The isochron ray in seismic modeling and imaging

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1053-1070 ◽  
Author(s):  
Einar Iversen
Keyword(s):  
Seismic Imaging ◽  
Model Updating ◽  
Velocity Model ◽  
Seismic Modeling ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Geometric Spreading ◽  
Model Independent ◽  
Map Migration ◽  
Upper Level

The isochron, the name given to a surface of equal two‐way time, has a profound position in seismic imaging. In this paper, I introduce a framework for construction of isochrons for a given velocity model. The basic idea is to let trajectories called isochron rays be associated with iso chrons in an way analogous to the association of conventional rays with wavefronts. In the context of prestack depth migration, an isochron ray based on conventional ray theory represents a simultaneous downward continuation from both source and receiver. The isochron ray is a generalization of the normal ray for poststack map migration. I have organized the process with systems of ordinary differential equations appearing on two levels. The upper level is model‐independent, and the lower level consists of conventional one‐way ray tracing. An advantage of the new method is that interpolation in a ray domain using isochron rays is able to treat triplications (multiarrivals) accurately, as opposed to interpolation in the depth domain based on one‐way traveltime tables. Another nice property is that the Beylkin determinant, an important correction factor in amplitude‐preserving seismic imaging, is closely related to the geometric spreading of isochron rays. For these reasons, the isochron ray has the potential to become a core part of future implementations of prestack depth migration. In addition, isochron rays can be applied in many contexts of forward and inverse seismic modeling, e.g., generation of Fresnel volumes, map migration of prestack traveltime events, and generation of a depth‐domain–based cost function for velocity model updating.

Tomographic velocity model updating for prestack depth migration

1999 ◽  
Author(s):  
Robert Bloor ◽  
Alfonso Gonzalez ◽  
Uwe Albertin ◽  
David Yingst
Keyword(s):  
Model Updating ◽  
Velocity Model ◽  
Prestack Depth Migration ◽  
Depth Migration

Nonlinear 3D tomographic least-squares inversion of residual moveout in Kirchhoff prestack-depth-migration common-image gathers

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE13-VE23 ◽  
Author(s):  
Frank Adler ◽  
Reda Baina ◽  
Mohamed Amine Soudani ◽  
Pierre Cardon ◽  
Jean-Baptiste Richard
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Layer Velocity ◽  
Map Migration

Velocity-model estimation with seismic reflection tomography is a nonlinear inverse problem. We present a new method for solving the nonlinear tomographic inverse problem using 3D prestack-depth-migrated reflections as the input data, i.e., our method requires that prestack depth migration (PSDM) be performed before tomography. The method is applicable to any type of seismic data acquisition that permits seismic imaging with Kirchhoff PSDM. A fundamental concept of the method is that we dissociate the possibly incorrect initial migration velocity model from the tomographic velocity model. We take the initial migration velocity model and the residual moveout in the associated PSDM common-image gathers as the reference data. This allows us to consider the migrated depth of the initial PSDM as the invariant observation for the tomographic inverse problem. We can therefore formulate the inverse problem within the general framework of inverse theory as a nonlinear least-squares data fitting between observed and modeled migrated depth. The modeled migrated depth is calculated by ray tracing in the tomographic model, followed by a finite-offset map migration in the initial migration model. The inverse problem is solved iteratively with a Gauss-Newton algorithm. We applied the method to a North Sea data set to build an anisotropic layer velocity model.

Anisotropic parsimonious prestack depth migration

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. S25-S36 ◽  
Author(s):  
Ernesto V. Oropeza ◽  
George A. McMechan
Keyword(s):  
Model Building ◽  
Computing Time ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Velocity Model ◽  
P Wave ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Tti Media ◽  
Map Migration

An efficient Kirchhoff-style prestack depth migration, called “parsimonious” migration, was developed a decade ago for isotropic 2D and 3D media by using measured slownesses to reduce the amount of ray tracing by orders of magnitude. It is conceptually similar to “map” migration, but its implementation has some differences. We have extended this approach to 2D tilted transversely isotropic (TTI) media and illustrated it with synthetic P-wave data. Although the framework of isotropic parsimonious may be retained, the extension to TTI media requires redevelopment of each of the numerical components, calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle isotropic shooting ray-trace algorithm for an anisotropic one. The model parameterization consists of Thomsen’s parameters ([Formula: see text], [Formula: see text], [Formula: see text]) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The elapsed computing time for 101 shots for the Marmousi2 TTI model is 35 s per shot (each with 501 traces) in 32 Opteron cores.

Velocity rays for heterogeneous anisotropic media: Theory and implementation

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. T117-T127 ◽  
Author(s):  
Einar Iversen
Keyword(s):  
Model Updating ◽  
Seismic Velocity ◽  
Velocity Model ◽  
Media Theory ◽  
First Order ◽  
Velocity Models ◽  
Model Independent ◽  
Upper Level ◽  
The Time Domain ◽  
Seismic Images

The surface of equal two-way time referred to as the isochron is a fundamental concept in seismic imaging. The shape of an isochron depends on the source and receiver locations, on the wave type, and on the parameters constituting the seismic velocity model. A perturbation of a parameter of the velocity model forces the isochron points to move along trajectories called velocity rays, with the selected model parameter as the variable along the rays. Based on earlier work describing first-order approximations to velocity rays, I develop a general theory for velocity rays valid for 3D heterogeneous and anisotropic velocity models. By this theory, velocity rays can be obtained in a way similar to the way conventional rays are computed by numeric integration of a system of ordinary differential equations (ODEs). The process is organized with ODE solvers on two levels, where the upper level is model independent. The lower level includes conventional one-way kinematic and dynamic tracing of source and receiver rays, as well as calculation of ray perturbation quantities. Accurate velocity rays are expected to be useful for perturbation of reflectors mapped from the time domain to the depth domain, for remigration of seismic images in the depth domain, and for velocity model updating.

Kinematic interpretation in the prestack depth‐migrated domain

Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger
Keyword(s):  
Signal To Noise Ratio ◽  
Velocity Model ◽  
Point Of View ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Models ◽  
Time Domain Data ◽  
And Migration ◽  
Point To Point ◽  
Homogeneous Media

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.

Rhyl Field: developing a new structural model by integrating basic geological principles with advanced seismic imaging in the Irish Sea

2016 ◽  
Vol 8 (1) ◽  
pp. 355-371 ◽  
Author(s):  
Gavin Ward ◽  
Dean Baker
Keyword(s):  
Structural Model ◽  
Seismic Imaging ◽  
Critical Factor ◽  
Integrated Approach ◽  
Velocity Model ◽  
Irish Sea ◽  
Depth Migration ◽  
Processing Power ◽  
And Migration ◽  
Automated Quality Control

AbstractA new model of compression in the Upper Triassic overlying the Rhyl Field has been developed for the Keys Basin, Irish Sea. This paper highlights the significance of the overburden velocity model in revealing the true structure of the field. The advent of 3D seismic and pre-stack depth migration has improved the interpreter's knowledge of complex velocity fields, such as shallow channels, salt bodies and volcanic intrusions. The huge leaps in processing power and migration algorithms have advanced the understanding of many anomalous features, but at a price: seismic imaging has always been a balance of quality against time and cost. As surveys get bigger and velocity analyses become more automated, quality control of the basic geological assumptions becomes an even more critical factor in the processing of seismic data and in the interpretation of structure. However, without knowledge of both regional and local geology, many features in the subsurface can be processed out of the seismic by relying too heavily on processing algorithms to image the structural model. Regrettably, without an integrated approach, this sometimes results in basic geological principles taking second place to technology and has contributed to hiding the structure of the Rhyl Field until recently.

Efficient velocity model building for prestack depth migration

1996 ◽  
Vol 15 (6) ◽  
pp. 751-753 ◽  
Author(s):  
Y. C. Kim ◽  
C. M. Samuelsen ◽  
T. A. Hauge
Keyword(s):  
Model Building ◽  
Velocity Model ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Velocity Model Building

Integrated prestack depth migration of vertical seismic profile and surface seismic data from the Rocky Mountain Foothills of southern Alberta, Canada

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1782-1791 ◽  
Author(s):  
M. Graziella Kirtland Grech ◽  
Don C. Lawton ◽  
Scott Cheadle
Keyword(s):  
Seismic Data ◽  
Rocky Mountain ◽  
Velocity Model ◽  
Seismic Profile ◽  
Vertical Seismic Profile ◽  
Prestack Depth Migration ◽  
Data Set ◽  
Depth Migration ◽  
Southern Alberta ◽  
Vsp Data

We have developed an anisotropic prestack depth migration code that can migrate either vertical seismic profile (VSP) or surface seismic data. We use this migration code in a new method for integrated VSP and surface seismic depth imaging. Instead of splicing the VSP image into the section derived from surface seismic data, we use the same migration algorithm and a single velocity model to migrate both data sets to a common output grid. We then scale and sum the two images to yield one integrated depth‐migrated section. After testing this method on synthetic surface seismic and VSP data, we applied it to field data from a 2D surface seismic line and a multioffset VSP from the Rocky Mountain Foothills of southern Alberta, Canada. Our results show that the resulting integrated image exhibits significant improvement over that obtained from (a) the migration of either data set alone or (b) the conventional splicing approach. The integrated image uses the broader frequency bandwidth of the VSP data to provide higher vertical resolution than the migration of the surface seismic data. The integrated image also shows enhanced structural detail, since no part of the surface seismic section is eliminated, and good event continuity through the use of a single migration–velocity model, obtained by an integrated interpretation of borehole and surface seismic data. This enhanced migrated image enabled us to perform a more robust interpretation with good well ties.

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