Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions

Ravasi, Matteo; Curtis, Andrew

doi:10.1190/geo2012-0286.1

Cited by 30 publications

(32 citation statements)

References 60 publications

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“…By applying the methodology at each depth level in the subsurface and taking the response at zero time lag and zero space lag, an image with accurate amplitudes can be obtained without artefacts from internal multiple reflections Broggini et al 2014a;Behura et al 2014). By including non-zero lags, equivalent extended images can also be created (Vasconcelos & Rickett 2013), which can be useful input for migration velocity analysis (Sava & Vasconcelos 2011), reservoir characterization (De Bruin et al 1990;Thomson 2012) and novel schemes for nonlinear imaging (Fleury & Vasconcelos 2012;Ravasi & Curtis 2012) and waveform inversion (Vasconcelos et al 2014a). Alternatively, we can use the Marchenko equations to retrieve internal multiples at the acquisition level, which could then be adaptively subtracted from the recorded data .…”

Section: Introductionmentioning

confidence: 99%

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Neut¹,

Vasconcelos

Wapenaar³

2015

Geophys. J. Int.

118

114

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S U M M A R YIterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections.

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Section: Introductionmentioning

confidence: 99%

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Neut¹,

Vasconcelos

Wapenaar³

2015

Geophys. J. Int.

118

114

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“…It indicates that the perturbed wavefield at any position inside ∂ D can be retrieved from the values along the closed surface ∂ D. The equation 4 is the same as that in Ravasi and Curtis (2013); however, these authors do not consider a non-welded interface. We obtain the same equation due to our assumption of the compliances as real-valued functions.…”

Section: Theorymentioning

confidence: 95%

“…In this case, the imaging condition is a nonlinear function of the perturbed wavefield, where the perturbed wavefield is defined as the difference between total wavefield and background wavefield. This new imaging condition allows achieving higher resolution in the migrated image than with the conventional imaging condition which is linear with respect to the perturbed wavefield (Ravasi and Curtis, 2013).…”

Section: Introductionmentioning

confidence: 99%

“…Although we have considered horizontal fractures to derive equation 3, equation 4 is valid for fractures of arbitrary orientation, because ∆η T and ∆η N always vanish. We obtain the imaging condition at imaging point x P as the zero-time and zero-offset amplitude of the perturbed wavefield (Ravasi and Curtis, 2013):…”

Section: Theorymentioning

confidence: 99%

“…Recently, a non-linear imaging condition has been proposed for high-resolution imaging of the boundary of contrasting acoustic or elastic constants (Fleury and Vasconcelos, 2012;Ravasi and Curtis, 2013). In this case, the imaging condition is a nonlinear function of the perturbed wavefield, where the perturbed wavefield is defined as the difference between total wavefield and background wavefield.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear imaging condition to image fractures as non-welded interfaces

Minato

Ghose

2014

SEG Technical Program Expanded Abstracts 2014

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SUMMARYHydraulic properties of a fractured reservoir are often controlled by large fractures. In order to seismically detect and characterize them, a high-resolution imaging method is necessary. We apply a non-linear imaging condition to image fractures, considered as non-welded interfaces. We derive the imaging condition from the general correlation-type representation theorem, assuming compliances to be real-valued functions. We investigate the P-wave image due to P-wave sources and the effect of source illumination. We present here numerical modeling results for (1) a single dry fracture, (2) orthogonally intersecting fractures, and (3) deviated multiple fractures in a multi-layered subsurface. Our results show that the nonlinear terms in the imaging condition help to cancel the artefacts appearing in case of conventional imaging condition, and improve the resolution of the final image. For a multi-layered model, the one-sided source illumination from the earth's surface can image the multiple fractures. However, an incomplete source illumination restricts the removal of all the artefacts. In this case, installing additional borehole sources can greatly improve the resolution of the fracture distribution.

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Constructing new seismograms from old earthquakes: Retrospective seismology at multiple length scales

et al. 2015

Self Cite

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If energy emitted by a seismic source such as an earthquake is recorded on a suitable backbone array of seismometers, source‐receiver interferometry (SRI) is a method that allows those recordings to be projected to the location of another target seismometer, providing an estimate of the seismogram that would have been recorded at that location. Since the other seismometer may not have been deployed at the time at which the source occurred, this renders possible the concept of “retrospective seismology” whereby the installation of a sensor at one period of time allows the construction of virtual seismograms as though that sensor had been active before or after its period of installation. Here we construct such virtual seismograms on target sensors in both industrial seismic and earthquake seismology settings, using both active seismic sources and ambient seismic noise to construct SRI propagators, and on length scales ranging over 5 orders of magnitude from ∼40 m to ∼2500 km. In each case we compare seismograms constructed at target sensors by SRI to those actually recorded on the same sensors. We show that spatial integrations required by interferometric theory can be calculated over irregular receiver arrays by embedding these arrays within 2‐D spatial Voronoi cells, thus improving spatial interpolation and interferometric results. The results of SRI are significantly improved by restricting the backbone receiver array to include approximately those receivers that provide a stationary‐phase contribution to the interferometric integrals. Finally, we apply both correlation‐correlation and correlation‐convolution SRI and show that the latter constructs fewer nonphysical arrivals.

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Nonlinear scattering based imaging in elastic media: Theory, theorems, and imaging conditions

Cited by 30 publications

References 60 publications

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

On Green's function retrieval by iterative substitution of the coupled Marchenko equations

Non-linear imaging condition to image fractures as non-welded interfaces

Constructing new seismograms from old earthquakes: Retrospective seismology at multiple length scales

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