Preconditioning for Linearised Inversion of Attenuation and Velocity Perturbations

Hak, Bobby; Mulder, W.A.

doi:10.3997/2214-4609.20147759

Cited by 5 publications

(3 citation statements)

References 7 publications

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“…According to Devaney and Sherman (1982), the non-uniqueness in scattering should disappear if multiple experiments are performed, for instance, at more than a single offset. Ribodetti et al (1995) and Hak and Mulder (2008a) consider deltafunction type perturbations or point scatterers. Its Fourier transform in depth contains long-wavelength components, including the zero wavelength.…”

Section: Discussionmentioning

confidence: 99%

Imaging velocity and attenuation scatterers with wave equation migration

Hak

2011

GEOPHYSICS

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Geophysics publishes abstracts of dissertations and titles of master’s theses both in print and online. Recent graduates are invited to submit their abstracts or titles by completing and submitting the appropriate form found at http://seg.org/dissertationabstracts. Abstracts and titles will be reviewed and accepted or rejected based on their relevance to the readers of Geophysics. Abstracts must be written in English and defended in 2009 or later.

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Section: Discussionmentioning

confidence: 99%

Imaging velocity and attenuation scatterers with wave equation migration

Hak

2011

GEOPHYSICS

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“…Ribodetti et al (1995) and Hak & Mulder (2008) consider delta‐function type perturbations or point scatterers. Its Fourier transform in depth contains long‐wavelength components, including the zero wavelength.…”

Section: Discussionmentioning

confidence: 99%

An ambiguity in attenuation scattering imaging

Mulder¹,

Hak²

2009

Geophysical Journal International

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S U M M A R YMigration constructs a subsurface image by mapping band-limited seismic data to reflectors in the Earth, given a background velocity model that describes the kinematics of the seismic waves. Classically, the reflectors correspond to impedance perturbations on length scales of the order of the seismic wavelength. The Born approximation of the visco-acoustic wave equation enables the computation of synthetic data for such a model. Migration then amounts to solving the linear inverse problem for perturbations in density, velocity, and attenuation.Here, the problem is simplified by assuming the density to be constant, leaving only velocity and attenuation perturbations. In the frequency domain, a single complex-valued model parameter that depends on subsurface position describes both. Its real part is related to the classic reflectivity, its imaginary part also involves attenuation variations. Attenuation scattering is usually ignored but, when included in the migration, might provide information about, for instance, the presence of fluids. We found, however, that it is very difficult to solve simultaneously for both velocity and attenuation perturbations. The problem already occurs when computing synthetic data in the Born approximation for a given scattering model: after applying a weighted Hilbert transform in the depth coordinate to a given scattering model, we obtained almost the same synthetic data if the scatterers had small dip and were located at not-too-shallow depths. This implies that it will be nearly impossible to simultaneously determine the real and imaginary part of the scattering parameters by linearized inversion without imposing additional constraints.

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“…We consider simple 2D examples for which the Green functions are available and the full Hessian can be readily computed. In earlier publications (Hak and Mulder 2008a,b), we considered various non‐diagonal preconditioners for the linearized inverse problems but once we realized the existence of the ambiguity mentioned above, we concluded that such preconditioning will never help in providing a proper answer.…”

Section: Introductionmentioning

confidence: 94%

Migration for velocity and attenuation perturbations

Hak

Mulder

2010

Geophysical Prospecting

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A B S T R A C TMigration maps seismic data to reflectors in the Earth. Reflections are not only caused by small-scale variations of the velocity and density but also of the quality factor that describes attenuation. We investigated scattering due to velocity and attenuation perturbations by computing the resolution function or point-spread function in a homogeneous background model. The resolution function is the migration image of seismic reflection data generated by a point scatterer. We found that the resolution function mixes velocity and attenuation parameter perturbations to the extent that they cannot be reconstructed independently. This is true for a typical seismic setting with sources and receivers at the surface and a buried scatterer. As a result, it will be impossible to simultaneously invert for velocity and attenuation perturbations in the scattering approach, also known as the Born approximation.We proceeded to investigate other acquisition geometries that may resolve the ambiguity between velocity and attenuation perturbations. With sources and receivers on a circle around the scatterer, in 2D, the ambiguity disappears. It still shows up in a cross-well setting, although the mixing of velocity and attenuation parameters is less severe than in the surface-to-surface case. We also consider illumination of the target by diving waves in a background model that has velocity increasing linearly with depth. The improvement in illumination is, however, still insufficient to remove the ambiguity.

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Preconditioning for Linearised Inversion of Attenuation and Velocity Perturbations

Cited by 5 publications

References 7 publications

Imaging velocity and attenuation scatterers with wave equation migration

Imaging velocity and attenuation scatterers with wave equation migration

An ambiguity in attenuation scattering imaging

Migration for velocity and attenuation perturbations

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