Zero Offset For Ramp Inputs

1988 ◽  
pp. 227
Keyword(s):  
Zero Offset

DIVERGENCE EFFECTS IN A LAYERED EARTH

Geophysics ◽  
1973 ◽  
Vol 38 (3) ◽  
pp. 481-488 ◽  
Author(s):  
P. Newman
Keyword(s):  
Normal Incidence ◽  
Wave Theory ◽  
Diagnostic Value ◽  
Earth Model ◽  
Correction Factors ◽  
Amplitude Correction ◽  
Multiple Attenuation ◽  
Seismic Recording ◽  
Zero Offset ◽  
Special Case

Of the various factors which influence reflection amplitudes in a seismic recording, divergence effects are possibly of least direct interest to the interpreter. Nevertheless, proper compensation for these effects is mandatory if reflection amplitudes are to be of diagnostic value. For an earth model consisting of horizontal, isotropic layers, and assuming a point source, we apply ray theory to determine an expression for amplitude correction factors in terms of initial incidence, source‐receiver offset, and reflector depth. The special case of zero offset yields an expression in terms of two‐way traveltime, velocity in the initial layer, and the time‐weighted rms velocity which characterizes reflections. For this model it follows that information which is needed for divergence compensation in the region of normal incidence is available from the customary analysis of normal moveout (NMO). It is hardly surprising that NMO and divergence effects are intimately related when one considers the expanding wavefront situation which is responsible for both phenomena. However, it is evident that an amplitude correction which is appropriate for the primary reflection sequence cannot in general be appropriate for the multiples. At short offset distances the disparity in displayed amplitude varies as the square of the ratio of primary to multiple rms velocities, and favors the multiples. These observations are relevant to a number of concepts which are founded upon plane‐wave theory, notably multiple attenuation processes and record synthesis inclusive of multiples.

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

Analysis of the spectral hole in velocity versus depth resolution for reflection traveltimes with limited aperture

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U37-U45 ◽  
Author(s):  
Kenneth P. Bube ◽  
Robert T. Langan ◽  
Tamas Nemeth
Keyword(s):  
Taylor Expansion ◽  
Depth Resolution ◽  
Theoretical Explanation ◽  
Velocity Versus ◽  
Angle Of Incidence ◽  
Vertical Variation ◽  
Spectral Hole ◽  
Maximum Angle ◽  
Zero Offset ◽  
Horizontal Wavelength

It is difficult to resolve the ambiguity between velocity and reflector depth using reflection traveltimes when the aperture is small, as is common for deep reflectors. For velocity perturbations that are independent of the vertical variable, there is an even stronger velocity-versus-depth ambiguity at a horizontal wavelength of 2.5 times the reflector depth. We give a theoretical explanation of why this spectral hole occurs. When the maximum offset is small, there are velocity and reflector depth perturbations that cause almost cancelling traveltime perturbations; the net traveltime perturbations are second order in offset, making resolution between velocity and depth difficult at all wavelengths. But for the particular wavelength [Formula: see text] ≈ 2.565 times the reflector depth, an extra term in the Taylor expansion for traveltime near zero offset vanishes; the net traveltime perturbations are fourth order in offset. Thus velocity-versus-depth resolution degrades much sooner at this wavelength as the maximum offset gets small. We show in addition that this behavior extends to velocity perturbations that can depend on the vertical variable, and spectral holes in velocity-versus-depth resolution can appear at any horizontal wavelength. Velocity perturbations with very simple vertical variation are sufficient to create these spectral holes. This behavior is not limited to extremely small apertures; the effect of this spectral hole can be felt when the maximum angle of incidence is as large as 25°.

Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C171-C180 ◽  
Author(s):  
Qifan Liu ◽  
Ilya Tsvankin
Keyword(s):  
Parameter Estimation ◽  
Subsurface Layer ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Waves ◽  
Additional Information ◽  
Reflection Data ◽  
Anisotropic Layers ◽  
Zero Offset ◽  
Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

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