τ-migration and velocity analysis: application to data from the Red Sea

Imaging pre‐salt reflections for data acquired from the coastal region of the Red Sea is a task that requires prestack migration velocity analysis. Conventional post‐stack time processing lacks the lateral inhomogeneity capability, necessary for such a problem. Prestack migration velocity analysis in the vertical time domain reduces the velocity–depth ambiguity that usually hampers the performance of prestack depth‐migration velocity analysis. In prestack τ‐migration velocity analysis, the interval velocity model and the output images are defined in τ (i.e. vertical time). As a result, we avoid placing reflectors at erroneous depths during the velocity analysis process and thus avoid inaccurately altering the shape of the velocity model, which in turn speeds up the convergence to the true model. Using a 1D velocity update scheme, the prestack τ‐migration velocity analysis produces good images of data from the Midyan region of the Red Sea. For the first seismic line from this region, only three prestack τ‐migration velocity analysis iterations were required to focus pre‐salt reflections in τ. However, the second line, which crosses the first line, is slightly more complicated and thus required five iterations to reach the final, reasonably focused, τ‐image. After mapping the images for the two crossing lines to depth, using the final velocity models, the placements of reflectors in the two 2D lines were consistent at their crossing point. Some errors occurred due to the influence of out‐of‐plane reflections on 2D imaging. However, such errors are identifiable and are generally small.     

Short‐term intertidal bar mobility on a ridge‐and‐runnel beach,Merlimont, northern France

Digital elevation models and topographic pro?les of a beach with intertidal bar and trough (ridge‐and‐runnel) morphology in Merlimont, northern France, were analysed in order to assess patterns of cross‐shore and longshore intertidal bar mobility. The beach exhibited a pronounced dual bar–trough system that showed cross‐shore stationarity. The bars and troughs were, however, characterized by signi?cant longshore advection of sand under the in?uence of suspension by waves and transport by strong tide‐ and wind‐driven longshore currents. Pro?le changes were due in part to the longshore migration of medium‐sized bedforms. The potential for cross‐shore bar migration appears to be mitigated by the large size of the two bars relative to incident wave energy, which is modulated by high vertical tidal excursion rates on this beach due to the large tidal range (mean spring tidal range = 8·3 m). Cross‐shore bar migration is also probably hindered by the well‐entrenched troughs which are maintained by channelled high‐energy intertidal ?ows generated by swash bores and by tidal discharge and drainage. The longshore migration of intertidal bars affecting Merlimont beach is embedded in a regional coastal sand transport pathway involving tidal and wind‐forced northward residual ?ows affecting the rectilinear northern French coast in the eastern English Channel. Copyright © 2004 John Wiley & Sons, Ltd.     

Converted‐wave beam migration with sparse sources or receivers

Gaussian beam depth migration overcomes the single‐wavefront limitation of most implementations of Kirchhoff migration and provides a cost‐effective alternative to full‐wavefield imaging methods such as reverse‐time migration. Common‐offset beam migration was originally derived to exploit symmetries available in marine towed‐streamer acquisition. However, sparse acquisition geometries, such as cross‐spread and ocean bottom, do not easily accommodate requirements for common‐offset, common‐azimuth (or common‐offset‐vector) migration. Seismic data interpolation or regularization can be used to mitigate this problem by forming well‐populated common‐offset‐vector volumes. This procedure is computationally intensive and can, in the case of converted‐wave imaging with sparse receivers, compromise the final image resolution. As an alternative, we introduce a common‐shot (or common‐receiver) beam migration implementation, which allows migration of datasets rich in azimuth, without any regularization pre‐processing required. Using analytic, synthetic, and field data examples, we demonstrate that converted‐wave imaging of ocean‐bottom‐node data benefits from this formulation, particularly in the shallow subsurface where regularization for common‐offset‐vector migration is both necessary and difficult.     

Implementation aspects of attenuation compensation in reverse‐time migration

Attenuation compensation in reverse‐time migration has been shown to improve the resolution of the seismic image. In this paper, three essential aspects of implementing attenuation compensation in reverse‐time migration are studied: the physical justification of attenuation compensation, the choice of imaging condition, and the choice of a low‐pass filter. The physical illustration of attenuation compensation supports the mathematical implementation by reversing the sign of the absorption operator and leaving the sign of the dispersion operator unchanged in the decoupled viscoacoustic wave equation. Further theoretical analysis shows that attenuation compensation in reverse‐time migration using the two imaging conditions (cross‐correlation and source‐normalized cross‐correlation) is able to effectively mitigate attenuation effects. In numerical experiments using a simple‐layered model, the source‐normalized cross‐correlation imaging condition may be preferable based on the criteria of amplitude corrections. The amplitude and phase recovery to some degree depend on the choice of a low‐pass filter. In an application to a realistic Marmousi model with added Q, high‐resolution seismic images with correct amplitude and kinematic phase are obtained by compensating for both absorption and dispersion effects. Compensating for absorption only can amplify the image amplitude but with a shifted phase.     

Cross‐hole resistivity tomography using different electrode configurations

This paper investigates the relative merits and effectiveness of cross‐hole resistivity tomography using different electrode configurations for four popular electrode arrays: pole–pole, pole–bipole, bipole–pole and bipole–bipole. By examination of two synthetic models (a dipping conductive strip and a dislocated fault), it is shown that besides the popular pole–pole array, some specified three‐ and four‐electrode configurations, such as pole–bipole AM–N, bipole–pole AM–B and bipole–bipole AM–BN with their multispacing cross‐hole profiling and scanning surveys, are useful for cross‐hole resistivity tomography. These configurations, compared with the pole–pole array, may reduce or eliminate the effect of remote electrodes (systematic error) and yield satisfactory images with 20% noise‐contaminated data. It is also shown that the configurations which have either both current electrodes or both potential electrodes in the same borehole, i.e. pole–bipole A–MN, bipole–pole AB–M and bipole–bipole AB–MN, have a singularity problem in data acquisition, namely low readings of the potential or potential difference in cross‐hole surveying, so that the data are easily obscured by background noise and yield images inferior to those from other configurations.     

Dynamics of intertidal drainage channels on a multi‐barred macrotidal beach

The intertidal drainage channels on a macrotidal bar–trough (ridge‐and‐runnel) beach were monitored during a 17‐day survey. Type 1 channels were persistent, dominantly longshore systems essentially limited to the wide intertidal zone between mean high and low water neap tidal levels. The cumulative length of this channel type fluctuated as a function of topographically controlled through‐flow or flow impedance in troughs, and showed no correlation with the semi‐lunar tidal cycle. Smaller, ephemeral type 2 channels appeared as dominantly cross‐shore systems incising bars on the narrower upper and lower beach zones during spring tides. They disappeared during neap tides through infill by waves and aeolian activity. The only significant phase of type 1 channel mobility occurred during a brief moderate‐energy storm at the start of the survey. The effect of this mobility on beach morphology was inextricably linked to that of waves and currents. Meander bend migration, forced by wave‐ and longshore‐current‐induced migration of a bar during the storm, resulted in important but highly localized morphological change that was only a minor part of an irregular saw‐tooth pattern of change that affected the entire beach profile, and that was largely controlled by wave processes and longshore currents. The flow velocities in channels on this beach are too weak to generate the formation and longshore migration of high‐energy bedforms. Channel mobility and impact on beach morphology are expected to increase under storm conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

Gabor‐frame‐based Gaussian packet migration

We present a Gaussian packet migration method based on Gabor frame decomposition and asymptotic propagation of Gaussian packets. A Gaussian packet has both Gaussian‐shaped time–frequency localization and space–direction localization. Its evolution can be obtained by ray tracing and dynamic ray tracing. In this paper, we first briefly review the concept of Gaussian packets. After discussing how initial parameters affect the shape of a Gaussian packet, we then propose two Gabor‐frame‐based Gaussian packet decomposition methods that can sparsely and accurately represent seismic data. One method is the dreamlet–Gaussian packet method. Dreamlets are physical wavelets defined on an observation plane and can represent seismic data efficiently in the local time–frequency space–wavenumber domain. After decomposition, dreamlet coefficients can be easily converted to the corresponding Gaussian packet coefficients. The other method is the Gabor‐frame Gaussian beam method. In this method, a local slant stack, which is widely used in Gaussian beam migration, is combined with the Gabor frame decomposition to obtain uniform sampled horizontal slowness for each local frequency. Based on these decomposition methods, we derive a poststack depth migration method through the summation of the backpropagated Gaussian packets and the application of the imaging condition. To demonstrate the Gaussian packet evolution and migration/imaging in complex models, we show several numerical examples. We first use the evolution of a single Gaussian packet in media with different complexities to show the accuracy of Gaussian packet propagation. Then we test the point source responses in smoothed varying velocity models to show the accuracy of Gaussian packet summation. Finally, using poststack synthetic data sets of a four‐layer model and the two‐dimensional SEG/EAGE model, we demonstrate the validity and accuracy of the migration method. Compared with the more accurate but more time‐consuming one‐way wave‐equation‐based migration, such as beamlet migration, the Gaussian packet method proposed in this paper can correctly image the major structures of the complex model, especially in subsalt areas, with much higher efficiency. This shows the application potential of Gaussian packet migration in complicated areas.     

Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.     

Multipathing in three‐parameter common‐image gathers from reverse‐time migration

Reverse‐time migration gives high‐quality, complete images by using full‐wave extrapolations. It is thus not subject to important limitations of other migrations that are based on high‐frequency or one‐way approximations. The cross‐correlation imaging condition in two‐dimensional pre‐stack reverse‐time migration of common‐source data explicitly sums the product of the (forward‐propagating) source and (backward‐propagating) receiver wavefields over all image times. The primary contribution at any image point travels a minimum‐time path that has only one (specular) reflection, and it usually corresponds to a local maximum amplitude. All other contributions at the same image point are various types of multipaths, including prismatic multi‐arrivals, free‐surface and internal multiples, converted waves, and all crosstalk noise, which are imaged at later times, and potentially create migration artefacts. A solution that facilitates inclusion of correctly imaged, non‐primary arrivals and removal of the related artefacts, is to save the depth versus incident angle slice at each image time (rather than automatically summing them). This results in a three‐parameter (incident angle, depth, and image time) common‐image volume that integrates, into a single unified representation, attributes that were previously computed by separate processes. The volume can be post‐processed by selecting any desired combination of primary and/or multipath data before stacking over image time. Separate images (with or without artifacts) and various projections can then be produced without having to remigrate the data, providing an efficient tool for optimization of migration images. A numerical example for a simple model shows how primary and prismatic multipath contributions merge into a single incident angle versus image time trajectory. A second example, using synthetic data from the Sigsbee2 model, shows that the contributions to subsalt images of primary and multipath (in this case, turning wave) reflections are different. The primary reflections contain most of the information in regions away from the salt, but both primary and multipath data contribute in the subsalt region.     

Variation in reach‐scale thalweg‐migration intensity in a braided reach of the lower Yellow River in 1986–2015

Thalweg migration of an alluvial river plays a key role in channel evolution, which may influence the effect of existing river training works and biodiversity on floodplains, and cause losses in riparian land and property. The braided reach of the Lower Yellow River underwent continuous channel aggradation during the period from 1986 to 1999, and then remarkable channel degradation in 1999–2015 owing to the state of operation of the Xiaolangdi Reservoir in 1999. Here we quantify associated thalweg migration changes and identify the key influencing factor in the braided reach. Thalweg‐migration distances and intensities at section‐ and reach‐scales were calculated during the past 30 years from 1986 to 2015, in order to investigate the characteristics of thalweg migration in the reach. There was a 47% reduction in the reach‐scale thalweg‐migration distance and a 35% reduction in the corresponding migration intensity after the reservoir operation. It is also revealed that fluvial erosion intensity is a dominant factor in controlling the thalweg migration, based on the investigation into various influencing factors in the study reach. The thalweg‐migration intensity of the braided reach can be expressed as a power function of the previous four‐year average fluvial erosion intensity. The calculated thalweg‐migration intensities in 1986–2015 using the proposed relation generally agree with the observed data. Copyright © 2017 John Wiley & Sons, Ltd.     

Double-square-root one-way wave equation prestack tau migration in heterogeneous media

In this paper, source‐receiver migration based on the double‐square‐root one‐way wave equation is modified to operate in the two‐way vertical traveltime (τ) domain. This tau migration method includes reasonable treatment for media with lateral inhomogeneity. It is implemented by recursive wavefield extrapolation with a frequency‐wavenumber domain phase shift in a constant background medium, followed by a phase correction in the frequency‐space domain, which accommodates moderate lateral velocity variations. More advanced τ‐domain double‐square‐root wave propagators have been conceptually discussed in this paper for migration in media with stronger lateral velocity variations. To address the problems that the full 3D double‐square‐root equation prestack tau migration could meet in practical applications, we present a method for downward continuing common‐azimuth data, which is based on a stationary‐phase approximation of the full 3D migration operator in the theoretical frame of prestack tau migration of cross‐line constant offset data. Migrations of synthetic data sets show that our tau migration approach has good performance in strong contrast media. The real data example demonstrates that common‐azimuth prestack tau migration has improved the delineation of the geological structures and stratigraphic configurations in a complex fault area. Prestack tau migration has some inherent robust characteristics usually associated with prestack time migration. It follows a velocity‐independent anti‐aliasing criterion that generally leads to reduction of the computation cost for typical vertical velocity variations. Moreover, this τ‐domain source‐receiver migration method has features that could be of help to speed up the convergence of the velocity estimation.     

Retrieval of super‐virtual refraction by cross‐correlation

Topography and severe variations of near‐surface layers lead to travel‐time perturbations for the events in seismic exploration. Usually, these perturbations could be estimated and eliminated by refraction technology. The virtual refraction method is a relatively new technique for retrieval of refraction information from seismic records contaminated by noise. Based on the virtual refraction, this paper proposes super‐virtual refraction interferometry by cross‐correlation to retrieve refraction wavefields by summing the cross‐correlation of raw refraction wavefields and virtual refraction wavefields over all receivers located outside the retrieved source and receiver pair. This method can enhance refraction signal gradually as the source–receiver offset decreases. For further enhancement of refracted waves, a scheme of hybrid virtual refraction wavefields is applied by stacking of correlation‐type and convolution‐type super‐virtual refractions. Our new method does not need any information about the near‐surface velocity model, which can solve the problem of directly unmeasured virtual refraction energy from the virtual source at the surface, and extend the acquisition aperture to its maximum extent in raw seismic records. It can also reduce random noise influence in raw seismic records effectively and improve refracted waves’ signal‐to‐noise ratio by a factor proportional to the square root of the number of receivers positioned at stationary‐phase points, based on the improvement of virtual refraction's signal‐to‐noise ratio. Using results from synthetic and field data, we show that our new method is effective to retrieve refraction information from raw seismic records and improve the accuracy of first‐arrival picks.     

Late Pleistocene–Holocene river dynamics at the Trent‐Soar confluence,England, UK

Although river confluences have received geomorphic attention in recent years it is difficult to upscale these studies, so confluence‐dominated reaches are commonly presumed to be either: (1) braided; or (2) meandering and characterized by laterally migrating channels. If the geomorphology of a confluence zone is to be considered over longer timescales, changes in river style need to be taken into account. This paper uses a combination of remote sensing techniques (LiDAR, GPR, ER), borehole survey and chronometric dating to test this differentiation in the confluence‐zone of a medium‐sized, mixed‐load, temperate river system (Trent, UK), which on the basis of planform evidence appears to conform to the meandering model. However, the analysis of ‘confluence sediment body stratigraphy’ demonstrates that the confluence does not correspond with a simple meander migration model and chronostratigraphic data suggests it has undergone two major transformations. Firstly, from a high‐energy braid‐plain confluence in the Lateglacial (25–13 K yrs cal BP), to a lower‐energy braided confluence in the early to middle Holocene (early Holocene‐2.4 kyr BP), which created a compound terrace. Second, incision into this terrace, creating a single‐channel confluence (2.4–0.5 kyr cal BP) with a high sinuosity south bank tributary (the River Soar). The confluence sediment‐body stratigraphy is characterized by a basal suite of Late Pleistocene gravels bisected by younger channel fills, which grade into the intervening levee and overbank sediments. The best explanation for the confluence sediment body stratigraphy encountered is that frequent switching (soft‐avulsions sensu Edmonds et al., 2011) of the tributary are responsible for the downstream movement of the channel confluence (at an average rate of approximately 0.5 m per year) dissecting and reworking older braid‐plain sediments. The late Holocene evolution of the confluence can be seen as a variant of the incisional‐frequent channel reorganization (avulsion) model with sequential downstream migration of the reattachment point. Copyright © 2012 John Wiley & Sons, Ltd.     

Two‐dimensional joint inversions of cross‐hole resistivity data and resolution analysis of combined arrays

In this study, a new two‐dimensional inversion algorithm was developed for the inversion of cross‐hole direct current resistivity measurements. In the last decades, various array optimisation methods were suggested for resistivity tomography. However, researchers have still collected data by using classical electrode arrays in most cross‐hole applications. Therefore, we investigated the accuracy of both the individual and the joint inversion of the classical cross‐hole arrays by using both synthetic and field data with the developed algorithm. We showed that the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole electrode arrays gives inverse solutions that are closer to the real model than the individual inversions of the electrode array datasets for the synthetic data inversion. The model resolution matrix of the suggested arrays was used to analyse the inversion results. This model resolution analysis also showed the advantage of the joint inversion of bipole–bipole, pole–bipole, bipole–pole, and pole–tripole arrays. We also used sensitivity sections from each of the arrays and their superpositions to explain why joint inversion gives better resolution than the any individual inversion result.     

Morphodynamics of a bedrock‐alluvial meander bend that incises as it migrates outward: approximate solution of permanent form

In meandering rivers cut into bedrock, erosion across a channel cross‐section can be strongly asymmetric. At a meander apex, deep undercutting of the outer bank can result in the formation of a hanging cliff (which may drive hillslope failure), whereas the inner bank adjoins a slip‐off slope that connects to the hillslope itself. Here we propose a physically‐based model for predicting channel planform migration and incision, point bar and slip‐off slope formation, bedrock abrasion, the spatial distribution of alluvial cover, and adaptation of channel width in a mixed bedrock‐alluvial channel. We simplify the analysis by considering a numerical model of steady, uniform bend flow satisfying cyclic boundary conditions. Thus in our analysis, ‘sediment supply’, i.e. the total volume of alluvium in the system, is conserved. In our numerical simulations, the migration rate of the outer bank is a specified parameter. Our simulations demonstrate the existence of an approximate state of dynamic equilibrium corresponding to a near‐solution of permanent form in which a bend of constant curvature, width, cross‐sectional shape and alluvial cover distribution migrates diagonally downward at constant speed, leaving a bedrock equivalent of a point bar on the inside of the bend. Channel width is set internally by the processes of migration and incision. We find that equilibrium width increases with increasing sediment supply, but is insensitive to outer bank migration rate. The slope of the bedrock point bar varies inversely with both outer bank migration rate and sediment supply. Although the migration rate of the outer bank is externally imposed here, we discuss a model modification that would allow lateral side‐wall abrasion to be treated in a manner similar to the process of bedrock incision. Copyright © 2016 John Wiley & Sons, Ltd.     

Point‐spread functions for interferometric imaging

Interferometric redatuming is a data‐driven method to transform seismic responses with sources at one level and receivers at a deeper level into virtual reflection data with both sources and receivers at the deeper level. Although this method has traditionally been applied by cross‐correlation, accurate redatuming through a heterogeneous overburden requires solving a multidimensional deconvolution problem. Input data can be obtained either by direct observation (for instance in a horizontal borehole), by modelling or by a novel iterative scheme that is currently being developed. The output of interferometric redatuming can be used for imaging below the redatuming level, resulting in a so‐called interferometric image. Internal multiples from above the redatuming level are eliminated during this process. In the past, we introduced point‐spread functions for interferometric redatuming by cross‐correlation. These point‐spread functions quantify distortions in the redatumed data, caused by internal multiple reflections in the overburden. In this paper, we define point‐spread functions for interferometric imaging to quantify these distortions in the image domain. These point‐spread functions are similar to conventional resolution functions for seismic migration but they contain additional information on the internal multiples in the overburden and they are partly data‐driven. We show how these point‐spread functions can be visualized to diagnose image defocusing and artefacts. Finally, we illustrate how point‐spread functions can also be defined for interferometric imaging with passive noise sources in the subsurface or with simultaneous‐source acquisition at the surface.     

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.     

Groundwater–surface water interaction in Lake Nasser,Southern Egypt

A cross‐sectional model, based on the two dimensional groundwater flow equation of Edelman, was applied at seven transects distributed over four geological cross sections to estimate groundwater heads and recharge from/or groundwater discharge to Lake Nasser. The lake with a length of 500 km and an average width of 12 km was created over the period 1964–1970, the time for constructing the Aswan High Dam (AHD). The model, constrained by regional‐scale groundwater flow and groundwater head data in the vicinity of the lake, was successfully calibrated to timeseries of piezometeric heads collected at the cross sections in the period 1965–2004. Inverse modeling yielded high values for the horizontal hydraulic conductivity in the range of 6.0 to 31.1 m day^?1 and storage coefficient between 0.01 and 0.40. The results showed the existence of a strong vertical anisotropy of the aquifer. The calibrated horizontal permeability is systematically higher than the vertical permeability (≈1000:1). The calibrated model was used to explore the recharge from/or groundwater discharge to Lake Nasser at the seven transects for a 40‐year period, i.e. from 1965 to 2004. The analysis for the last 20‐year period, 1985–2004, revealed that recharge from Lake Nasser reduced by 37% compared to the estimates for the first 20‐year period, 1965–1984. In the period 1965–2004, seepage of Lake Nasser to the surrounding was estimated at 1.15 × 10⁹ m³ year^?1. This led to a significant rise of the groundwater table. Variance‐based sensitivity and uncertainty analysis on the Edelman results were conducted applying quasi‐Monte Carlo sequences (Latin Hypercube sampling). The maximum standard deviation of the total uncertainty on the groundwater table was 0.88 m at Toshka (west of the lake). The distance from the lake, followed by the storage coefficient and hydraulic conductivity, were identified as the most sensitive parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Wavefield interpolation in 3D large‐step Fourier wavefield extrapolation

Extrapolating wavefields and imaging at each depth during three‐dimensional recursive wave‐equation migration is a time‐consuming endeavor. For efficiency, most commercial techniques extrapolate wavefields through thick slabs followed by wavefield interpolation within each thick slab. In this article, we develop this strategy by associating more efficient interpolators with a Fourier‐transform‐related wavefield extrapolation method. First, we formulate a three‐dimensional first‐order separation‐of‐variables screen propagator for large‐step wavefield extrapolation, which allows for wide‐angle propagations in highly contrasting media. This propagator significantly improves the performance of the split‐step Fourier method in dealing with significant lateral heterogeneities at the cost of only one more fast Fourier transform in each thick slab. We then extend the two‐dimensional Kirchhoff and Born–Kirchhoff local wavefield interpolators to three‐dimensional cases for each slab. The three‐dimensional Kirchhoff interpolator is based on the traditional Kirchhoff formula and applies to moderate lateral velocity variations, whereas the three‐dimensional Born–Kirchhoff interpolator is derived from the Lippmann–Schwinger integral equation under the Born approximation and is adapted to highly laterally varying media. Numerical examples on the three‐dimensional salt model of the Society of Exploration Geophysicists/European Association of Geoscientists demonstrate that three‐dimensional first‐order separation‐of‐variables screen propagator Born–Kirchhoff depth migration using thick‐slab wavefield extrapolation plus thin‐slab interpolation tolerates a considerable depth‐step size of up to 72 ms, eventually resulting in an efficiency improvement of nearly 80% without obvious loss of imaging accuracy. Although the proposed three‐dimensional interpolators are presented with one‐way Fourier extrapolation methods, they can be extended for applications to general migration methods.     

One‐dimensional and two‐dimensional hydrodynamic modeling derived flow properties: impacts on aquatic habitat quality predictions

Studies of the effects of hydrodynamic model dimensionality on simulated flow properties and derived quantities such as aquatic habitat quality are limited. It is important to close this knowledge gap especially now that entire river networks can be mapped at the microhabitat scale due to the advent of point‐cloud techniques. This study compares flow properties, such as depth and velocity, and aquatic habitat quality predicted from pseudo‐2D and fully 2D hydrodynamic modeling. The models are supported by high‐resolution, point‐cloud derived bathymetries, from which close‐spaced cross‐sections were extracted for the 1D modeling, of three morphologically and hydraulically different river systems. These systems range from small low‐gradient meandering pool–riffle to large steep confined plane‐bed rivers. We test the effects of 1D and 2D models on predicted hydraulic variables at cross‐sections and over the full bathymetry to quantify the differences due to model dimensionality and those from interpolation. Results show that streambed features, whose size is smaller than cross‐sectional spacing, chiefly determine the different results of 1D and 2D modeling whereas flow discharge, stream size, morphological complexity and model grid sizes have secondary effects on flow properties and habitat quality for a given species and life stage predicted from 1D and 2D modeling. In general, the differences in hydraulic variables are larger in the bathymetric than in the cross‐sectional analysis, which suggests that some errors are introduced from interpolation of spatially disaggregated simulated variables with a 1D model, instead of model dimensionality 1D or 2D. Flow property differences are larger for velocity than for water surface elevation and depth. Differences in weighted usable area (WUA) derived from 1D and 2D modeling are relatively small for low‐gradient meandering pool–riffle systems, but the differences in the spatial distribution of microhabitats can be considerable although clusters of same habitat quality are spatially comparable. Copyright © 2014 John Wiley & Sons, Ltd.