Allon Bartana

Full-Azimuth Angle Domain Imaging

This work presents a new seismic imaging system for generating and extracting high-resolution information about subsurface angle dependent reflectivity, with simultaneous emphasis on both continuous structural surfaces and discontinuous objects, such as faults and small-scale fractures. The system enables full-azimuth, angledependent seismic imaging using reflection data recorded through seismic acquisition surveys, especially wideazimuth and long offset data. Geometrical attributes, such as dip-azimuth and continuity of the local reflecting surfaces, can be automatically extracted directly from the full-azimuth angle gathers. Azimuthal anisotropy can be detected, leading to an accurate anisotropy model representation.

Discussion and Reply

Sava and Fomel (2003) present an original approach for the generation of angle-domain common-image gathers (CIGs) by wave-equation migration. Their procedure consists of two steps. First, local-offset gathers are created during the migration. Second, depth-migrated angle gathers are generated by applying a slant stack to the local-offset gathers. Angle-domain gathers are very important for velocity analysis and amplitude versus offset (AVO) studies. Unfortunately, we believe that the procedure outlined in the article does not yield correct angle gathers when there are velocity errors. In the following, this is demonstrated for the simplest example of a single horizontal reflector embedded in a uniform-velocity medium.

Automatic Picking of Delays On 3D Angle Gathers

Migrated gathers are a key input for velocity model building and for subsurface characterization. Kinematic information is used for velocity model updates, and amplitude and phase attributes are used for the derivation of material properties. Conventional gathers are two dimensional: a vertical axis that is either time, time migrated or depth, and a horizontal axis that can be offset, or angle in the depth migrated domain. With wide azimuth acquisition the gathers are 3D by nature. The additional horizontal axis is the azimuth angle. The importance of the azimuthal information for short wavelength velocity determination has been demonstrated theoretically (Bartana et. al., 2009). The naive way of describing the 3D gathers is by a set of azimuth sectors, where the offsets or angles are binned at each azimuthal sector. In other words, the separation for azimuth sectors treats the 3D gather as a set of multi 2D gathers. In this work we show a different approach, in which the azimuthal information is represented in a continuous manner for the purpose of delay analysis. The method for representing the 3D angle gather and the delay analysis performed in this domain are described. The method is demonstrated on a synthetic example and on field data.

On “Angle-domain common-image gathers by wavefield continuation methods” (Paul C. Sava and Sergey Fomel, 2003, GEOPHYSICS, 68, 1065–1074)

Sava and Fomel (2003) present an original approach for the generation of angle-domain common-image gathers (CIGs) by wave-equation migration. Their procedure consists of two steps. First, local-offset gathers are created during the migration. Second, depth-migrated angle gathers are generated by applying a slant stack to the local-offset gathers. Angle-domain gathers are very important for velocity analysis and amplitude versus offset (AVO) studies. Unfortunately, we believe that the procedure outlined in the article does not yield correct angle gathers when there are velocity errors. In the following, this is demonstrated for the simplest example of a single horizontal reflector embedded in a uniform-velocity medium.

Resolution of Small Velocity Anomalies by Wide Azimuth Reflection Data Tomography

In this study we examine the capability of multi azimuth acquisition in resolving small velocity anomalies by means of a 3D synthetic example. The model consists of a layered structure which contains two small velocity anomalies. The study compares the resolution when the migrated gathers contain no azimuthal information to the case when the gathers are binned both according to offset and azimuth. The results show that conventional gathers can only obtain a blurred image of the velocity anomalies, whereas with multi azimuth gathers the velocity anomalies appear distinctly.

Three dimensional wave equation depth migration by a direct solution method

We propose a new method for wave equation depth migration which is carried out by depth stepping in the space-temporal frequency domain. The propagation of the solution is based on a rational expansion of the formal solution to the acoustic wave equation. The expansion coefficients are calculated by a filter design approach. The method is not based on one way wave equations or on perturbations to constant velocity solutions to the wave equation, but rather it uses the constant density variable velocity wave equation as the basis. The method has a good steep dip response and can handle strong lateral variations in the subsurface velocity. The new method is tested against the Sigsbee data set and the 3D SEG salt model.

Discussion and Reply: On “Angle-domain common-image gathers by wavefield continuation methods” (Paul C. Sava and Sergey Fomel, 2003, GEOPHYSICS, 68, 1065–1074)

Sava and Fomel (2003) present an original approach for the generation of angle-domain common-image gathers (CIGs) by wave-equation migration. Their procedure consists of two steps. First, local-offset gathers are created during the migration. Second, depth-migrated angle gathers are generated by applying a slant stack to the local-offset gathers. Angle-domain gathers are very important for velocity analysis and amplitude versus offset (AVO) studies. Unfortunately, we believe that the procedure outlined in the article does not yield correct angle gathers when there are velocity errors. In the following, this is demonstrated for the simplest example of a single horizontal reflector embedded in a uniform-velocity medium.

On “Angle-domain common-image gathers by wavefield continuation methods” (Paul C. Sava and Sergey Fomel, 2003, GEOPHYSICS, 68, 1065–1074)Discussion and Reply

Sava and Fomel (2003) present an original approach for the generation of angle-domain common-image gathers (CIGs) by wave-equation migration. Their procedure consists of two steps. First, local-offset gathers are created during the migration. Second, depth-migrated angle gathers are generated by applying a slant stack to the local-offset gathers. Angle-domain gathers are very important for velocity analysis and amplitude versus offset (AVO) studies. Unfortunately, we believe that the procedure outlined in the article does not yield correct angle gathers when there are velocity errors. In the following, this is demonstrated for the simplest example of a single horizontal reflector embedded in a uniform-velocity medium.

Limitations of the exploding reflector model in sub‐salt imaging

The exploding reflector model has been the basis for wave equation post stack migration. It enables imaging of zero offset data with one downward continuation step, as opposed to the multiple downward continuation steps required in pre-stack migration. However, the exploding reflector model does not account for reflections for which the corresponding down-going ray path differs from the upgoing ray path. By means of a synthetic example which includes a high velocity inclusion, different alternatives for imaging of zero offset data are tested. The results show that the restriction to identical down-going and up-going ray paths causes discontinuities in the image of reflectors in regions beneath the high velocity inclusion. The limitations of the exploding reflector can be overcome by using multi arrival Kirchhoff migration, or for wave equation imaging, using pre-stack migration algorithms for the imaging of post-stack data. Both alternatives require an economic price.