Wavefield Migration Research Articles

An Accurate Propagator for Heterogeneous Media in Full Wavefield Migration

An Accurate Propagator for Heterogeneous Media in Full Wavefield Migration

First‐Order Transition in Appalachian Orogenic Processes Revealed by Along‐Strike Variation of the Moho Geometry

AbstractAlong‐strike variation of the Laurentian rifted margin and the Appalachian orogen has long been recognized in the geologic record. We investigated the manifestation of this along‐strike variation at depth by generating scattered wavefield migration profiles from four dense seismic arrays deployed across the Appalachian orogen at different latitudes. All profiles exhibit a similar crustal thickness decrease of 15–20 km from the Mesoproterozoic Grenville Province to the Paleozoic Appalachian accreted terranes, but the Moho architecture differs dramatically along strike. The profiles beneath the central and southern Appalachians show a smoothly varying Moho geometry; in contrast, there is an abrupt Moho depth offset beneath the New England Appalachians. This contrast in Moho geometry may result from variations in the Laurentian rifted margin architecture, changes in Taconic orogeny subduction polarity, and greater crustal shortening during the Acadian‐Neoacadian orogeny in southern New England and the Alleghanian orogeny in the central and southern Appalachians. A first‐order along‐strike transition in the behavior of Appalachian orogenic processes is located between the central and New England Appalachians.

Wavefield Migration Imaging of Moho Geometry and Upper Mantle Structure Beneath Southern New England

AbstractThe crust and upper mantle beneath the New England Appalachians exhibit a large offset of the Moho across the boundary between Laurentia and accreted terranes and several dipping discontinuities, which reflect Paleozoic or younger tectonic movements. We apply scattered wavefield migration to the SEISConn array deployed across northern Connecticut and obtain insights not previously available from receiver function studies. We resolve a doubled Moho at a previously imaged Moho offset, which may reflect westward thrusting of rifted Grenville crust. The migration image suggests laterally variable velocity contrasts across the Moho, perhaps reflecting mafic underplating during continental rifting. A west‐dipping feature in the lithospheric mantle is further constrained to have a slab‐like geometry, representing a relict slab subducted during an Appalachian orogenic event. Localized low seismic velocities in the upper mantle beneath the eastern portion of the array may indicate that the Northern Appalachian Anomaly extends relatively far to the south.

Local primary-and-multiple orthogonalization for leaked internal multiple crosstalk estimation and attenuation on full-wavefield migrated images

An important imaging challenge is creating reliable seismic images without internal multiple crosstalk, especially in cases with strong overburden reflectivity. Several data-driven methods have been proposed to attenuate the internal multiple crosstalk, for which fully sampled data in the source and receiver side are usually required. To overcome this acquisition constraint, model-driven full-wavefield migration (FWM) can automatically include internal multiples and only needs dense sampling in either the source or receiver side. In addition, FWM can correct for transmission effects at the reflecting interfaces. Although FWM has been shown to work effectively in compensating for transmission effects and suppressing internal multiple crosstalk compared to conventional least-squares primary wavefield migration (PWM), it tends to generate relatively weaker internal multiples during modeling. Therefore, some leaked internal multiple crosstalk can still be observed in the FWM image, which tends to blend in the background and can be misinterpreted as real geology. Thus, we adopted a novel framework using local primary-and-multiple orthogonalization (LPMO) on the FWM image as a postprocessing step for leaked internal multiple crosstalk estimation and attenuation. Due to their opposite correlation with the FWM image, a positive-only LPMO weight can be used to estimate the leaked internal multiple crosstalk, whereas a negative-only LPMO weight indicates the transmission effects that need to be retained. Application to North Sea field data validates the performance of the proposed framework for removing the weak but misleading leaked internal multiple crosstalk in the FWM image. Therefore, with this new framework, FWM can provide a reliable solution to the long-standing issue of imaging primaries and internal multiples automatically, with proper primary restoration.

Refraction wavefield migration

Refraction methods are often applied to model and image near-surface velocity structures. However, near-surface imaging is very challenging, and no single method can resolve all of the land seismic problems across the world. In addition, deep interfaces are difficult to image from land reflection data due to the associated low signal-to-noise ratio. Following previous research, we have developed a refraction wavefield migration method for imaging shallow and deep interfaces via interferometry. Our method includes two steps: converting refractions into virtual reflection gathers and then applying a prestack depth migration method to produce interface images from the virtual reflection gathers. With a regular recording offset of approximately 3 km, this approach produces an image of a shallow interface within the top 1 km. If the recording offset is very long, the refractions may follow a deep path, and the result may reveal a deep interface. We determine several factors that affect the imaging results using synthetics. We also apply the novel method to one data set with regular recording offsets and another with far offsets; both cases produce sharp images, which are further verified by conventional reflection imaging. This method can be applied as a promising imaging tool when handling practical cases involving data with excessively weak or missing reflections but available refractions.

A Kirchhoff migration imaging method based on grounded-source TEM virtual wave-fields and its applications

This research study was based on a Kirchhoff migration imaging method, and the aim of the study was to realize grounded-source transient electromagnetic virtual wave-field migration. Diffusion equations mainly characterize the induction characteristics of low-frequency electromagnetic waves which are not suitable for wave-fields. Wave equations mainly characterize wave reflections, refractions, and other propagation features, which are suitable for wave-field imaging processes. A unique mathematical transformation relationship exists between the diffusion fields of transient electromagnetic fields and seismic wave-fields. After the transformations from diffusion fields to virtual wave-fields are achieved, seismic interpretation methods can be used for the transient electromagnetic data interpretations. First, in order to realize Kirchhoff migration imaging based on transient electromagnetic wave-fields, precondition regularization methods are used for the wave-field inverse transformations. Then, after obtaining the wave-field data, dynamic correction methods are adopted to convert the grounded-source transient electromagnetic virtual wave-fields to quasi-seismic zero offset data. At that point, a Kirchhoff integral can be applied to realize the grounded-source transient electromagnetic quasi-seismic migration imaging. A theoretical model was used to test the method which was proposed in this study. The results showed that the Kirchhoff migration imaging was able to determine the geometric formations of underground dielectric interfaces, which fully demonstrated the applicability of the proposed method. Finally, migration imaging processing was performed on the data obtained from a mining area, and the imaging results were found to be consistent with the known geological data. Therefore, the feasibility of using a wave-field transform method and Kirchhoff migration imaging technology for grounded-source transient electromagnetic data interpretations was successfully confirmed.

3D radar wavefield migration of comet interiors

Imaging the interior structure of small planetary bodies facilitates a deep understanding of their origin and evolution, thus addressing fundamental questions about the formation of the Solar System. We show that high resolution 3D imaging of their interior structure is possible using radar waves that reflect from internal discontinuities of dielectric properties. A radar imaging mission at a comet nucleus would have the benefit of orbiting all around a finite and transparent body, collecting echoes that derive only from the target, and processing them collectively in phase.As is the case in the medical field, imaging a comet nucleus requires its illumination from multiple directions, which can be accomplished with a spacecraft in slow polar orbit around the studied object. Long acquisition time leads to a dense acquisition array resembling that of conventional synthetic aperture radar systems, but completely surrounding the nucleus (4π steradians). Acquisition with an orbiter at large distance from the comet nucleus (5× the mean diameter) results in relatively coarse data sampling relative to the radar wavelength, thus enabling 3D imaging with a short (<90 days) mission.Radar migration is performed using techniques adapted from terrestrial exploration seismology. Wavefield migration identifies interior reflectors by time reversal of monostatic radar data redatumed to the known comet surface for computational speed-up. This technique is applicable to nuclei of arbitrary shape and interior complexity, and it is complementary to wavefield tomography tasked with constraining physical properties in-between the interior interfaces. Migration resolution is identical in all directions (range and cross-range) and it is equivalent to the range resolution of the radar system. Least-squares migration enhances resolution further by deconvolution of the radar wavelet from the reflectivity image.

Imaging a Crustal Low‐Velocity Layer Using Reflected Seismic Waves From the 2014 Earthquake Swarm at Long Valley Caldera, California: The Magmatic System Roof?

AbstractThe waveforms generated by the 2014 Long Valley Caldera earthquake swarm recorded at station MLH show clear reflected waves that are often stronger than direct P and S waves. With waveform analyses, we discover that these waves are reflected at the top of a low‐velocity body, which may be residual magma from the ∼767 ka caldera‐forming eruption. The polarity of the reflection compared to direct P and S waves suggests that the reflection is SP waves (S from hypocenters to reflector and then convert to P waves to the surface). Because the wavefields are coherent among different earthquakes and hold high signal‐to‐noise ratios, we apply them to a wavefield migration method for imaging reflectors. The depth of the imaged magmatic system roof is around 8.2 km below the surface. This is consistent with previous studies. Even though we use only one station and waveforms from one earthquake swarm, the dense cluster of accurately located earthquakes provides a high‐resolution image of the roof.

Anisotropic elastic wavefield imaging using the energy norm

Based on the energy conservation principle, we derive a scalar imaging condition for anisotropic elastic wavefield migration. Compared with conventional imaging conditions that correlate displacement components or potentials from source and receiver wavefields, the proposed imaging condition does not suffer from polarity reversal, which degrades the image quality after stacking over shots. Our imaging condition also accounts for the directionality of the wavefields in space and time, leading to the attenuation of backscattering artifacts, which commonly appear in elastic reverse time migration images in the presence of strong model contrasts. In addition, our new imaging condition does not require wave-mode decomposition, which demands significant additional cost for elastic wavefields in anisotropic media. To properly image structures, we rely on the anisotropy parameters used in migration, as one would do for any other imaging condition. Our imaging condition is suitable for arbitrary anisotropy. We show the successful application of the anisotropic energy imaging condition by performing numerical experiments on simple and complex geologic models. We compare its quality with conventional counterparts by simulating complex geologic settings with vertical or tilted transverse isotropy.

Imaging crustal structure beneath the southern Appalachians with wavefield migration

AbstractTo constrain crustal structures in the southern Appalachians and the suture zone with the Gondwanan‐affinity Suwannee terrane, we applied the 2‐D generalized Radon transform wavefield migration method to the scattered incident P wavefield recorded by the EarthScope Southeastern Suture of the Appalachian Margin Experiment and adjacent Transportable Array stations. We resolve the root of thickened crust beneath the high topography of the Blue Ridge Mountains and estimate its density contrast with the mantle to be only 104 ± 20 kg/m3. A weak velocity contrast across the crustal root Moho is observed and may be related to an ongoing crustal delamination event, possibly contributing to local tectonic rejuvenation. Beneath the Suwannee terrane, we confirm prior observations of a gently south‐southeastward dipping crustal suture, indicating the terminal collision of Laurentia and Gondwana involved several hundred kilometers of overthrusting.

Utilization of multiple scattering: the next big step forward in seismic imaging

Surface removal and internal multiple removal are explained by recursively separating the primary and multiple responses at each depth level with the aid of wavefield prediction error filtering. This causal removal process is referred to as “data linearization.” The linearized output (primaries only) is suitable for linear migration algorithms. Next, a summary is given on the migration of full wavefields (primaries multiples) by using the concept of secondary sources in each subsurface gridpoint. These secondary sources are two-way and contain the gridpoint reflection and the gridpoint transmission properties. In full wavefield migration, a local inversion process replaces the traditional linear imaging conditions. Finally, Marchenko redatuming is explained by iteratively separating the full wavefield response from above a new datum and the full wavefield response from below a new datum. The redatuming output is available for linear migration (Marchenko imaging) or, even better, for full wavefield migration. Linear migration, full wavefield migration, and Marchenko imaging are compared with each other. The principal conclusion of this essay is that multiples should not be removed, but they should be utilized, yielding two major advantages: (i) illumination is enhanced, particularly in the situation of low signal-to-noise primaries; and (ii) both the upper side and the lower side of reflectors are imaged. It is also concluded that multiple scattering algorithms are more transparent if they are formulated in a recursive depth manner. In addition to transparency, a recursive depth algorithm has the flexibility to enrich the imaging process by inserting prior geological knowledge or by removing numerical artefacts at each depth level. Finally, it is concluded that nonlinear migration algorithms must have a closed-loop architecture to allow successful imaging of incomplete seismic data volumes (reality of field data).

Complete wavefield seismic structural, stratigraphic, geomorphic and elastic interpretation in the offshore Browse Basin

The first quantitative interpretation project in the Browse Basin that used complete wavefields from dual-sensor streamer data to characterise a variety of overburden and reservoir seismic structural, sedimentary and geomorphic features is discussed in this extended abstract. Having established that complete wavefield pre-stack angle data are amplitude versus angle (AVA) compliant, the authors analyse the elastic response from thin gas sands in a location where well control predicts a weak gas response in terms of the Vp/Vs ratio and negligible response in terms of the acoustic impedance. Various seismic expressions in the near-surface are better resolved using complete wavefield imaging, including deltaic deposits, potentially prospective patch reefs and intersecting channel systems, and shallow hazards associated with historic drilling failures appear to be resolvable with greater confidence. On the larger scale, the overall data interpretability is substantially enhanced in texture and character by broadband imaging of primary reflections, and then by subsequent reservoir characterisation. Initial (deeper) interpretation focused around mapping of the prospective Early Jurassic Plover Formation and the Early Cretaceous Upper Vulcan Formation, in which evidence of channelisation can be demonstrated on conventional migration volumes and reinforced using complete wavefield migration. Ultra-low frequency signal penetration to the deeper Triassic level has been limited historically, but the first complete seismic wavefield data analysis presented demonstrates that a combination of volume attributes provide substantially improved geologic information from the seafloor to the deepest targets.

Radio reflection imaging of asteroid and comet interiors II: Results and recommendations

We modeled orbital surface-penetrating radar of an asteroid and comet using two-dimensional finite-difference wavefield migration, in order to assess key target properties and experiment parameters required to fully image internal structure. Migration places radar echoes in their correct positions in a complex subsurface and is a complementary tool to travel-time tomography. The target shape was scaled from 433 Eros to 0.5-km mean diameter for an asteroid and 10km for a comet. The interiors were populated with a power-law distribution of spherical blocks. We used an image structural similarity index to compare the internal surfaces reconstructed under different assumptions to a “best” image using optimum parameters. We found that successful internal imaging of the asteroid was not sensitive to whether the block interstices were regolith or void. Frequency dependence between 5 and 15MHz was also minor. Internal interfaces could also be imaged if the attenuation was higher than that inferred within volcanic plains on Mars, but not as high as measured in a strongly fractured volcanic tuff on Earth. The overall imaging quality for the comet was statistically similar to the asteroid, but there was less variability due to smaller internal contrasts. A key finding is that imaging was vastly improved by using a second spacecraft as a radar receiver. A subsatellite with a different orbit will eventually provide a range of different illumination geometries over each part of the target. Finally, the results depend strongly on the specified internal velocity distribution, representing partial progress in complementary tomographic velocity estimation. The modeled impedance contrasts within the asteroid are larger than those typically encountered in exploration seismology and very much larger than in medical imaging, and so the velocity used to migrate the reflections must be close to the actual distribution. This again emphasizes the need for joint traveltime tomography and wavefield migration for asteroid imaging, which is optimized using two orbiters.

Review Paper: An outlook on the future of seismic imaging, Part III: Joint Migration Inversion

ABSTRACTThe next generation seismic imaging algorithms will consider multiple scattering as indispensable information, referred to as Full Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, referred to as Joint Migration Inversion. Full wavefield migration and joint migration inversion address the industrial needs of improving images of very complex reservoirs as well as the industry ambition of producing these images in a more automatic manner (‘automation in seismic processing’).In this vision paper on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed‐loop, estimation algorithm that can be physically explained by an iterative double focusing process (full wavefield Common‐Focus‐Point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (‘closing the loop’). For this purpose a full wavefield modelling module has been developed that utilizes an operator description of complex geology. Full wavefield modelling module is pre‐eminently suited to function in the feedback path of a closed‐loop migration algorithm.‘The Future of Seismic Imaging’ is presented as a coherent trilogy, proposing in three consecutive parts the migration framework of the future. In part I it was shown that the proposed full wavefield modelling module algorithm differs fundamentally from finite difference modelling, as velocities and densities need not be provided. Instead, full wavefield modelling module uses an operator description of the subsurface. In Part II it was shown how the theory of Primary Wavefield Migration can be extended to Full Wavefield Migration by correcting for elastic transmission effects and by utilizing multiple scattering. In Part III it is shown how the full wavefield migration technology can be extended to Joint Migration Inversion, allowing full wavefield migration of blended data without knowledge of the velocity. Velocities are part of the joint migration inversion output, being obtained by an operator‐driven parametric inversion process. The potential of the proposed joint migration inversion algorithm is illustrated with numerical examples.

Review Paper: An outlook on the future of seismic imaging, Part I: forward and reverse modelling

ABSTRACTThe next generation of seismic imaging algorithms will use full wavefield migration, which regards multiple scattering as indispensable information. These algorithms will also include autonomous velocity‐updating in the migration process, called joint migration inversion. Full wavefield migration and joint migration inversion address industrial requirements to improve the images of highly complex reservoirs as well as the industrial ambition to produce these images more automatically (automation in seismic processing).In these vision papers on seismic imaging, full wavefield migration and joint migration inversion are formulated in terms of a closed‐loop, estimation algorithm that can be physically explained by an iterative double‐focusing process (full wavefield Common Focus Point technology). A critical module in this formulation is forward modelling, allowing feedback from the migrated output to the unmigrated input (‘closing the loop’). For this purpose, a full wavefield modelling module has been developed, which uses an operator description of complex geology. Full wavefield modelling is pre‐eminently suited to function in the feedback path of a closed‐loop migration algorithm.‘The Future of Seismic Imaging’ is presented as a coherent trilogy of papers that propose the migration framework of the future. In Part I, the theory of full wavefield modelling is explained, showing the fundamental distinction with the finite‐difference approach. Full wavefield modelling allows the computation of complex shot records without the specification of velocity and density models. Instead, an operator description of the subsurface is used. The capability of full wavefield modelling is illustrated with examples. Finally, the theory of full wavefield modelling is extended to full wavefield reverse modelling (FWMod−1), which allows accurate estimation of (blended) source properties from (blended) shot records.

Review Paper: An outlook on the future of seismic imaging, Part II: Full‐Wavefield Migration

ABSTRACTThe next‐generation seismic imaging algorithms will consider multiple scattering as indispensable information, being referred to as Full‐Wavefield Migration. In addition, these algorithms will also include autonomous velocity updating in the migration process, being referred to as Joint Migration Inversion. Full‐Wavefield Migration and Joint Migration Inversion address the industrial needs to improve images of very complex reservoirs as well as the industrial ambition to produce these images in a more automatic manner (automation in seismic processing).In this vision paper on seismic imaging, Full‐Wavefield Migration and Joint Migration Inversion are formulated in terms of a closed‐loop estimation algorithm that can be physically explained by an iterative double focusing process (full‐wavefield common‐focus‐point technology). A critical module in this formulation is forward modelling, allowing feedback from migrated output to unmigrated input (closing the loop). For this purpose, a full‐wavefield modelling module has been developed, which utilizes an operator description of complex geology. The full‐wavefield modelling module is pre‐eminently suited to function in the feedback path of a closed‐loop migration algorithm.‘The Future of Seismic Imaging’ is presented as a coherent trilogy, proposing the migration framework of the future in three consecutive parts. In Part I, it was shown that the proposed full‐wavefield modelling module algorithm differs fundamentally from finite‐difference modelling because velocities and densities need not be provided. Instead, an operator description of the subsurface is used. In addition, the concept of reverse modelling was introduced. In Part II, it is shown how the theory of Primary Wavefield Migration can be extended to Full‐Wavefield Migration by correcting for angle‐dependent transmission effects and by utilizing multiple scattering. The potential of the Full‐Wavefield Migration algorithm is illustrated with numerical examples. A multidirectional migration strategy is proposed that navigates the Full‐Wavefield Migration algorithm through the seismic data cube in different directions.

Using higher-order scattering in seismic imaging

For seismic exploration, acoustic sources and receivers are positioned at the earth's surface in order to measure the reflection response from the subsurface inhomogeneities. However, in most current imaging algorithms, only the primary reflections are being taken into account and multiple reflections are being discarded as noise. In the recently proposed method of full wavefield imaging, the higher-order scattering is taken into account in the imaging process where they contribute to extend the illumination area and no longer produce spurious imaging artifacts. This method involves an inversion process, where a recursive modeling method is used to predict the measured reflection response—including all its higher-order scattering effects—based on estimated reflectivity values and background velocity model. Because the background velocity cannot be assumed to be homogeneous in the earth, background velocity model estimation is a crucial component of the imaging process. It appears that automatic estimation of velocity models can be accomplished within the concept of full wavefield migration, in which higher-order scattering events can also be fully accommodated. Finally, the results of full wavefield imaging can be combined with localized, target-oriented full waveform inversion in order to get the final details, being the elastic properties, at the target zone.

The Research of Reverse-Time Migration for Cross-Hole Seismic

Cross-hole seismic is the leading technology of development seismology, which is still developing and improving. With the development of down-hole acquisition equipment, cross-hole seismic acquisition technology is getting mature, providing better data for imaging. According to the features of cross-hole survey and cross-hole data, we put forward a reverse-time migration method which is suitable for the wave equation for cross-hole seismic data. We propose finite difference scheme of higher order, and then derive its stability condition in cross-hole seismic. The frequency dispersion problem in cross-hole seismic wave field extrapolation is also discussed. Cross correlation imaging condition is used to realize migration, and Laplace filter is applied to remove low-frequency noise from migration section. Thus finite-difference reverse-time migration method for cross-hole seismic is established. Finally, we build geological models with anomalous ellipsoids, and apply cross-hole seismic wave field simulation and migration to them, thus our method proves its effectiveness. When dealing with real cross-hole seismic data with this method, high-resolution migration sections can be achieved. Key words : Cross-hole seismic; Reverse-time migration; Model test

Invariant properties and rotation transformations of the GPR scattering matrix

Abstract We analyze the properties of the scattering matrix associated with the incident and scattered electric fields used in GPR. The elements of the scattering matrix provide information produced by different polarizations of the incident wave field. Rotationally invariant quantities such as trace, determinant and Frobenius norm lead to images that combine the information contained in the four elements of the scattering matrix in a mathematically simple and sound manner. The invariant quantities remove the directional properties implicit in the dipolar field used in GPR allowing the application of standard processing techniques designed for scalar fields, such as those used in seismic data processing. We illustrate the non-directional properties of the invariants using a 3D simulation of the wavefield produced by a point scatterer. The estimation of the azimuth angle of elongated targets is also explored using rotation transformations that maximize alternatively the co-polarized or the cross-polarized responses. The angle estimation is essentially an unstable process, particularly if low amplitudes or noisy data are involved. We apply the Frobenius norm ‖S‖F as a criterion for selection of the best amplitudes to use for a more stable and significant angle estimation. The performance of our formulation was tested with synthetic data produced by a 3D model of an air-filled metal pipe buried in a homogeneous halfspace. The images resulting from the invariants show a clear diffraction hyperbola suitable for a scalar wavefield migration, while the azimuth of the pipe is neatly resolved for amplitudes selected with ‖S‖F ≥ 0.4. A field experiment conducted above an aqueduct pipe illustrates the proposed methods with real data. The images obtained from the invariants are better than those from the individual elements of the scattering matrix. The azimuth estimated using our formulation is in agreement with the probable orientation of the aqueduct. Finally, a field experiment above a buried air-filled barrel shows that combining the information in the way proposed in this work may lead to an improved image of the subsurface target, the cost to pay is the lost of directional information contained in the scattering matrix. In general, we claim that the methods proposed in this work can be useful to analyze the information acquired by multicomponent GPR surveys using standard scalar wavefield algorithms.

To: “Flux-normalized wavefield decomposition and migration of seismic data,” Bjørn Ursin, Ørjan Pedersen, and Børge Arntsen, Geophysics, 77, no. 3, S83–S92.

<b>To: “Flux-normalized wavefield decomposition and migration of seismic data,”</b> <i>Bjørn Ursin, Ørjan Pedersen, and Børge Arntsen</i>, <scp>Geophysics</scp>, <b>77</b>, no. 3, S83–S92.