Sparse Geometry Research Articles

Unified coprime array with multi-period subarrays for direction-of-arrival estimation

The original coprime array is a sparse geometry with a pair of one-period subarrays, where the interelement spacing and number of sensors are coprime so that no elements overlap except at the zeroth position. In this paper, we unify the coprime array by extending two subarrays from one period to multiple periods. Each subarray can have an arbitrary number of periods and therefore more than one element of the unified structure coincide. The resulting configuration treats the nested array as well as the existing coprime structures, such as the original coprime array, the extended one and the coprime array with compressed inter-element spacing (CACIS) as its special cases. The new coprime array has a lower peak side-lobe level than the nested array and the CACIS. An improved structure based on the multi-period coprime array is further proposed to improve the degrees-of-freedom (DOF) of the unified geometry with one of the subarrays displaced by a certain number of spacings. Although the improved configuration does not reach the same DOF as the CACIS and the coprime array with displaced subarrays (CADiS), it can acquire a low peak side-lobe level with the DOF not being decreased too much. Different from CADiS, we focus on the analysis and proper choice of the displacement to acquire more consecutive lags. The properties of coarray of the proposed array design strategy are provided as well. Finally, the direction-of-arrival estimation, physical aperture and peak side-lobe level performance of the unified structures are examined through numerical simulations.

Source deghosting by depth apparition

Marine seismic data are distorted by ghosts as waves propagating upward reflect downward from the sea surface. Ghosts appear on the source side and the receiver side. However, whereas the receiver-side ghost problem has been studied in detail, and many different solutions have been proposed and implemented commercially, the source-side ghost problem has remained largely unsolved with few satisfactory solutions available. We have developed a new and simple method to remove sea-surface ghosts that is related to the recently introduced concept of signal apparition. As opposed to the temporal/spatial source signature modulation functions used in the original signal apparition theory, our source deghosting method relies on using sources at different depths but not at the same lateral positions. The new method promises to be particularly suitable for 3D applications on sparse or incomplete acquisition geometries.

Moho imaging based on receiver function analysis with teleseismic wavefield reconstruction: Application to South China

A detailed and reliable Moho structure can improve our understanding of the tectonic evolution of crust and mantle. Most researchers directly interpolate the imaging results of receiver functions (RFs) from the sparse stations to obtain a continuous Moho image. However, the interpolation process is usually not robust because of the sparse and irregular geometry of seismic networks. In light of the approximate plane-wave feature of the teleseismic wavefront, we introduce the Radial Basis Function (RBF) technique, a high-precision interpolator with strong adaptability, into teleseismic wavefield reconstruction. Then, we use the reconstructed wavefield to image the Moho structure beneath South China with RF analysis. Compared to the conventional H-κ stacking methods, the Moho that is obtained through this reconstructed wavefield exhibits more details and shows greater consistency to the tectonic provinces. The Moho depths beneath South China gradually shallow from ~50km at the Yangtze Block (YB) in the northwest to ~25km to the southwest of the Cathaysia Block (CB). The Vp/Vs ratio at the YB is ~1.80, decreasing to ~1.57 at the Jiangnan Orogen, and then increasing to ~1.70 at the CB. Obviously varying Moho depths and Vp/Vs ratios in both the Ganjiang Fault (GF) and Tancheng-Lujiang Fault (TLF) regions is observed, which indicates a great similarity in the deep tectonic environment of the GF and TLF. The mantle corner flow under South China is suspected to invade into the interior of the Yangtze Craton. Teleseismic wavefield reconstruction, as a pre-processing technique, can effectively improve the imaging quality of RF analysis.

Rupture directivity of fluid‐induced microseismic events: Observations from an enhanced geothermal system

AbstractThe rupture process of fluid‐induced microseismic events is still poorly understood, mainly due to usually small magnitudes and sparse monitoring geometries. The high‐quality recordings of the earthquake sequence 2006–2007 at the enhanced geothermal system at Basel, Switzerland, constitute a rare exception, allowing a systematic directivity study of 195 events using the empirical Green's function method. We observe clear directivity signatures for about half the events which demonstrates that rupture directivity persists down to small magnitudes (ML∼1). The predominant rupture behavior is unilateral. We further find evidence that directivity is magnitude dependent and varies systematically with distance from the injection source. Whereas pore pressure seems to play the dominant role close to the injection source and no preferred rupture direction is observable, directivity aligns parallel to the event distribution with increasing distance ( m) and is preferably oriented away from the injection point. The largest analyzed events (ML∼2) show a distinct behavior: They rupture toward the injection source, suggesting that they nucleate in the vicinity of the pressure front and propagate backward into the perturbed volume. This finding is of particular relevance for seismic hazard assessment of georeservoirs, since it implies that maximum event size is related to dimension of the fluid‐perturbed volume. Our study also resolves rupture complexities for a small group of events. This shows that small fault heterogeneities exist down to a scale of a few tens of meters. The observation of directivity and complexity in induced microseismic events suggest that future source studies account for these phenomena.

Refractive 3D reconstruction on underwater images

Cameras can be considered measurement devices complementary to acoustic sensors when it comes to surveying marine environments. When calibrated and used correctly, these visual sensors are well-suited for automated detection, quantification, mapping, and monitoring applications and when aiming at high-accuracy 3D models or change detection. In underwater scenarios, cameras are often set up in pressure housings with a flat glass window, a flat port, which allows them to observe the environment. In this contribution, a geometric model for image formation is discussed that explicitly considers refraction at the interface under realistic assumptions like a slightly misaligned camera (w.r.t. the glass normal) and thick glass ports as common for deep sea applications. Then, starting from camera calibration, a complete, fully automated 3D reconstruction system is discussed that takes an image sequence and produces a 3D model. Newly derived refractive estimators for sparse two-view geometry, pose estimation, bundle adjustment, and dense depth estimation are discussed and evaluated in detail.

Innovative Processing Approaches to Overcome Sampling Sparseness and Irregularity in 3D OBC Seismic Data Offshore Abu Dhabi

Due mainly to commercial and operational constraints, seismic data are often sparsely and irregularly sampled, leading to several challenges in processing of 3D OBC seismic data offshore Abu Dhabi. Conventional linear noise attenuation techniques are not effective with Scholte waves as they are usually aliased with typical sampling interval in 3D OBC seismic data, and sometimes scattered because of near-surface heterogeneity. To address this, we apply model-based surface wave attenuation, Surface Wave Analysis Modeling and Inversion (SWAMI), which enables an estimate of local near-surface properties by analysing dispersion curves. Thus, both direct and scattered Scholte waves are effectively modelled and attenuated without suffering a lack of spatial sampling. We also highlight the shortcomings of the application of interferometry to scattered noise attenuation for sparse acquisition geometry. Matching Pursuit Fourier Interpolation (MPFI) is then implemented to deal with insufficient sampling in crossline direction caused by acquisition geometry. MPFI employs anti-aliasing capability so optimum data reconstruction can be performed for any frequency ranges. In addition to regularization aspect, MPFI with 5D implementation (4 spatial coordinates and time) is targeted to densify receiver line interval and extend source lines, which consequently enhances fold, offset and azimuth distributions of the data.

A Case for Regional Seismic Reflection Surveys in the Gawler Craton, South Australia

SUMMARY The seismic reflection method provides the possibility for delineation of very complex geological and this method might be good for detecting the presence of Iron Oxide Copper-Gold (IOCG) deposits. Despite many technically superior attributes, no arguments for regional seismic exploration have been proposed; probably because a cost-benefit analysis has never been conducted at such a scale. In this study we analyse such a case by modelling a Hillside IOCG deposit scenario where 2D seismic with relatively sparse source-receiver geometry is used to detect the presence of a possible intrusive package near a deep fault. The modelling results show that seismic reflection using 20m geophones and 40m shot spacing as an exploration tool is feasible, and that with the spacing halved we can definitely recover reasonable images of the upper parts of the mineralisation. The presences of such intrusives are clearly detectable and with the seismic method are detectable from 100m to 1000m deep. Thus, we propose that using 2D seismic is viable for IOCG exploration as it can detect mineralised intrusive structures along known favourable corridors or structures.

A feasibility and efficiency study of seismic waveform inversion for time-lapse monitoring of onshore CO2 geological storage sites using reflection seismic acquisition geometries

Monitoring of the CO2 distribution at depth is imperative for onshore geological storage of CO2. Seismic methods are effective monitoring tools during and after the injection process, but are generally expensive and time consuming to perform. In this paper we perform a series of synthetic experiments in order to compare the seismic waveform inversion method with conventional seismic monitoring methods for time-lapse monitoring at CO2 geological storage sites. We mainly focus our study on seismic data sets with typical reflection acquisition geometries that is far offset limited. Two synthetic seismic data sets (consisting of one baseline and repeat) were generated by a third party 2D forward modeling code to compare the waveform inversion method with a conventional time-lapse procedure. The velocity models are based on a simplified structure of the Heletz site in Israel. The area into which CO2 is injected is on the order of a few hundred meters wide and a few 10s of meters high. We compare the waveform inversion results and conventional time-lapse results to determine how sparse spatial sampling affects the results by increasing both the shot and receiver spacing. We test the waveform inversion method for a synthetic time-lapse data set with different inversion strategies. First, we invert each data set independently by using both phase and amplitude information. Then we invert them by using only phase information. We also test the influence of the starting model. Finally, we test the double difference inversion method which is equivalent to only inverting the difference between the baseline and repeat data sets. During the test a relative coarse starting model and higher starting frequency were used in order to better represent real seismic reflection data. Our results show that, under certain noise conditions, it may be possible to use a combination of sparse spatial sampling geometries and seismic waveform inversion to monitor the velocity changes caused by CO2 injection. We conclude that seismic waveform inversion may be a good complement to standard CDP processing when monitoring CO2 injection.

A Fast and Robust Framework for Semiautomatic and Automatic Registration of Photographs to 3D Geometry

We present a simple, fast, and robust complete framework for 2D/3D registration capable to align in a semiautomatic or completely automatic manner a large set of unordered images to a massive point cloud. Our method converts the hard to solve image-to-geometry registration task in a Structure-from-Motion (SfM) plus a 3D/3D alignment problem. We exploit a SfM framework that, starting just from an unordered image collection, computes an estimate of the camera parameters and a sparse 3D geometry deriving from matched image features. We then coarsely register this model to the given 3D geometry by estimating a global scale and absolute orientation using two solutions: a minimal user intervention or a stochastic global point set registration approach. A specialized sparse bundle adjustment (SBA) step, that exploits the correspondence between the sparse geometry and the fine input 3D model, is then used to refine intrinsic and extrinsic parameters of each camera. Output data is suitable for photo blending frameworks to produce seamless colored models. The effectiveness of the method is demonstrated on a series of synthetic and real-world 2D/3D Cultural Heritage datasets.

Converted‐wave beam migration with sparse sources or receivers

ABSTRACTGaussian 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.

An experimental study of the flow through and over two dimensional rectangular roughness elements: Deductions for urban boundary layer parameterizations and exchange processes

This paper investigates the flow through and over two-dimensional rectangular roughness elements, arranged in a building-street canyon geometry through a series of experiments. Geometries of different packing densities of the roughness elements (λp) were examined and the packing density values ranged from λp = 0.30 to 0.67. The purpose of the work is: (i) to investigate the flow physics observed both at the boundary layer scale as well as at the scale within the roughness elements for a range of packing densities, (ii) to deduce parameterizations of the adjusted rough boundary layer and their variation with a change in the packing density, and (iii) given a particular interest in and application to the urban atmosphere, a final aim at the roughness-element scale is to deduce the variation of the breathability with the packing density variation. Particle image velocimetery measurements of the velocity flow field as well as the turbulent kinetic energy and the Reynolds Stress (within and up to well-above the street canyons) were conducted. The results reveal qualitative flow features as well as features of the adjusted boundary layer structure—in particular the roughness and inertial sublayers, which can be associated with the surface roughness length, zero-plane displacement thickness, and the friction velocity. The lowest friction velocities are exhibited in the geometries with the highest- and lowest packing densities while the maximum friction velocities are observed in the medium-packed geometries. The exchange processes and breathability at the level of the roughness elements top were characterized and quantified by a mean exchange velocity. The results show that unlike friction velocity, the normalized exchange velocity (over the mean bulk velocity) for the most dense and sparse geometries differ by more than 80%, with the denser-packed geometries exhibiting lower exchange velocities; this is shown to be related with the thickness of the developed roughness sublayer.

Buoyant flexure and basal crevassing in dynamic mass loss at Helheim Glacier

Despite the role that calving plays in Greenland mass loss, the mechanisms of calving are poorly constrained. Observations of Greenland’s Helheim Glacier suggest that buoyant flexure at the glacier terminus leads to the propagation of basal crevasses and iceberg calving. Iceberg calving accounts for a significant proportion of annual mass loss from marine-terminating glaciers1,2 and may have been a factor in the rapid demise of ancient ice sheets3. The largest contributions from the main outlet glaciers of the Greenland ice sheet to sea-level rise over the next two centuries have been projected to be dynamic in origin, that is, driven by glacier flow and calving4. However, present physical models remain a coarse approximation of real calving mechanisms because models are poorly constrained by sparse glacier geometry observations5. Here we present a record of daily digital elevation models from the calving margin of Greenland’s Helheim Glacier at a high spatial resolution. Our digital elevation models are derived from stereo terrestrial photography taken over the summers of 2010 and 2011. We find that during these two summers dynamic mass loss at Helheim Glacier was dominated by calving events exceeding 1 km3 that were the result of buoyant flexure and the propagation of basal crevasses. We suggest that this buoyancy-driven mechanism for calving may be common elsewhere in Greenland and could be a first-order control on the ice sheet’s future contribution to sea-level rise.

The possibilities of compressed-sensing-based Kirchhoff prestack migration

An approximate subsurface reflectivity distribution of the earth is usually obtained through the migration process. However, conventional migration algorithms, including those based on the least-squares approach, yield structure descriptions that are slightly smeared and of low resolution caused by the common migration artifacts due to limited aperture, coarse sampling, band-limited source, and low subsurface illumination. To alleviate this problem, we use the fact that minimizing the L1-norm of a signal promotes its sparsity. Thus, we formulated the Kirchhoff migration problem as a compressed-sensing (CS) basis pursuit denoise problem to solve for highly focused migrated images compared with those obtained by standard and least-squares migration algorithms. The results of various subsurface reflectivity models revealed that solutions computed using the CS based migration provide a more accurate subsurface reflectivity location and amplitude. We applied the CS algorithm to image synthetic data from a fault model using dense and sparse acquisition geometries. Our results suggest that the proposed approach may still provide highly resolved images with a relatively small number of measurements. We also evaluated the robustness of the basis pursuit denoise algorithm in the presence of Gaussian random observational noise and in the case of imaging the recorded data with inaccurate migration velocities.

Analysing and modelling the performance of the HemeLB lattice-Boltzmann simulation environment

We investigate the performance of the HemeLB lattice-Boltzmann simulator for cerebrovascular blood flow, aimed at providing timely and clinically relevant assistance to neurosurgeons. HemeLB is optimised for sparse geometries, supports interactive use, and scales well to 32,768 cores for problems with ∼81 million lattice sites. We obtain a maximum performance of 29.5 billion site updates per second, with only an 11% slowdown for highly sparse problems (5% fluid fraction). We present steering and visualisation performance measurements and provide a model which allows users to predict the performance, thereby determining how to run simulations with maximum accuracy within time constraints.

Time-lapse analysis of sparse 3D seismic data from the CO2 storage pilot site at Ketzin, Germany

The Ketzin pilot site is the first European on-shore CO2 storage project site. Injection started in June 2008 and until the latest repeat survey in February 2011 around 45,000 t of CO2 had been injected into a saline aquifer at approximately 630 m depth. Seismic monitoring methods that have been applied at the Ketzin site comprise baseline and repeat observations at various scales. We present here time-lapse results from sparse 3D seismic data measurements at Ketzin, which were acquired to link downhole surveys with conventional 3D surface seismic surveys. The results are consistent with the 3D seismic time-lapse studies over the injection site and show that the sparse 3D geometry can be used to map the CO2 in the reservoir at a significantly lower effort than the conventional 3D surveying. The last repeat survey indicates preferential migration of the CO2 to the west. There are no indications of migration into the caprock on either of the repeat surveys.

Turbulent Transfer Between Street Canyons and the Overlying Atmospheric Boundary Layer

The turbulent exchange of momentum between a two-dimensional cavity and the overlying boundary layer has been studied experimentally, using hot-wire anemometry and particle image velocimetry (PIV). Conditions within the boundary layer were varied by changing the width of the canyons upstream of the test canyon, whilst maintaining the square geometry of the test canyon. The results show that turbulent transfer is due to the coupling between the instabilities generated in the shear layer above the canyons and the turbulent structures in the oncoming boundary layer. As a result, there is no single, unique velocity scale that correctly characterizes all the processes involved in the turbulent exchange of momentum across the boundary layer. Similarly, there is no single velocity scale that can characterize the different properties of the turbulent flow within the canyon, which depends strongly on the way in which turbulence from the outer flow is entrained into the cavity and carried round by the mean flow. The results from this study will be useful in developing simple parametrizations for momentum exchange in the urban canopy, in situations where the street geometry consists principally of relatively long, uniform streets arranged in grid-like patterns; they are unlikely to be applicable to sparse geometries composed of isolated three-dimensional obstacles.

Microscale Liquid Dynamics and the Effect on Macroscale Propagation in Pillar Arrays

Liquid dynamics in micropillar arrays have received significant fundamental interest and have offered opportunities for the development of advanced microfluidic, thermal management, and energy-harvesting devices. However, a comprehensive understanding of complex liquid behavior and the effect on macroscopic propagation rates in micropillar arrays is needed. In this work, we investigated the microscopic sweeping behavior of the liquid front along the spreading direction in micropillar arrays where the sweeping distance scales with the one-fifth power of time. We explain the scaling with a simplified model that captures the capillary pressure gradient at the liquid front. Furthermore, we show that such microscopic dynamics is the mechanism that decreases the macroscopic propagation rate. This effect is a result of the reduction in the interfacial energy difference used to generate the capillary pressure, which is explained with an energy-based model and corroborated with experiments. The results indicate the importance of accounting for the microscopic dynamics of the liquid on microstructured surfaces, particularly in sparse geometries.

3D symmetric sampling of sparse acquisition geometries

3D symmetric sampling introduced in the 1990s is characterized by dense sampling of two of the four spatial coordinates. The two sparsely sampled coordinates determine the periodicity of the geometry and the dimension of the offset-vector tiles that can be used to generate pseudocommon-offset-vector gathers. These gathers turn out to be useful for prestack processing applications, such as regularization, migration velocity analysis, and azimuthal anisotropy analysis. Although single-point acquisition is the ideal acquisition method, it is not necessarily better than array-based acquisition. Field arrays are still useful in suppressing noise and need not harm signal in most practical cases. In hybrid geometries three spatial coordinates are sampled densely. In all published cases at least two of the three are sampled quite coarsely and may not provide the best quality for the given trace density. Coil geometry (sailing in circles) is a special case of wide-azimuth towed streamer acquisition. It is essentially a random geometry that should be modifiable into a geometry with regularly sampled midpoints, absolute offsets and azimuths. Despite recent technological developments, the basic idea of 3D symmetric sampling still is a highly useful principle for the design of land and marine 3D seismic surveys.

Prestack depth imaging of ocean-bottom node data

Ocean-bottom node acquisitions provide high-quality data but usually have large distances between the nodes because of cost. This makes the use of conventional processing difficult and has led to relatively little interest in such data for industrial purposes. We have considered a three-step workflow specifically designed for prestack depth imaging of P-waves recorded by ocean-bottom nodes. It consists of multiple attenuation, velocity model estimation, and prestack depth migration. Whereas multiple attenuation and tomography use data in the common-receiver domain, migration is performed in the common-angle domain. One of the main features is the handling of the sparse receiver geometry during velocity model estimation: the reciprocity of the PP-Green’s functions is used to obtain the required tomographic input using only the common-receiver gathers. The tomographic method also provides an estimate of the geologic dip, which is used to limit the migration operator. This provides migrated images free of migration smiles. The workflow contains no additional assumptions compared to those used to process ocean-bottom cable data. We validate the workflow on a 2D line extracted from a 3D real data set acquired in the North Sea. The results show that it is possible to use ocean-bottom data efficiently for prestack depth imaging.

Application of compressive sampling to passive sonar signals.

Recently the compressive sampling (CS) paradigm has generated considerable interest in the signal processing community because it offers the potential to fully characterize signals without satisfying the Nyquist requirement (sampling frequency must be more than twice the highest frequency in the signal). Signal compression itself is not new; it is used in all file compression algorithms. However, it generally requires that all coefficients be generated, many or most of which are discarded and only a few are transmitted. The theoretical basis for CS has been presented in a number of signal processing and statistics journal articles [e.g., Candès and Wakin, IEEE SP (March 2008)]. CS is fixed (non-adaptive) and is efficient in that only the coefficients required for signal characterization are calculated. The key requirement of CS is to find a basis in which the signal representation is sparse and thus can be represented with a minimum number of coefficients. Here we explore possible benefits of applying CS to sonar signals, including signal compression, bandwidth reduction, and exploitation of sparse sampling geometries. [Work sponsored by ONR Undersea Signal Processing.]