Using focusing operators to estimate velocity models

Hegge, Rob; Fokkema, J.T.; Duijndam, A. J. W.

doi:10.1190/1.1820227

Cited by 5 publications

(8 citation statements)

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“…The proposed algorithm is suitable for updating focusing operators for two reasons. First, pseudolayer constraints are often available after CFP migration (Hegge et al, 1998), initial poststack depth migration and picking (in this example), or after operator updating by automatic tracking (Bolte et al, 2000) and second, the algorithm is made stable for a few (sparsely distributed) focus points by interpolating the velocities in the less sampled zones to either side of each focus point and by applying smoothing to the updated velocity model.…”

Section: Discussionmentioning

confidence: 99%

“…Each operator is estimated individually, and the operators are therefore independent of each other. This enables grouping of a subset of focusing operators, each of which is connected with its focus point lying on a specific reflecting interface (Hegge et al, 1998). The grouping is necessary to define inferred interfaces that connect the focus points to guide the velocity updates in the less sampled zones to either side of each focus point.…”

Section: Input Data To the Tomography: Focusing Operatorsmentioning

confidence: 99%

“…The strategy begins by individually migrating each of the focusing operators by poststack depth migration (Kirchhoff summation or RTM) with an initial velocity model to identify spatially related groups of focus points (pseudointerfaces) that correspond to the main reflectors (Hegge et al, 1998) and hence the regions of the velocity grids that can be treated as pseudolayers for the purpose of velocity updates.…”

Section: Inversion Strategy: a Three-parameterization Sequencementioning

confidence: 99%

“…One approach to reduce the computation time is to use a layered parameterization (Hegge et al, 1998Hegge, 2000;Santos et al, 2010Santos et al, , 2012 or an irregular grid parameterization Cox, 2004). Here, we develop a new, fast acoustic velocity tomography of focusing operators that is based on a simultaneous iterative reconstruction technique (SIRT) solution (instead of Jacobian matrix inversion), a hybrid parameterization, and a new idea of estimating local velocities over an area (instead of along rays), by borrowing ideas from common-reflection-point (CRP)-based MVA (Fei and McMechan, 2006) for its implementation.…”

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confidence: 99%

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Fast acoustic velocity tomography of focusing operators

McMechan

2014

GEOPHYSICS

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A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth's surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was ∼0.2 km∕s and the final mean focal point position error was ∼0.5 wavelength.

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Section: Discussionmentioning

confidence: 99%

Section: Input Data To the Tomography: Focusing Operatorsmentioning

confidence: 99%

Section: Inversion Strategy: a Three-parameterization Sequencementioning

confidence: 99%

mentioning

confidence: 99%

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Fast acoustic velocity tomography of focusing operators

McMechan

2014

GEOPHYSICS

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“…All implementations of CFP-based tomography (Hegge et al, 1996(Hegge et al, , 1997(Hegge et al, , 1998(Hegge et al, , 1999Kabir, 1997;Hegge, 2000;Kabir and Verschurr, 2000;Cox, 2004;Liu et al, 2006) require CFP operators (CFPOs). Conventional methods to estimate CFPOs use multioffset data (Berkhout, 1997a(Berkhout, , 1997bThorbecke, 1997;Bolte, 2003;Rijzen et al, 2004) and they work better if the reflections are laterally continuous.…”

Section: Introductionmentioning

confidence: 99%

Tomography of diffraction-based focusing operators

2012

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Diffractions carry the same kinematic information provided by common focus point operators (CFPOs). Thus CFPO and diffraction time trajectories may be used separately, or combined into a single unified tomography for velocity analysis. Velocity estimation by tomography of CFPOs reduces the depth-velocity ambiguity compared to two-way time tomography. CFPO estimation is complicated where there are event discontinuities and diffractions. This problem is overcome by using the kinematic information in diffractions in near-offset common-offset gathers. The procedure is illustrated using synthetic data, and a single-channel field seismic profile from the Blake Ridge (off the east coast of the United States). The results show the effectiveness of the proposed method for estimation of velocity from single channel seismic data, and for refinement of the velocity field from multichannel data. Both applications are costcompetitive.

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Infilling of sparse 3D data for 3D focusing operator estimation

Rijzen

Gisolf

Verschuur

2004

Geophysical Prospecting

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A B S T R A C TSeismic migration can be formulated in terms of two consecutive downward extrapolation steps: refocusing the receivers and refocusing the sources. Applying only the first focusing step with an estimate of the focusing operators results in a common focal point (CFP) gather for each depth point at a reflecting boundary. The CFP gathers, in combination with the estimates of the focusing operators, can be used in an iterative procedure to obtain the correct operators. However, current 3D seismic data acquisition geometries do not contain the dense spatial sampling required for calculation of full 3D CFP gathers. We report on the construction of full 3D CFP gathers using a non-full 3D acquisition geometry. The proposed method uses a reflector-orientated data infill procedure based on the azimuthal redundancy of the reflection data. The results on 3D numerical data in this paper show that full 3D CFP gathers, which are kinematically and dynamically correct for the target event, can be obtained. These gathers can be used for iterative updating of the 3D focusing operators. I N T R O D U C T I O NMost migration techniques use a velocity model to correct for two-way wave propagation in the medium. These two-way propagation operators are constructed from one-way propagation operators, forward modelled in the velocity model. After the correction for two-way wave propagation, the result obtained is analysed and the velocity model is updated until a certain criterion is satisfied, e.g. a flat common-image gather (Al-Yahya 1989). Owing to the complex nature of two-way wave propagation, this updating can be difficult and in addition, due to the fact that the updating is not performed directly on the one-way operators but on a parametrization of the velocity model, a restriction to the one-way operator solution space is imposed.To overcome these problems a new migration methodology was introduced by Berkhout (1997a,b), which is called the common focal point (CFP) method. In this method, the correction for two-way wave propagation is split into two separate steps, both correcting for one-way wave propagation. This correction is performed by means of applying focusing operators, which can be seen as time-reversed Green's functions that describe one-way wave propagation in the medium. These operators are simpler in nature than operators that describe two-way wave propagation. Besides this simplification, a very elegant updating criterion can also be derived in which the update is directly performed on the one-way propagation operators without the need for a velocity model (Berkhout 1997b;Bolte, Verschuur and Hegge 1999). While this so-called CFP technology was initially introduced as a migration tool, a number of other applications have been developed since then, including: the inversion of the focusing operators to obtain a velocity model of the subsurface (Hegge, Fokkema and Duijndam 1998;Kabir and Verschuur 2000;Cox and Verschuur 2003); estimating the angle-dependent reflectivities in the twice-focused domain (Ber...

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Using focusing operators to estimate velocity models

Cited by 5 publications

References 1 publication

Fast acoustic velocity tomography of focusing operators

Fast acoustic velocity tomography of focusing operators

Tomography of diffraction-based focusing operators

Infilling of sparse 3D data for 3D focusing operator estimation

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