Interferometric imaging condition for wave-equation migration

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. S47-S61 ◽  
Author(s):  
Paul Sava ◽  
Oleg Poliannikov
Keyword(s):  
Large Scale ◽  
Wigner Distribution ◽  
Random Noise ◽  
Velocity Model ◽  
Distribution Functions ◽  
Small Scale ◽  
Interferometric Imaging ◽  
Imaging Data ◽  
Imaging Condition ◽  
Velocity Models

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component of the velocity model as a random function with local spatial correlations. Imaging data perturbed by such random variations is characterized by statistical instability, i.e., various wavefield components image at wrong locations that depend on the actual realization of the random model. Statistical stability can be achieved by preprocessing the reconstructed wavefields prior to the imaging condition. We use Wigner distribution functions to attenuate the random noise present in the reconstructed wavefields, parameterized as a function of image coordinates. Wavefield filtering using Wigner distribution functions and conventional imaging can be lumped together into a new form of imaging condition that we call an interferometric imaging condition because of its similarity to concepts from recent work on interferometry. The interferometric imaging condition can be formulated both for zero-offset and for multioffset data, leading to robust, efficient imaging procedures that effectively attenuate imaging artifacts caused by unknown velocity models.

Nonlinear velocity inversion by a two‐step Monte Carlo method.

Geophysics ◽  
1994 ◽  
Vol 59 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Side Jin ◽  
Raul Madariaga
Keyword(s):  
Monte Carlo ◽  
Velocity Model ◽  
Small Scale ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Ray Theory ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Reference Velocity

Seismic reflection data contain information on small‐scale impedance variations and a smooth reference velocity model. Given a reference velocity model, the reflectors can be obtained by linearized migration‐inversion. If the reference velocity is incorrect, the reflectors obtained by inverting different subsets of the data will be incoherent. We propose to use the coherency of these images to invert for the background velocity distribution. We have developed a two‐step iterative inversion method in which we separate the retrieval of small‐scale variations of the seismic velocity from the longer‐period reference velocity model. Given an initial background velocity model, we use a waveform misfit‐functional for the inversion of small‐scale velocity variations. For this linear step we use the linearized migration‐inversion method based on ray theory that we have recently developed with Lambaré and Virieux. The reference velocity model is then updated by a Monte Carlo inversion method. For the nonlinear inversion of the velocity background, we introduce an objective functional that measures the coherency of the short wavelength components obtained by inverting different common shot gathers at the same locations. The nonlinear functional is calculated directly in migrated data space to avoid expensive numerical forward modeling by finite differences or ray theory. Our method is somewhat similar to an iterative migration velocity analysis, but we do an automatic search for relatively large‐scale 1-D reference velocity models. We apply the nonlinear inversion method to a marine data set from the North Sea and also show that nonlinear inversion can be applied to realistic scale data sets to obtain a laterally heterogeneous velocity model with a reasonable amount of computer time.

PS Energy Imaging Condition for Microseismic Data - Part 1: Theory and Applications in 3D Isotropic Media

Geophysics ◽  
2020 ◽  
pp. 1-79
Author(s):  
Can Oren ◽  
Jeffrey Shragge
Keyword(s):  
Wave Velocity ◽  
Model Building ◽  
Velocity Model ◽  
Microseismic Monitoring ◽  
Elastic Model ◽  
S Wave ◽  
Imaging Condition ◽  
Velocity Models ◽  
Monitoring Programs ◽  
Imaging Conditions

Accurately estimating event locations is of significant importance in microseismic investigations because this information greatly contributes to the overall success of hydraulic fracturing monitoring programs. Full-wavefield time-reverse imaging (TRI) using one or more wave-equation imaging conditions offers an effective methodology for locating surface-recorded microseismic events. To be most beneficial in microseismic monitoring programs, though, the TRI procedure requires using accurate subsurface models that account for elastic media effects. We develop a novel microseismic (extended) PS energy imaging condition that explicitly incorporates the stiffness tensor and exhibits heightened sensitivity to isotropic elastic model perturbations compared to existing imaging conditions. Numerical experiments demonstrate the sensitivity of microseismic TRI results to perturbations in P- and S-wave velocity models. Zero-lag and extended microseismic source images computed at selected subsurface locations yields useful information about 3D P- and S-wave velocity model accuracy. Thus, we assert that these image volumes potentially can serve as the input into microseismic elastic velocity model building algorithms.

Fast and accurate dynamic raytracing in heterogeneous media

1990 ◽  
Vol 80 (5) ◽  
pp. 1284-1296
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Shooting Method ◽  
Heterogeneous Media ◽  
Velocity Model ◽  
Travel Times ◽  
Complex Velocity ◽  
Geometrical Spreading ◽  
Imaging Condition ◽  
Depth Migration ◽  
Velocity Models ◽  
Complex Velocity Model

Abstract We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step. We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver. The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.

scholarly journals Corotation-driven magnetosphere-ionosphere coupling currents in Saturn’s magnetosphere and their relation to the auroras

2003 ◽  
Vol 21 (8) ◽  
pp. 1691-1707 ◽  
Author(s):  
S. W. H. Cowley ◽  
E. J. Bunce
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Equatorial Plane ◽  
Large Scale ◽  
Spatial Scales ◽  
Outer Boundary ◽  
Time Variability ◽  
Small Scale ◽  
Velocity Models ◽  
Field Aligned Current

Abstract. We calculate the latitude profile of the equatorward-directed ionospheric Pedersen currents that are driven in Saturn’s ionosphere by partial corotation of the magnetospheric plasma. The calculation incorporates the flattened figure of the planet, a model of Saturn’s magnetic field derived from spacecraft flyby data, and angular velocity models derived from Voyager plasma data. We also employ an effective height-integrated ionospheric Pedersen conductivity of 1 mho, suggested by a related analysis of Voyager magnetic field data. The Voyager plasma data suggest that on the largest spatial scales, the plasma angular velocity declines from near-rigid corotation with the planet in the inner magnetosphere, to values of about half of rigid corotation at the outer boundary of the region considered. The latter extends to ~ 15–20 Saturn radii (RS) in the equatorial plane, mapping along magnetic field lines to ~ 15° co-latitude in the ionosphere. We find in this case that the ionospheric Pedersen current peaks near the poleward (outer) boundary of this region, and falls toward zero over ~ 5°–10° equator-ward of the boundary as the plasma approaches rigid corotation. The peak current near the poleward boundary, integrated in azimuth, is ~ 6 MA. The field-aligned current required for continuity is directed out of the ionosphere into the magnetosphere essentially throughout the region, with the current density peaking at ~ 10 nA m-2 at ~ 20° co-latitude. We estimate that such current densities are well below the limit requiring field-aligned acceleration of magnetospheric electrons in Saturn’s environment ( ~ 70 nAm-2), so that no significant auroral features associated with this ring of upward current is anticipated. The observed ultraviolet auroras at Saturn are also found to occur significantly closer to the pole (at ~ 10°–15° co-latitude), and show considerable temporal and local time variability, contrary to expectations for corotation-related currents. We thus conclude that Saturn’s ‘main oval’ auroras are not associated with corotation-enforcing currents as they are at Jupiter, but instead are most probably associated with coupling to the solar wind as at Earth. At the same time, the Voyager flow observations also suggest the presence of radially localized ‘dips’ in the plasma angular velocity associated with the moons Dione and Rhea, which are ~ 1–2 RS in radial extent in the equatorial plane. The presence of such small-scale flow features, assumed to be azimuthally extended, results in localized several-MA enhancements in the ionospheric Pedersen current, and narrow bi-polar signatures in the field-aligned currents which peak at values an order of magnitude larger than those associated with the large-scale currents. Narrow auroral rings (or partial rings) ~ 0.25° co-latitude wide with intensities ~ 1 kiloRayleigh may be formed in the regions of upward field-aligned current under favourable circumstances, located at co-latitudes between ~ 17° and ~ 20° in the north, and ~ 19° and ~22° in the south.Key words. Magnetospheric physics (current systems; magnetosphere-ionosphere interactions; planetary magnetospheres)

scholarly journals Meta-matching: a simple framework to translate phenotypic predictive models from big to small data

2020 ◽  
Author(s):  
Tong He ◽  
Lijun An ◽  
Jiashi Feng ◽  
Danilo Bzdok ◽  
Avram J Holmes ◽  
...  
Keyword(s):  
Brain Imaging ◽  
Predictive Models ◽  
Large Scale ◽  
Prediction Performance ◽  
Small Sample ◽  
Small Scale ◽  
Small Data ◽  
Imaging Data ◽  
Resting State Functional Connectivity ◽  
Wide Range

AbstractThere is significant interest in using brain imaging data to predict non-brain-imaging phenotypes in individual participants. However, most prediction studies are underpowered, relying on less than a few hundred participants, leading to low reliability and inflated prediction performance. Yet, small sample sizes are unavoidable when studying clinical populations or addressing focused neuroscience questions. Here, we propose a simple framework – “meta-matching” – to translate predictive models from large-scale datasets to new unseen non-brain-imaging phenotypes in boutique studies. The key observation is that many large-scale datasets collect a wide range inter-correlated phenotypic measures. Therefore, a unique phenotype from a boutique study likely correlates with (but is not the same as) some phenotypes in some large-scale datasets. Meta-matching exploits these correlations to boost prediction in the boutique study. We applied meta-matching to the problem of predicting non-brain-imaging phenotypes using resting-state functional connectivity (RSFC). Using the UK Biobank (N = 36,848), we demonstrated that meta-matching can boost the prediction of new phenotypes in small independent datasets by 100% to 400% in many scenarios. When considering relative prediction performance, meta-matching significantly improved phenotypic prediction even in samples with 10 participants. When considering absolute prediction performance, meta-matching significantly improved phenotypic prediction when there were least 50 participants. With a growing number of large-scale population-level datasets collecting an increasing number of phenotypic measures, our results represent a lower bound on the potential of meta-matching to elevate small-scale boutique studies.

Common‐angle migration: A strategy for imaging complex media

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1877-1894 ◽  
Author(s):  
Sheng Xu ◽  
Hervé Chauris ◽  
Gilles Lambaré ◽  
Mark Noble
Keyword(s):  
A Priori ◽  
Velocity Model ◽  
Complex Velocity ◽  
Data Set ◽  
Depth Imaging ◽  
Imaging Condition ◽  
Velocity Models ◽  
Inversion Operator ◽  
Single Fold ◽  
Lateral Variations

Complex velocity models characterized by strong lateral variations are certainly a great motivation, but also a great challenge, for depth imaging. In this context, some unexpected results can occur when using depth imaging algorithms. In general, after a common shot or common offset migration, the resulting depth images are sorted into common‐image gathers (CIG), for further processing such as migration‐based velocity analysis or amplitude‐variation‐with‐offset analysis. In this paper, we show that CIGs calculated by common‐shot or common‐offset migration can be strongly affected by artifacts, even when a correct velocity model is used for the migration. The CIGs are simply not flat, due to unexpected curved events (kinematic artifacts) and strong lateral variations of the amplitude (dynamic artifacts). Kinematic artifacts do not depend on the migration algorithm provided it can take into account lateral variations of the velocity model. This can be observed when migrating the 2‐D Marmousi dataset either with a wave‐equation migration or with a multivalued Kirchhoff migration/inversion. On the contrary, dynamic artifacts are specific to multi‐arrival ray‐based migration/inversion. This approach, which should provide a quantitative estimation of the reflectivity of the model, provides in this context dramatic results. In this paper, we propose an analysis of these artifacts through the study of the ray‐based migration/inversion operator. The artifacts appear when migrating a single‐fold subdata set with multivalued ray fields. They are due to the ambiguous focusing of individual reflected events at different locations in the image. No information is a priori available in the single‐fold data set for selecting the focusing position, while migration of multifold data would provide this information and remove the artifacts by the stack of the CIGs. Analysis of the migration/inversion operator provides a physical condition, the imaging condition, for insuring artifact free CIGs. The specific cases of common‐shot and common‐offset single‐fold gathers are studied. It appears clearly that the imaging condition generally breaks down in complex velocity models for both these configurations. For artifact free CIGs, we propose a novel strategy: compute CIGs versus the diffracting/reflecting angle. Working in the angle domain seems the natural way for unfolding multivalued ray fields, and it can be demonstrated theoretically and practically that common‐angle imaging satisfies the imaging condition in the great majority of cases. Practically, the sorting into angle gathers can not be done a priori over the data set, but is done in the inner depth migration loop. Depth‐migrated images are obtained for each angle range. A canonical example is used for illustrating the theoretical derivations. Finally, an application to the Marmousi model is presented, demonstrating the relevance of the approach.

scholarly journals Using the SAL Technique for Spatial Verification of Cloud Processes: A Sensitivity Analysis

2016 ◽  
Vol 55 (9) ◽  
pp. 2091-2108 ◽  
Author(s):  
Michael Weniger ◽  
Petra Friederichs
Keyword(s):  
Large Scale ◽  
Threshold Level ◽  
Object Identification ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Spectral Radiance ◽  
Small Scale ◽  
Structure Amplitude ◽  
Cloud Data ◽  
Spatial Verification

AbstractThe feature-based spatial verification method named for its three score components: structure, amplitude, and location (SAL) is applied to cloud data, that is, two-dimensional spatial fields of total cloud cover and spectral radiance. Model output is obtained from the German-focused Consortium for Small-Scale Modeling (COSMO-DE) forward operator Synthetic Satellite Simulator (SynSat) and compared with SEVIRI satellite data. The aim of this study is twofold: first, to assess the applicability of SAL to this kind of data and, second, to analyze the role of external object identification algorithms (OIA) and the effects of observational uncertainties on the resulting scores. A comparison of three different OIA shows that the threshold level, which is a fundamental part of all studied algorithms, induces high sensitivity and unstable behavior of object-dependent SAL scores (i.e., even very small changes in parameter values lead to large changes in the resulting scores). An in-depth statistical analysis reveals significant effects on distributional quantities commonly used in the interpretation of SAL, for example, median and interquartile distance. Two sensitivity indicators that are based on the univariate cumulative distribution functions are derived. They make it possible to assess the sensitivity of the SAL scores to threshold-level changes without computationally expensive iterative calculations of SAL for various thresholds. The mathematical structure of these indicators connects the sensitivity of the SAL scores to parameter changes with the effect of observational uncertainties. Last, the discriminating power of SAL is studied. It is shown that—for large-scale cloud data—changes in the parameters may have larger effects on the object-dependent SAL scores (i.e., the S and L2 scores) than does a complete loss of temporal collocation.

Application of diffraction wavefront tomography to GPR data from a glacier

2020 ◽  
Author(s):  
Alexander Bauer ◽  
Benjamin Schwarz ◽  
Richard Delf ◽  
Dirk Gajewski
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
High Amplitude ◽  
Small Scale ◽  
Coherence Analysis ◽  
Raw Data ◽  
Seismic Reflection Data ◽  
Velocity Models ◽  
Passive Seismic ◽  
Zero Offset

<p>In the recent years, the diffracted wavefield has gained increasing attention in the field of applied seismics. While classical seismic imaging and inversion schemes mainly focus on high-amplitude reflected measurements, the faint and often masked diffracted wavefield is neglected or even treated as noise. In order to be able to extract depth-velocity models from seismic reflection data, sufficiently large source-receiver offsets are needed. However, the acquisition of such multi-channel seismic data is expensive and often only feasible for the hydrocarbon industry, while academia has to cope with low-fold or zero-offset data. The diffracted wavefield is the key for extracting depth velocities from such data, as the moveout of diffractions – in contrast to reflections – can be measured in the zero-offset domain. Recently, we have demonstrated on multi-channel, single-channel and passive seismic data that by means of wavefront tomography depth-velocity models can be retrieved solely based on diffractions or passive seismic events along with the localizations of these scatterers. The input for wavefront tomography are so-called wavefront attributes, which can be extracted from the data in an unsupervised fashion by means of coherence analysis. In order to obtain the required diffraction-only data, we use a recently proposed scheme that adaptively subtracts the high-amplitude reflected wavefield from the raw data. Due to their most common acquisition geometry, most ground-penetrating-radar (GPR) data inherently lack offsets. In addition, GPR data generally contain a rich diffracted wavefield, which in turn contains information about sought-after structures, as diffractions are caused by small-scale heterogeneities such as faults, tips or edges. In this work, we show an application of the suggested workflow – coherence analysis, diffraction separation and diffraction wavefront tomography – to GPR data acquired at a glacier, resulting in a depth-velocity model and the localizations of the scatterers, both obtained in a fully unsupervised fashion. While the resulting  velocity model may be used for depth migration of the raw data, the localizations of the scatterers may in addition provide important information on the inner structure of the glacier in order to, for instance, localize water intrusions or fractures.</p>

scholarly journals Inspiration for Seismic Diffraction Modelling, Separation, and Velocity in Depth Imaging

2020 ◽  
Vol 10 (12) ◽  
pp. 4391
Author(s):  
Yasir Bashir ◽  
Nordiana Mohd Muztaza ◽  
Seyed Yaser Moussavi Alashloo ◽  
Syed Haroon Ali ◽  
Deva Prasad Ghosh
Keyword(s):  
Travel Time ◽  
Seismic Data ◽  
Oil And Gas ◽  
Model Building ◽  
Research Work ◽  
Velocity Model ◽  
Small Scale ◽  
Velocity Models ◽  
Analysis Methods ◽  
Impedance Contrast

Fractured imaging is an important target for oil and gas exploration, as these images are heterogeneous and have contain low-impedance contrast, which indicate the complexity in a geological structure. These small-scale discontinuities, such as fractures and faults, present themselves in seismic data in the form of diffracted waves. Generally, seismic data contain both reflected and diffracted events because of the physical phenomena in the subsurface and due to the recording system. Seismic diffractions are produced once the acoustic impedance contrast appears, including faults, fractures, channels, rough edges of structures, and karst sections. In this study, a double square root (DSR) equation is used for modeling of the diffraction hyperbola with different velocities and depths of point diffraction to elaborate the diffraction hyperbolic pattern. Further, we study the diffraction separation methods and the effects of the velocity analysis methods (semblance vs. hybrid travel time) for velocity model building for imaging. As a proof of concept, we apply our research work on a steep dipping fault model, which demonstrates the possibility of separating seismic diffractions using dip frequency filtering (DFF) in the frequency–wavenumber (F-K) domain. The imaging is performed using two different velocity models, namely the semblance and hybrid travel time (HTT) analysis methods. The HTT method provides the optimum results for imaging of complex structures and imaging below shadow zones.

scholarly journals Observations of small-scale energetic events in the solar transition region: explosive events, UV bursts, and network jets

2019 ◽  
Vol 5 (2) ◽  
pp. 58-68 ◽  
Author(s):  
Хуан Чжэнхуа ◽  
Huang Zhenghua ◽  
Ли Бо ◽  
Li Bo ◽  
Ся Лидун ◽  
...  
Keyword(s):  
Transition Region ◽  
Solar Atmosphere ◽  
Large Scale ◽  
Small Scale ◽  
Solar Chromosphere ◽  
Imaging Data ◽  
Solar Transition Region ◽  
Solar Transition ◽  
Physical Mechanisms ◽  
Explosive Events

In this paper, we review observational aspects of three common small-scale energetic events in the solar transition region (TR), namely TR explosive events, ultraviolet bursts and jets. These events are defined in either (both) spectral or (and) imaging data. The development of multiple instruments capable of observing the TR has allowed researchers to gain numerous insights into these phenomena in recent years. These events have provided a proxy to study how mass and energy are transported between the solar chromosphere and the corona. As the physical mechanisms responsible for these small-scale events might be similar to the mechanisms responsible for large-scale phenomena, such as flares and coronal mass ejections, analysis of these events could also help our understanding of the solar atmosphere from small to large scales. The observations of these small-scale energetic events demonstrate that the TR is extremely dynamic and is a crucial layer in the solar atmosphere between the chromosphere and the corona.

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