Imaging and inversion at depth without a velocity model: Theory, concepts and initial evaluation

Weglein, Arthur B.; Matson, Ken H.; Foster, Douglas J.; Corrigan, Dennis A.; Carvalho, Paulo M.; Shaw, Sylvie

doi:10.1190/1.1815555

Cited by 24 publications

(23 citation statements)

References 4 publications

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“…Weglein et al ͑2000͒ demonstrate that the first-order approximation to T͑p,k͒, i.e., T 1 ͑p,k͒, or s , at all depths requires all frequency components contained within the surface data to predict one frequency of s at all depths. Hence, the inverse-scattering series allows one frequency of the wavefield at all depths in the earth to be predicted as a series, order-by-order in the surface data, using all the frequency information therein.…”

Section: Inverse Series Data Mapping Si129mentioning

confidence: 99%

“…Recently, a taskspecific subseries aimed at performing imaging, i.e., locating reflectors in space, has been identified and tested on analytic data for simple 1D-earth examples with encouraging results ͑Weglein et al Shaw, 2001;Shaw et al, 2001;Weglein et al, 2001;Shaw et al, 2002a, b;Innanen and Weglein, 2003;Shaw et al, 2003a, b;Weglein et al, 2003;Shaw et al, 2004;Shaw, 2005;Liu et al 2005a, b͒ have shown the first multidimensional acoustic examples of the methods for determining the correct spatial location of reflectors without knowing or determining the overburden velocity model. As the analysis of Weglein et al ͑2000͒ andShaw et al ͑2004͒, with respect to the possibility and requirements for a model-type independent imaging algorithm, and the diagrams of describing inverse scattering interactions within the imaging subseries, show, a model-type independent algorithm would require both reflection and transmission data.…”

Section: Introductionmentioning

confidence: 97%

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Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

et al. 2006

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The starting point for the derivation of a new set of approaches for predicting both the wavefield at depth in an unknown medium and transmission data from measured reflection data is the inverse scattering series. We present a selection of these maps that differ in order ͑i.e., linear or nonlinear͒, capability, and data requirements. They have their roots in the consideration of a data format known as the T-matrix and have direct applicability to the data construction techniques motivating this special issue. Of particular note, one of these, a construction of the wavefield at any depth ͑includ-ing the transmitted wavefield͒, order-by-order in the measured reflected wavefield, has an unusual set of capabilities ͑e.g., it does not involve an assumption regarding the minimum-phase nature of the data and is accomplished with processing in the simple reference medium only͒ and requirements ͑e.g., a suite of frequencies from surface data are required to compute a single frequency of the wavefield at depth when the subsurface is unknown͒. An alternative reflection-to-transmission data mapping ͑which does not require a knowledge of the wavelet, and in which the component of the unknown medium that is linear in the reflection data is used as a proxy for the component of the unknown medium that is linear in the transmission data͒ is also derivable from the inverse scattering series framework.

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Section: Inverse Series Data Mapping Si129mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

et al. 2006

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“…A more formal approach than the direct-series expansion of equation 10 is to start from the Lippmann-Schwinger equation. According to Weglein et al (2000), the solution of the Lippmann-Schwinger equation in terms of an inversescattering series actually solves the seismic imaging and inversion problem. It is therefore of some interest to put seismic depth extrapolation properly within this framework.…”

Section: Mittetmentioning

confidence: 99%

“…Further discussion on this application to depth imaging and inversion is given by Weglein et al (2000). The relation- ship to other multiple removal schemes is treated by Ikelle et al (2003).…”

Section: Introductionmentioning

confidence: 99%

Perturbation approach to depth extrapolation

Mittet

2005

GEOPHYSICS

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The Born-series solution of the Lippmann-Schwinger equation does not necessarily converge properly for depth-extrapolation problems. Even more seriously, the Lippmann-Schwinger equation is not necessarily selfconsistent for depth extrapolation, unless it is interpreted correctly.A solution is proposed by using the generalized Lippmann-Schwinger equation that includes boundary value contributions that normally are ignored. A modified version of the Lippmann-Schwinger equation for depth extrapolation is obtained. The corrections to the Born-series expansion for depth extrapolation are demonstrated. The new system has the desired convergence and self-consistency properties. Explicit depth extrapolation is discussed in the context of the Lippmann-Schwinger equation. A partial explanation for why explicit depth extrapolation works reasonably well in laterally inhomogeneous media may be that the contribution from the perturbation term in the Lippmann-Schwinger equation for that problem is small for a wide variety of velocity models.

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“…Also, it may be argued that MF and CRS are still parameter‐optimization approaches and, by re‐parametrization (from wavefront attributes to stacking velocities), velocity‐estimation techniques in disguise. A different approach, based on inverse scattering, was developed by Weglein et al . (2000), which has the potential of providing a subsurface image without a defined velocity.…”

Section: Introductionmentioning

confidence: 99%

Path‐integral seismic imaging

Landa¹,

Fomel

Moser

2006

Geophysical Prospecting

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A B S T R A C TA new type of seismic imaging, based on Feynman path integrals for waveform modelling, is capable of producing accurate subsurface images without any need for a reference velocity model. Instead of the usual optimization for traveltime curves with maximal signal semblance, a weighted summation over all representative curves avoids the need for velocity analysis, with its common difficulties of subjective and timeconsuming manual picking. The summation over all curves includes the stationary one that plays a preferential role in classical imaging schemes, but also multiple stationary curves when they exist. Moreover, the weighted summation over all curves also accounts for non-uniqueness and uncertainty in the stacking/migration velocities. The path-integral imaging can be applied to stacking to zero-offset and to time and depth migration. In all these cases, a properly defined weighting function plays a vital role: to emphasize contributions from traveltime curves close to the optimal one and to suppress contributions from unrealistic curves. The path-integral method is an authentic macromodel-independent technique in the sense that there is strictly no parameter optimization or estimation involved. Development is still in its initial stage, and several conceptual and implementation issues are yet to be solved. However, application to synthetic and real data examples shows that it has the potential for becoming a fully automatic imaging technique.

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Imaging and inversion at depth without a velocity model: Theory, concepts and initial evaluation

Cited by 24 publications

References 4 publications

Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

Using the inverse scattering series to predict the wavefield at depth and the transmitted wavefield without an assumption about the phase of the measured reflection data or back propagation in the overburden

Perturbation approach to depth extrapolation

Path‐integral seismic imaging

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