scholarly journals Image-domain wavefield tomography for VTI media

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. C119-C128 ◽  
Author(s):  
Vladimir Li ◽  
Antoine Guitton ◽  
Ilya Tsvankin ◽  
Tariq Alkhalifah
Keyword(s):  
P Wave ◽  
Ocean Bottom ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Data Set ◽  
Acoustic Image ◽  
Image Domain ◽  
Image Guided ◽  
Time Migration ◽  
The Impact

Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of [Formula: see text]-estimation. The impact of the trade-off between [Formula: see text] and [Formula: see text] is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of [Formula: see text]. Assuming that the depth profile of the Thomsen parameter [Formula: see text] is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and of the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters ([Formula: see text], [Formula: see text], and [Formula: see text]) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.

The impact of common‐offset migration on porosity estimation by AVO inversion

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 755-762 ◽  
Author(s):  
Arild Buland ◽  
Martin Landrø
Keyword(s):  
P Wave ◽  
High Porosity ◽  
S Wave ◽  
Seismic Line ◽  
Data Set ◽  
The North ◽  
Avo Inversion ◽  
Time Migration ◽  
The Impact ◽  
Porosity Estimation

The impact of prestack time migration on porosity estimation has been tested on a 2-D seismic line from the Valhall/Hod area in the North Sea. Porosity is estimated in the Cretaceous chalk section in a two‐step procedure. First, P-wave and S-wave velocity and density are estimated by amplitude variation with offset (AVO) inversion. These parameters are then linked to porosity through a petrophysical rock data base based on core plug analysis. The porosity is estimated both from unmigrated and prestack migrated seismic data. For the migrated data set, a standard prestack Kirchhoff time migration is used, followed by simple angle and amplitude corrections. Compared to modern high‐cost, true amplitude migration methods, this approach is faster and more practical. The test line is structurally fairly simple, with a maximum dip of 5°; but the results differ significantly, depending on whether migration is applied prior to the inversion. The maximum difference in estimated porosity is of the order of 10% (about 50% relative change). High‐porosity zones estimated from the unmigrated data were not present on the porosity section estimated from the migrated data.

3D acoustic least-squares reverse time migration using the energy norm

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. S261-S270 ◽  
Author(s):  
Daniel Rocha ◽  
Paul Sava ◽  
Antoine Guitton
Keyword(s):  
Least Squares ◽  
Convergence Rates ◽  
Energy Norm ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Image Domain ◽  
Time Migration ◽  
And Migration

We have developed a least-squares reverse time migration (LSRTM) method that uses an energy-based imaging condition to obtain faster convergence rates when compared with similar methods based on conventional imaging conditions. To achieve our goal, we also define a linearized modeling operator that is the proper adjoint of the energy migration operator. Our modeling and migration operators use spatial and temporal derivatives that attenuate imaging artifacts and deliver a better representation of the reflectivity and scattered wavefields. We applied the method to two Gulf of Mexico field data sets: a 2D towed-streamer benchmark data set and a 3D ocean-bottom node data set. We found LSRTM resolution improvement relative to RTM images, as well as the superior convergence rate obtained by the linearized modeling and migration operators based on the energy norm, coupled with inversion preconditioning using image-domain nonstationary matching filters.

Feasibility of nonhyperbolic moveout inversion in transversely isotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 957-969 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Vertical Velocity ◽  
Transverse Isotropy ◽  
Horizontal Velocity ◽  
P Wave ◽  
Vacuum Field ◽  
Percentage Error ◽  
Correlated Errors ◽  
Data Set ◽  
Time Migration ◽  
Quartic Term

Inversion of reflection traveltimes in anisotropic media can provide estimates of anisotropic coefficients required for seismic processing and lithology discrimination. Nonhyperbolic P-wave moveout for transverse isotropy with a vertical symmetry axis (VTI media) is controlled by the parameter η (or, alternatively, by the horizontal velocity Vhor), which is also responsible for the influence of anisotropy on all time‐processing steps, including dip‐moveout (DMO) correction and time migration. Here, we recast the nonhyperbolic moveout equation, originally developed by Tsvankin and Thomsen, as a function of Vhor and normal‐moveout (NMO) velocity Vnmo and introduce a correction factor in the denominator that increases the accuracy at intermediate offsets. Then we apply this equation to obtain Vhor and η from nonhyperbolic semblance analysis on long common midpoint (CMP) spreads and study the accuracy and stability of the inversion procedure. Our error analysis shows that the horizontal velocity becomes relatively well‐constrained by reflection traveltimes if the spreadlength exceeds twice the reflector depth. There is, however, a certain degree of tradeoff between Vhor and Vnmo caused by the interplay between the quadratic and quartic term of the moveout series. Since the errors in Vhor and Vnmo have opposite signs, the absolute error in the parameter η (which depends on the ratio Vhor/Vnmo) turns out to be at least two times bigger than the percentage error in Vhor. Therefore, the inverted value of η is highly sensitive to small correlated errors in reflection traveltimes, with moveout distortions on the order of 3–4 ms leading to errors in η up to ±0.1—even in the simplest model of a single VTI layer. Similar conclusions apply to vertically inhomogeneous media, in which the interval horizontal velocity can be obtained with an accuracy often comparable to that of the NMO velocity, while the interval values of η are distorted by the tradeoff between Vhor and Vnmo that gets amplified by the Dix‐type differentiation procedure. We applied nonhyperbolic semblance analysis to a walkaway VSP data set acquired at Vacuum field, New Mexico, and obtained a significant value of η = 0.19 indicative of nonnegligible anisotropy in this area. Then we combined moveout inversion results with the known vertical velocity to resolve the anisotropic coefficients ε and δ. However, in agreement with our modeling results, η estimation was significantly compounded by the scatter in the measured traveltimes. Certain instability in η inversion has no influence on the results of anisotropic poststack time migration because all kinematically equivalent models obtained from nonhyperbolic moveout give an adequate description of long‐spread reflection traveltimes. Also, inversion of nonhyperbolic moveout provides a relatively accurate horizontal‐velocity function that can be combined with the vertical velocity (if it is available) to estimate the anisotropic coefficient ε. However, η represents a valuable lithology indicator that can be obtained from surface P-wave data. Therefore, for purposes of lithology discrimination, it is preferable to find η by means of the more stable DMO method of Alkhalifah and Tsvankin.

Real-time monitoring of seismic moment and radiated energy

2020 ◽  
Author(s):  
Davide Scafidi ◽  
Daniele Spallarossa ◽  
Matteo Picozzi ◽  
Dino Bindi
Keyword(s):  
Real Time ◽  
Seismic Moment ◽  
P Wave ◽  
Calibration Data ◽  
S Wave ◽  
Data Set ◽  
Local Networks ◽  
Radiated Energy ◽  
The Impact ◽  
Large Earthquakes

<p>Understanding the dynamics of faulting is a crucial target in earthquake source physics (Yoo et al., 2010). To study earthquake dynamics it is indeed necessary to look at the source complexity from different perspectives; in this regard, useful information is provided by the seismic moment (M0), which is a static measure of the earthquake size, and the seismic radiated energy (ER), which is connected to the rupture kinematics and dynamics (e.g. Bormann & Di Giacomo 2011a). Studying spatial and temporal evolution of scaling relations between scaled energy (i.e., e = ER/M0) versus the static measure of source dimension (M0) can provide valuable indications for understanding the earthquake generation processes, single out precursors of stress concentrations, foreshocks and the nucleation of large earthquakes (Picozzi et al., 2019). In the last ten years, seismology has undergone a terrific development. Evolution in data telemetry opened the new research field of real-time seismology (Kanamori 2005), which targets are the rapid determination of earthquake location and size, the timely implementation of emergency plans and, under favourable conditions, earthquake early warning. On the other hand, the availability of denser and high quality seismic networks deployed near faults made possible to observe very large numbers of micro-to-small earthquakes, which is pushing the seismological community to look for novel big data analysis strategies. Large earthquakes in Italy have the peculiar characteristic of being followed within seconds to months by large aftershocks of magnitude similar to the initial quake or even larger, demonstrating the complexity of the Apennines’ faults system (Gentili and Giovanbattista, 2017). Picozzi et al. (2017) estimated the radiated seismic energy and seismic moment from P-wave signals for almost forty earthquakes with the largest magnitude of the 2016-2017 Central Italy seismic sequence. Focusing on S-wave signals recorded by local networks, Bindi et al. (2018) analysed more than 1400 earthquakes in the magnitude ranges 2.5 ≤ Mw ≤ 6.5 of the same region occurred from 2008 to 2017 and estimated both ER and M0, from which were derived the energy magnitude (Me) and Mw for investigating the impact of different magnitude scales on the aleatory variability associated with ground motion prediction equations. In this work, exploiting first steps made in this direction by Picozzi et al. (2017) and Bindi et al. (2018), we derived a novel approach for the real-time, robust estimation of seismic moment and radiated energy of small to large magnitude earthquakes recorded at local scales. In the first part of the work, we describe the procedure for extracting from the S-wave signals robust estimates of the peak displacement (PDS) and the cumulative squared velocity (IV2S). Then, exploiting a calibration data set of about 6000 earthquakes for which well-constrained M0 and theoretical ER values were available, we describe the calibration of empirical attenuation models. The coefficients and parameters obtained by calibration were then used for determining ER and M0 of a testing dataset</p>

Analysis of multiazimuthal VSP data for anisotropy and AVO

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1172-1180 ◽  
Author(s):  
W. Scott Leaney ◽  
Colin M. Sayers ◽  
Douglas E. Miller
Keyword(s):  
Fractured Reservoirs ◽  
Vertical Axis ◽  
Horizontal Stress ◽  
Azimuthal Anisotropy ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Fractured Reservoir ◽  
Data Set ◽  
Vsp Data ◽  
The Impact

Multioffset vertical seismic profile (VSP) experiments, commonly referred to as walkaways, enable anisotropy to be measured reliably in the field. The results can be fed into modeling programs to study the impact of anisotropy on velocity analysis, migration, and amplitude versus offset (AVO). Properly designed multioffset VSPs can also provide the target AVO response measured under optimum conditions, since the wavelet is recorded just above the reflectors of interest with minimal reflection point dispersal. In this paper, the multioffset VSP technique is extended to include multioffset azimuths, and a multiazimuthal multiple VSP data set acquired over a carbonate reservoir is analyzed for P-wave anisotropy and AVO. Direct arrival times down to the overlying shale and reflection times and amplitudes from the carbonate are analyzed. Data analysis involves a three‐term fit to account for nonhyperbolic moveout, dip, and azimuthal anisotropy. Results indicate that the overlying shale is transversely isotropic with a vertical axis of symmetry (VTI), while the carbonate shows 4–5% azimuthal anisotropy in traveltimes. The fast direction is consistent with the maximum horizontal stress orientation determined from break‐out logs and is also consistent with the strike of major faults. AVO analysis of the reflection from the top of the carbonate layer shows a critical angle reduction in the fast direction and maximum gradient in the slow direction. This agrees with modeling and indicates a greater amplitude sensitivity in the slow direction—the direction perpendicular to fracture strike. In principle, 3-D surveys should have wide azimuthal coverage to characterize fractured reservoirs. If this is not possible, it is important to have azimuthal line coverage in the minimum horizontal stress direction to optimize the use of AVO for fractured reservoir characterization. This direction can be obtained from multiazimuthal walkaways using the azimuthal P-wave analysis techniques presented.

Separating quasi-P-wave in transversely isotropic media with a vertical symmetry axis by synthesized pressure applied to ocean-bottom seismic data elastic reverse time migration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. C295-C307 ◽  
Author(s):  
Pengfei Yu ◽  
Jianhua Geng ◽  
Chenlong Wang
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Ocean Bottom ◽  
Receiver Side ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Isotropic Media ◽  
Wave Imaging ◽  
Obs Data

Quasi-P (qP)-wavefield separation is a crucial step for elastic P-wave imaging in anisotropic media. It is, however, notoriously challenging to quickly and accurately obtain separated qP-wavefields. Based on the concepts of the trace of the stress tensor and the pressure fields defined in isotropic media, we have developed a new method to rapidly separate the qP-wave in a transversely isotropic medium with a vertical symmetry axis (VTI) by synthesized pressure from ocean-bottom seismic (OBS) data as a preprocessing step for elastic reverse time migration (ERTM). Another key aspect of OBS data elastic wave imaging is receiver-side 4C records back extrapolation. Recent studies have revealed that receiver-side tensorial extrapolation in isotropic media with ocean-bottom 4C records can sufficiently suppress nonphysical waves produced during receiver-side reverse time wavefield extrapolation. Similarly, the receiver-side 4C records tensorial extrapolation was extended to ERTM in VTI media in our studies. Combining a separated qP-wave by synthesizing pressure and receiver-side wavefield reverse time tensorial extrapolation with the crosscorrelation imaging condition, we have developed a robust, fast, flexible, and elastic imaging quality improved method in VTI media for OBS data.

Realistic weather conditions and removal of time-varying sea-surface effects: Application on ocean-bottom-cable data

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. V297-V315
Author(s):  
Elsa Cecconello ◽  
Walter Söllner
Keyword(s):  
Weather Conditions ◽  
Surface Effects ◽  
Sea Surface ◽  
Ocean Bottom ◽  
Time Varying ◽  
Theoretical Derivation ◽  
Data Set ◽  
Wave Heights ◽  
Sea Surface Effects ◽  
The Impact

In marine seismic acquisition, seismic reflections at the sea surface, such as sea-surface ghosts and multiples, affect the accuracy of the retrieved subsurface reflections and reduce the usable frequency bandwidth. These sea-surface effects tend to increase with the increasing roughness of the weather conditions. Consequently, processing techniques that neglect the roughness and time variation of the sea surface induce errors in the data that could compromise the validity of the final images and interpretations. We study the impact of time-varying rough sea surfaces using a modeling method derived from the Rayleigh reciprocity theorem for time-varying surfaces, and we analyze errors in the source-deghosting operation. We show that the source-deghosting limitations are weather dependent for data including sea-surface multiples: For calm sea states (wave heights below 1.25 m), the error made by the source-deghosting process is negligible; however, for rough seas (wave heights above 1.5 m), it becomes significant and blurs the deghosted image at the sea-surface multiple signals. To accurately remove all sea-surface effects from the seismic data, we simultaneously apply source-deghosting and multiple-removal operations to the same up-going wavefield. This procedure is shown to be weather independent based on our theoretical derivation and the synthetic results. Finally, this is tested on a 2D OBC data set. Comparing the proposed inversion to up-down deconvolution, we observe similar features in both wavefields: Source ghosts and sea-surface multiples seem to have been correctly removed from the data, and the inverted result indicates a slightly better resolution for deeper reflections.

scholarly journals Detecting a salt dome overhang with magnetotellurics: 3D inversion methodology and synthetic model studies

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. E251-E263 ◽  
Author(s):  
Anna Avdeeva ◽  
Dmitry Avdeev ◽  
Marion Jegen
Keyword(s):  
Laplace Operator ◽  
Salt Dome ◽  
Model Parameters ◽  
Inversion Algorithm ◽  
Data Set ◽  
Complementary Method ◽  
Model Studies ◽  
Spatial Gradients ◽  
The Laplace Operator ◽  
The Impact

Detecting a salt dome overhang is known to be problematic by seismic methods alone. We used magnetotellurics (MT) as a complementary method to seismics to investigate the detectability of a salt dome overhang. A comparison of MT responses for 3D synthetic salt models with and without overhang shows that MT is very sensitive to shallow salt structures and suggests that it should be possible to detect an overhang. To further investigate the resolution capability of MT for a salt dome overhang, we performed a 3D MT inversion study and investigated the impact of model parametrization and regularization. We showed that using the logarithms of the conductivities as model parameters is crucial for inverting data from resistive salt structures because, in this case, commonly used Tikhonov-type stabilizers work more equally for smoothing the resistive and conductive structures. The use of a logarithmic parametrization also accelerated the convergence and produced better inversion results. When the Laplace operator was used as a regularization functional, we still observed that the inversion algorithm allows spatial resistivity gradients. These spatial gradients are reduced if a regularization based on first derivatives in contrast to the Laplace operator is introduced. To demonstrate the favorable performance when logarithmic parametrization and gradient-based regularization are employed, we first inverted a data set simulated for a simple model of two adjacent blocks. Subsequently, we applied the code to a more realistic salt dome overhang detectability study. The results from the detectability study are encouraging and suggest that 3D MT inversion can be applied to decide whether the overhang is present in the shallow salt structure even in the case when only profile data are available. However, to resolve the overhang, a dense MT site coverage above the flanks of the salt dome is required.

scholarly journals Simultaneous time imaging, velocity estimation, and multiple suppression using local event slopes

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA65-WCA73 ◽  
Author(s):  
Dennis Cooke ◽  
Andrej Bóna ◽  
Benn Hansen
Keyword(s):  
Temporal Frequency ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Estimation ◽  
Data Set ◽  
Image Domain ◽  
Kirchhoff Migration ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Input Formula

Starting with the double-square-root equation we derive expressions for a velocity-independent prestack time migration and for the associated migration velocity. We then use that velocity to identify multiples and suppress them as part of the imaging step. To describe our algorithm, workflow, and products, we use the terms velocity-independent and oriented. While velocity-independent imaging does not require an input migration velocity, it does require input [Formula: see text]-values (also called local event slopes) measured in both the shot and receiver domains. There are many possible methods of calculating these required input [Formula: see text]-values, perhaps the simplest is to compute the ratio of instantaneous spatial frequency to instantaneous temporal frequency. Using a synthetic data set rich in multiples, we test the oriented algorithm and generate migrated prestack gathers, the oriented migration velocity field, and stacked migrations. We use oriented migration velocities for prestack multiple suppression. Without this multiple suppression step, the velocity-independent migration is inferior to a conventional Kirchhoff migration because the oriented migration will flatten primaries and multiples alike in the common image domain. With this multiple suppression step, the velocity-independent are very similar to a Kirchhoff migration generated using the known migration velocity of this test data set.

scholarly journals Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4C seismic data

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. S265-S284 ◽  
Author(s):  
Matteo Ravasi ◽  
Andrew Curtis
Keyword(s):  
Model Simulation ◽  
P Wave ◽  
Solid Boundary ◽  
Central Component ◽  
Ocean Bottom ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
True Time ◽  
Wavefield Extrapolation

A central component of imaging methods is receiver-side wavefield backpropagation or extrapolation in which the wavefield from a physical source scattered at any point in the subsurface is estimated from data recorded by receivers located near or at the Earth’s surface. Elastic reverse-time migration usually accomplishes wavefield extrapolation by simultaneous reversed-time ‘injection’ of the particle displacements (or velocities) recorded at each receiver location into a wavefield modeling code. Here, we formulate an exact integral expression based on reciprocity theory that uses a combination of velocity-stress recordings and quadrupole-dipole backpropagating sources, rather than the commonly used approximate formula involving only particle velocity data and dipole backpropagating sources. The latter approximation results in two types of nonphysical waves in the scattered wavefield estimate: First, each arrival contained in the data is injected upward and downward rather than unidirectionally as in the true time-reversed experiment; second, all injected energy emits compressional and shear propagating modes in the model simulation (e.g., if a recorded P-wave is injected, both P and S propagating waves result). These artifacts vanish if the exact wavefield extrapolation integral is used. Finally, we show that such a formula is suitable for extrapolation of ocean-bottom 4C data: Due to the fluid-solid boundary conditions at the seabed, the data recorded in standard surveys are sufficient to perform backpropagation using the exact equations. Synthetic examples provide numerical evidence of the importance of correcting such errors.

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