar watershed (983 km²) and tested on the 730 km² Anantapur watershed. At watershed scale, the effective porosity of the aquifer ranges from 0.5% to 2% in Kudaliar and between 0.3% and 1% in Anantapur, which agrees with earlier works. Results show that (a) depending on the geology and on the structure of the weathering profile, the vertical distribution of effective porosity can be very different and that the fractured layers in crystalline aquifers are not necessarily characterized by a rapid decrease in effective porosity and (b) that the lateral variations in effective porosity can be larger than the vertical ones. These variations suggest that within a same weathering profile, the density of open fractures and/or degree of weathering in the fractured zone may significantly vary from a place to another. The proposed method provides information on the spatial distribution of effective porosity that is of prime interest in terms of flux and contaminant transport in crystalline aquifers. Implications for mapping groundwater storage and scarcity are also discussed, which should help in improving groundwater resource management strategies.     

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks, which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block, and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization, which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models. The damped least squares method is employed in seismic traveltime inversion, which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.     

Centralized semi‐active control of post‐tensioned steel frames

Centralized semi‐active control is a technique for controlling the whole structure using one main computer. Centralized control systems introduce better control for relatively short to medium high structures where the response of any story cannot be separated from the adjacent ones. In this paper, two centralized control approaches are proposed for controlling the seismic response of post‐tensioned (PT) steel frames. The first approach, the stiffness control approach, aims to alter the stiffness of the PT frame so that it avoids large dynamic amplifications due to earthquake excitations. The second approach, deformation regulation control approach, aims at redistributing the demand/strength ratio in order to provide a more uniform distribution of deformations over the height of the structure. The two control approaches were assessed through simulations of the earthquake response of semi‐actively and passively controlled six‐story post‐tensioned steel frames. The results showed that the stiffness control approach is efficient in reducing the frame deformations and internal forces. The deformation regulation control approach was found to be efficient in reducing the frame displacements and generating a more uniform distribution of the inter‐story drifts. These results indicate that centralized semi‐active control can be used to improve the seismic performance of post‐tensioned steel frames. Copyright © 2014 John Wiley & Sons, Ltd.     

Bank erosion in agricultural drainage networks: new challenges from structure‐from‐motion photogrammetry for post‐event analysis

Drainage channels are an integral part of agricultural landscapes, and their impact on catchment hydrology is strongly recognized. In cultivated and urbanized floodplains, channels have always played a key role in flood protection, land reclamation, and irrigation. Bank erosion is a critical issue in channels. Neglecting this process, especially during flood events, can result in underestimation of the risk in flood‐prone areas. The main aim of this work is to consider a low‐cost methodology for the analysis of bank erosion in agricultural drainage networks, and in particular for the estimation of the volumes of eroded and deposited material. A case study located in the Veneto floodplain was selected. The research is based on high‐resolution topographic data obtained by an emerging low‐cost photogrammetric method (structure‐from‐motion or SfM), and results are compared to terrestrial laser scanning (TLS) data. For the SfM analysis, extensive photosets were obtained using two standalone reflex digital cameras and an iPhone5® built‐in camera. Three digital elevation models (DEMs) were extracted at the resolution of 0.1 m using SfM and were compared with the ones derived by TLS. Using the different DEMs, the eroded areas were then identified using a feature extraction technique based on the topographic parameter Roughness Index (RI). DEMs derived from SfM were effective for both detecting erosion areas and estimating quantitatively the deposition and erosion volumes. Our results underlined how smartphones with high‐resolution built‐in cameras can be competitive instruments for obtaining suitable data for topography analysis and Earth surface monitoring. This methodology could be potentially very useful for farmers and/or technicians for post‐event field surveys to support flood risk management. Copyright © 2015 John Wiley & Sons, Ltd.     

Diffraction imaging of sub‐vertical fractures and karst with full‐resolution 3D Ground‐Penetrating Radar

Vertical fractures with openings of less than one centimetre and irregular karst cause abundant diffractions in Ground‐Penetrating Radar (GPR) records. GPR data acquired with half‐wavelength trace spacing are uninterpretable as they are dominated by spatially undersampled scattered energy. To evaluate the potential of high‐density 3D GPR diffraction imaging a 200 MHz survey with less than a quarter wavelength grid spacing (0.05 m × 0.1 m) was acquired at a fractured and karstified limestone quarry near the village of Cassis in Southern France. After 3D migration processing, diffraction apices line up in sub‐vertical fracture planes and cluster in locations of karstic dissolution features. The majority of karst is developed at intersections of two or more fractures and is limited in depth by a stratigraphic boundary. Such high‐resolution 3D GPR imaging offers an unprecedented internal view of a complex fractured carbonate reservoir model analogue. As seismic and GPR wave kinematics are similar, improvements in the imaging of steep fractures and irregular voids at the resolution limit can also be expected from high‐density seismic diffraction imaging.     

High‐accuracy practical spline‐based 3D and 2D integral transformations in potential‐field geophysics

Potential, potential field and potential‐field gradient data are supplemental to each other for resolving sources of interest in both exploration and solid Earth studies. We propose flexible high‐accuracy practical techniques to perform 3D and 2D integral transformations from potential field components to potential and from potential‐field gradient components to potential field components in the space domain using cubic B‐splines. The spline techniques are applicable to either uniform or non‐uniform rectangular grids for the 3D case, and applicable to either regular or irregular grids for the 2D case. The spline‐based indefinite integrations can be computed at any point in the computational domain. In our synthetic 3D gravity and magnetic transformation examples, we show that the spline techniques are substantially more accurate than the Fourier transform techniques, and demonstrate that harmonicity is confirmed substantially better for the spline method than the Fourier transform method and that spline‐based integration and differentiation are invertible. The cost of the increase in accuracy is an increase in computing time. Our real data examples of 3D transformations show that the spline‐based results agree substantially better or better with the observed data than do the Fourier‐based results. The spline techniques would therefore be very useful for data quality control through comparisons of the computed and observed components. If certain desired components of the potential field or gradient data are not measured, they can be obtained using the spline‐based transformations as alternatives to the Fourier transform techniques.     

Quasi‐static and pseudo‐dynamic testing of unbonded post‐tensioned rocking bridge piers with external replaceable dissipaters

It has been well documented that following a major earthquake a substantial percentage of economic loss results from downtime of essential lifelines in and out of major urban centres. This has thus led to an improvement of both performance‐based seismic design philosophies and to the development of cost‐effective seismic structural systems capable of guaranteeing a high level of protection, low structural damage and reduced downtime after a design‐level seismic event. An example of such technology is the development of unbonded post‐tensioned techniques in combination with rocking–dissipating connections. In this contribution, further advances in the development of high‐performance seismic‐resistant bridge piers are achieved through the experimental validation of unbonded post‐tensioned bridge piers with external, fully replaceable, mild steel hysteretic dissipaters. The experimental response of three 1 : 3 scale unbonded, post‐tensioned cantilever bridge piers, subjected to quasi‐static and pseudo‐dynamic loading protocols, are presented and compared with an equivalently reinforced monolithic benchmark. Minimal physical damage is observed for the post‐tensioned systems, which exhibit very stable energy dissipation and re‐centring properties. Furthermore, the external dissipaters can be easily replaced if severely damaged under a major (higher than expected) earthquake event. Thus, negligible residual deformations, limited repair costs and downtime can be achieved for critical lifeline components. Satisfactory analytical–experimental comparisons are also presented as a further confirmation of the reliability of the design procedure and of the modelling techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Generalized diffraction‐stack migration and filtering of coherent noise

We reformulate the equation of reverse‐time migration so that it can be interpreted as summing data along a series of hyperbola‐like curves, each one representing a different type of event such as a reflection or multiple. This is a generalization of the familiar diffraction‐stack migration algorithm where the migration image at a point is computed by the sum of trace amplitudes along an appropriate hyperbola‐like curve. Instead of summing along the curve associated with the primary reflection, the sum is over all scattering events and so this method is named generalized diffraction‐stack migration. This formulation leads to filters that can be applied to the generalized diffraction‐stack migration operator to mitigate coherent migration artefacts due to, e.g., crosstalk and aliasing. Results with both synthetic and field data show that generalized diffraction‐stack migration images have fewer artefacts than those computed by the standard reverse‐time migration algorithm. The main drawback is that generalized diffraction‐stack migration is much more memory intensive and I/O limited than the standard reverse‐time migration method.     

Earthquake soil‐structure interaction of nuclear power plants,differences in response to 3‐D, 3 × 1‐D,and 1‐D excitations

In soil‐structure interaction modeling of systems subjected to earthquake motions, it is classically assumed that the incoming wave field, produced by an earthquake, is unidimensional and vertically propagating. This work explores the validity of this assumption by performing earthquake soil‐structure interaction modeling, including explicit modeling of sources, seismic wave propagation, site, and structure. The domain reduction method is used to couple seismic (near‐field) simulations with local soil‐structure interaction response. The response of a generic nuclear power plant model computed using full earthquake soil‐structure interaction simulations is compared with the current state‐of‐the‐art method of deconvolving in depth the (simulated) free‐field motions, recorded at the site of interest, and assuming that the earthquake wave field is spatially unidimensional. Results show that the 1‐D wave‐field assumption does not hold in general. It is shown that the way in which full 3‐D analysis results differ from those which assume a 1‐D wave field is dependent on fault‐to‐site geometry and motion frequency content. It is argued that this is especially important for certain classes of soil‐structure systems of which nuclear power plants subjected to near‐field earthquakes are an example.     

Gypsies in the palace: experimentalist's view on the use of 3‐D physics‐based simulation of hillslope hydrological response

As a fundamental unit of the landscape, hillslopes are studied for their retention and release of water and nutrients across a wide range of ecosystems. The understanding of these near‐surface processes is relevant to issues of runoff generation, groundwater–surface water interactions, catchment export of nutrients, dissolved organic carbon, contaminants (e.g. mercury) and ultimately surface water health. We develop a 3‐D physics‐based representation of the Panola Mountain Research Watershed experimental hillslope using the TOUGH2 sub‐surface flow and transport simulator. A recent investigation of sub‐surface flow within this experimental hillslope has generated important knowledge of threshold rainfall‐runoff response and its relation to patterns of transient water table development. This work has identified components of the 3‐D sub‐surface, such as bedrock topography, that contribute to changing connectivity in saturated zones and the generation of sub‐surface stormflow. Here, we test the ability of a 3‐D hillslope model (both calibrated and uncalibrated) to simulate forested hillslope rainfall‐runoff response and internal transient sub‐surface stormflow dynamics. We also provide a transparent illustration of physics‐based model development, issues of parameterization, examples of model rejection and usefulness of data types (e.g. runoff, mean soil moisture and transient water table depth) to the model enterprise. Our simulations show the inability of an uncalibrated model based on laboratory and field characterization of soil properties and topography to successfully simulate the integrated hydrological response or the distributed water table within the soil profile. Although not an uncommon result, the failure of the field‐based characterized model to represent system behaviour is an important challenge that continues to vex scientists at many scales. We focus our attention particularly on examining the influence of bedrock permeability, soil anisotropy and drainable porosity on the development of patterns of transient groundwater and sub‐surface flow. Internal dynamics of transient water table development prove to be essential in determining appropriate model parameterization. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

“Amount effect” of water isotopes and quantitative analysis of post‐condensation processes

A numerical model is proposed that describes the interaction between raindrops and water vapour near the planetary boundary layer to explain the “amount effect”. This model relates the intensity to the isotopic composition of precipitation. The model resolves raindrop sizes, and explicitly includes: (1) the isotopic equilibration time of raindrops that is drop‐size dependent; (2) raindrop transit times through the atmosphere; and (3) the evolution of the isotopic composition of vapour at various rain rates. At high rain rate, the precipitation through a layer is less equilibrated with the vapour because the isotopic equilibration time is long compared to the fast transit time, and there is a preponderance of large drops, which take longer to equilibrate. The δ¹⁸O of vapour in the lower atmosphere becomes lower as a result of the interaction with these raindrops of low δ¹⁸O, and the degree of depletion of ¹⁸O is higher when precipitation rates are high. The model reproduces time‐series observations of isotopic composition of precipitation in Japan, and a vapour replenishment rate is inferred by either advection or evaporation of about 5% of the precipitation rate. The results could be the basis for a new parameterization of the isotopic equilibration for different precipitation types and rates in General Circulation Models (GCMs). When the model is applied to a GCM, this parameterization is important for places where precipitation occurs at cold temperatures (<15 °C). Copyright © 2007 John Wiley & Sons, Ltd.     

Towards improved post‐processing of hydrologic forecast ensembles

Forecast ensembles of hydrological and hydrometeorologial variables are prone to various uncertainties arising from climatology, model structure and parameters, and initial conditions at the forecast date. Post‐processing methods are usually applied to adjust the mean and variance of the ensemble without any knowledge about the uncertainty sources. This study initially addresses the drawbacks of a commonly used statistical technique, quantile mapping (QM), in bias correction of hydrologic forecasts. Then, an auxiliary variable, the failure index (γ), is proposed to estimate the ineffectiveness of the post‐processing method based on the agreement of adjusted forecasts with corresponding observations during an analysis period prior to the forecast date. An alternative post‐processor based on copula functions is then introduced such that marginal distributions of observations and model simulations are combined to create a multivariate joint distribution. A set of 2500 hypothetical forecast ensembles with parametric marginal distributions of simulated and observed variables are post‐processed with both QM and the proposed multivariate post‐processor. Deterministic forecast skills show that the proposed copula‐based post‐processing is more effective than the QM method in improving the forecasts. It is found that the performance of QM is highly correlated with the failure index, unlike the multivariate post‐processor. In probabilistic metrics, the proposed multivariate post‐processor generally outperforms QM. Further evaluation of techniques is conducted for river flow forecast of Sprague River basin in southern Oregon. Results show that the multivariate post‐processor performs better than the QM technique; it reduces the ensemble spread and is a more reliable approach for improving the forecast. Copyright © 2012 John Wiley & Sons, Ltd.