A platform for Kirchhoff data mapping in scalar models of data acquisition

This thesis develops a novel target-oriented inversion framework that uses wavefields as carriers of information to image both low-and high-wavenumber components of the earth model in complex geological settings, such as subsalt regions. The lowwavenumber component of the earth model is often known as background velocity, whereas the high-wavenumber component of the earth model is often known as reflectivity. I address the problem of reflectivity imaging with target-oriented wavefield least-squares migration, and the problem of velocity estimation with target-oriented wavefield tomography.Reflectivity images of the subsurface are commonly produced by prestack depth migration. When the overburden is complex and the reflectors are unevenly or insufficiently illuminated, the migration operator alone is inadequate to provide an optimal image.I tackle the problem of distorted illumination in reflectivity imaging by wavefield least-squares migration. I formulate least-squares migration in the image domain and solve it in a target-oriented fashion. In the image-domain formulation, explicit computation of the Hessian operator (the resolution function that measures the illumination deficiency of the imaging system) is the most important and challenging step. I develop a novel method based on phase encoding to efficiently and accurately compute the target-oriented Hessian operator. By design, the phase-encoded Hessian converges to the exact Hessian either deterministically (for plane-wave phase encoding) or statistically (for random phase encoding), while having the important advantages that no Green's functions need to be stored during computation and that v the number of wavefield propagations is also drastically reduced. The target-oriented Hessian operator is then used to recover the reflectivity by iterative inverse filtering. I regularize the inversion with dip constraints, which naturally incorporate interpreted geological information into the inversion.Accurate imaging of the reflectivity also requires an accurate background velocity model. High-quality velocity model-building in complex geology requires wavefieldbased velocity analysis to properly model band-limited wave phenomena. However, the high cost and lack of flexibility of target-oriented model-building prevent this method from being widely used in practice.I overcome the cost and flexibility issues of wavefield-based migration velocity analysis by developing target-oriented wavefield tomography. Target-oriented wavefield tomography is achieved by synthesizing a new data set specifically for velocity analysis. The new data set is generated based on an initial unfocused target image and by a novel application of generalized Born wavefield modeling, which correctly preserves velocity kinematics by modeling both zero and non-zero subsurface-offset-

Section: Inversionmentioning

confidence: 99%

Section: Target-oriented Born Wavefield Modelingmentioning

confidence: 99%

Imaging and velocity analysis by target-oriented wavefield inversion

Tang

2011

“…This approach resemble that of Deregowski and Rocca (1981). It was also applied to a more general case of azimuth moveout (AMO) by Fomel and Biondi (1995) and fully generalized by Bleistein and Jaramillo (2000). The geometric approach implies that in order to find the summation pass of the OC operator, one should solve the kinematic problem of reflection from an elliptic reflector whose focuses are in the shot and receiver locations of the output seismic gather.…”

Section: Appendix a Second-order Reflection Traveltime Derivativesmentioning

confidence: 99%

“…An intuitive introduction to the concept of offset continuation is presented by Hill et al (2001). A general data mapping prospective is developed by Bleistein and Jaramillo (2000).…”

Section: The Partial Differential Equation Introduced In This Papermentioning

confidence: 99%

Theory of differential offset continuation

Fomel

2003

I introduce a partial differential equation to describe the process of prestack reflection data transformation in the offset, midpoint, and time coordinates. The equation is proved theoretically to provide correct kinematics and amplitudes on the transformed constant-offset sections. Solving an initial-value problem with the proposed equation leads to integral and frequency-domain offset continuation operators, which reduce to the known forms of dip moveout operators in the case of continuation to zero offset.

“…The 3-D analog is known as azimuth moveout or AMO (Biondi et al, 1998;Fomel, 2003a). Bleistein and Jaramillo (2000) developed a general platform for Kirchhoff data mapping, which includes offset continuation as a special case.…”

Section: Introductionmentioning

confidence: 99%

OC-seislet: Seislet transform construction with differential offset continuation

Liu

Fomel

2010

Many of the geophysical data analysis problems, such as signal-noise separation and data regularization, are conveniently formulated in a transform domain, where the signal appears sparse. Classic transforms such as the Fourier transform or the digital wavelet transform, fail occasionally in processing complex seismic wavefields, because of the nonstationarity of seismic data in both time and space dimensions. We present a sparse multiscale transform domain specifically tailored to seismic reflection data. The new wavelet-like transform -the OC-seislet transform -uses a differential offset-continuation (OC) operator that predicts prestack reflection data in offset, midpoint, and time coordinates. It provides high compression of reflection events. In the transform domain, reflection events get concentrated at small scales. Its compression properties indicate the potential of OC-seislets for applications such as seismic data regularization or noise attenuation. Results of applying the method to both synthetic and field data examples demonstrate that the OC-seislet transform can reconstruct missing seismic data and eliminate random noise even in structurally complex areas.