An inverse ray method for computing geologic structures from seismic reflections—Zero‐offset case

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 268-287 ◽  
Author(s):  
B. T. May ◽  
J. D. Covey
Keyword(s):  
Inverse Modeling ◽  
Fault Model ◽  
Ray Method ◽  
Practical Procedure ◽  
Time Migration ◽  
Rapid Construction ◽  
Interactive Algorithm ◽  
Zero Offset ◽  
The Time Domain ◽  
Seismic Reflections

Seismic interpretation of structures usually involves identifying and mapping marker reflections in the time domain; however, forward modeling has shown that it can be difficult to map the complex reflection images arising from geologic structures. Inverse modeling by ray techniques offers the potential of computing a structure in the depth domain where it is comparatively easy to evaluate a structural target. An interactive algorithm is presented which has its basis in the eikonal equation and results in a practical procedure to compute models with complex geometries and inhomogeneous layers. Input consists of interpreted reflection times from a CDP‐stacked section and spatial velocity functions determined externally to the algorithm. Output is a two‐dimensional (2-D) model having curvilinear reflectors that can terminate within the model, at faults, and at unconformities. Benefits of structural inverse modeling are realized in the rapid construction of models that have velocity fields defined in the depth domain, explicitly accounting for ray curvature and ray kinking. To illustrate the inverse technique, examples of a complex synthetic thrust fault model and a field‐recorded growth fault model are included. The capability to inverse model steeply dipping structures is of particular interest because it completes a full modeling cycle of (1) theoretical prediction that steep‐dip reflections should be observable, (2) processing of field‐recorded CDP trace data to produce interpretable steep‐dip reflections, and finally (3) computation of steep‐dip reflector positions in the depth domain. An interesting benefit is the application of this algorithm to computing image rays on complex structures and the subsequent implications about time migration of CDP‐stacked sections.

Reply by the authors to Arthur E. Barnes

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1944-1946
Author(s):  
M. Tygel ◽  
J. Schleicher ◽  
P. Hubral
Keyword(s):  
Destructive Interference ◽  
Depth Migration ◽  
Time Migration ◽  
Pulse Distortion ◽  
Nmo Correction ◽  
Important Processing ◽  
Offset Time ◽  
Zero Offset ◽  
Seismic Reflections ◽  
Processing Steps

We highly appreciate the useful remarks of Dr. Barnes relating our work to well‐known practical seismic processing effects. This is of particular interest as normal‐moveout (NMO) correction and post‐stack time migration are still two very important processing steps. Most exploration geophysicists know about the significance of pulse distortions known as “NM0 stretch” and “frequency shifting due to zero‐offset time migration.” As a result of the discussion of Dr. Barnes, it should now be possible to better appreciate the importance of our very general formulas (27) describing the pulse distortion of seismic reflections from an arbitrarily curved subsurface reflector when subjected to a prestack depth migration in 3‐D laterally inhomogeneous media. This discussion thus relates in particular to such important questions as how to correctly sample signals in the time or depth domain in order to avoid spatial aliasing, or how to stack seismic data without loss of information due to destructive interference of wavelets of different lengths.

scholarly journals Zero-offset sections with a deblurring filter in the time domain

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S239-S249
Author(s):  
Shihang Feng ◽  
Oz Yilmaz ◽  
Yuqing Chen ◽  
Gerard T. Schuster
Keyword(s):  
Time Domain ◽  
Constant Velocity ◽  
Field Data ◽  
Velocity Model ◽  
Velocity Models ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Zero Offset ◽  
Image Volume ◽  
The Time Domain

The conventional common-midpoint stack is not equivalent to the zero-offset section due to the existence of velocity uncertainty. To obtain a zero-offset reflection section that preserves most reflections and diffractions, we have developed a velocity-independent workflow for reconstructing a high-quality zero-offset reflection section from prestack data with a deblurring filter. This workflow constructs a migration image volume by prestack time migration using a series of constant-velocity models. A deblurring filter for each constant-velocity model is applied to each time-migration image to get a deblurred image volume. To preserve all events in the image volume, each deblurred image panel is demigrated and then summed over the velocity axis. Compared with the workflow without a deblurring filter, the composite zero-offset reflection section has higher resolution and fewer migration artifacts. We evaluate applications of our method to synthetic and field data to validate its effectiveness.

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.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

X-Ray Spectroscopy in the Clinical Laboratory

1959 ◽  
Vol 5 (6) ◽  
pp. 519-531 ◽  
Author(s):  
Samuel Natelson ◽  
Morton R Richelson ◽  
Bertram Sheid ◽  
Stephen L Bender
Keyword(s):  
Filter Paper ◽  
Proportional Counter ◽  
Clinical Laboratory ◽  
Ray Method ◽  
Helium Atmosphere ◽  
X Ray ◽  
Practical Procedure ◽  
Flame Photometer ◽  
Counting Time ◽  
Near Future

Abstract A practical procedure is described for the analysis of ultramicro quantities of serum for calcium and potassium using the x-ray spectrometer. The serum is applied and dried in a confined spot on filter paper. The sample is then exposed to the x-ray field. The Kα lines of these elements are isolated and their intensity measured, with a flow proportional counter in a helium atmosphere. Reproducibility is of the order of ±5% (2σ) for these elements, with an approximately one-minute counting time. The results compare favorably with those obtained with the flame photometer for potassium and the Clark-Collip method for calcium. The x-ray method for calcium is more rapid and simpler than methods generally used in the clinical laboratory. The flame photometer is faster at present, but the instrument is readily automated by placing the serum sample in confined spots on tape. In this form it will probably find routine use for the electrolytes and other elements in the near future.

Improving lateral and vertical resolution of seismic images by correcting for wavelet stretch in common-angle migration

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. C95-C104 ◽  
Author(s):  
Gabriel Perez ◽  
Kurt J. Marfurt
Keyword(s):  
Signal To Noise Ratio ◽  
Incident Angle ◽  
Large Angle ◽  
Acoustic Medium ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Velocity Anisotropy ◽  
Time Migration ◽  
Reflection Angle ◽  
Seismic Reflections

Long-offset or high-incident-angle seismic reflections provide us with improved velocity resolution, better leverage against multiples, less contamination by ground roll, and information that is often critical when estimating lithology and fluid product. Unfortunately, high-incident-angle seismic reflections suffer not only from nonhyperbolic moveout but also from wavelet stretch during imaging, resulting in lower-resolution images that mix the response from adjacent lithologies. For an arbitrary acoustic medium, wavelet stretch from prestack migration depends only on the cosine of the reflection angle, such that the amount of wavelet stretch will be the same for all samples of a common-reflection-angle migrated trace. Thus, we are able to implement a wavelet stretch correction by applying a simple stationary spectral shaping operation to common-angle migrated traces. We obtain such traces directly by a prestack Kirchhoff migration algorithm. Correcting for stretch effectively increases the fold of imaged data, far beyond that achieved in conventional migration, resulting in improved signal-to-noise ratio of the final stacked section. Increasing the fidelity of large incident angles results in images with improved vertical and lateral resolution and with increased angular illumination, valuable for amplitude variation with angle (AVA) and amplitude variation with offset (AVO) analysis. Finally, such large-angle images are more sensitive to and therefore provide increased leverage over errors in velocity and velocity anisotropy. These ideas were applied to prestack time migration on seismic data from the Fort Worth basin, in Texas.

Analyzing operators of 3-D imaging software with impulse responses

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1079-1092 ◽  
Author(s):  
William A. Schneider
Keyword(s):  
Impulse Response ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Impulse Responses ◽  
Step Size ◽  
Data Set ◽  
Time Migration ◽  
Offset Time ◽  
Zero Offset ◽  
Algorithm Implementation

No processing step changes seismic data more than 3-D imaging. Imaging techniques such as 3-D migration and dip moveout (DMO) generally change the position, amplitude, and phase of reflections as they are converted into reflector images. Migration and DMO may be formulated in many different ways, and various algorithms are available for implementing each formulation. These algorithms all make physical approximations, causing imaging software to vary with algorithm choice. Imaging software also varies because of additional implementation approximations, such as those that trade accuracy for efficiency. Imaging fidelity, then, generally depends upon algorithm, implementation, specific software parameters (such as aperture, antialias filter settings, and downward‐continuation step size), specific acquisition parameters (such as nominal x- and y-direction trace spacings and wavelet frequency range), and, of course, the velocity model. Successfully imaging the target usually requires using appropriate imaging software, parameters, and velocities. Impulse responses provide an easy way to quantitatively understand the operators of imaging software and then predict how specific imaging software will perform with the chosen parameters. (An impulse response is the image computed from a data set containing only one nonzero trace and one arrival on that trace.) I have developed equations for true‐amplitude impulse responses of 3-D prestack time migration, 3-D zero‐offset time migration, 3-D exploding‐reflector time migration, and DMO. I use these theoretical impulse responses to analyze the operators of actual imaging software for a given choice of software parameters, acquisition parameters, and velocity model. The procedure is simple: compute impulse responses of some software; estimate position, amplitude, and phase of the impulse‐response events; and plot these against the theoretical values. The method is easy to use and has proven beneficial for analyzing general imaging software and for parameter evaluation with specific imaging software.

Plumes: Response of time migration to lateral velocity variation

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1118-1127 ◽  
Author(s):  
Dimitri Bevc ◽  
James L. Black ◽  
Gopal Palacharla
Keyword(s):  
Impulse Response ◽  
Synthetic Data ◽  
Migration Velocity ◽  
Velocity Variation ◽  
Velocity Dependence ◽  
Geometrical Construction ◽  
Lateral Velocity ◽  
Time Migration ◽  
Offset Time ◽  
Zero Offset

We analyze how time migration mispositions events in the presence of lateral velocity variation by examining the impulse response of depth modeling followed by time migration. By examining this impulse response, we lay the groundwork for the development of a remedial migration operator that links time and depth migration. A simple theory by Black and Brzostowski predicted that the response of zero‐offset time migration to a point diffractor in a v(x, z) medium would be a distinctive, cusp‐shaped curve called a plume. We have constructed these plumes by migrating synthetic data using several time‐migration methods. We have also computed the shape of the plumes by two geometrical construction methods. These two geometrical methods compare well and explain the observed migration results. The plume response is strongly influenced by migration velocity. We have studied this dependency by migrating synthetic data with different velocities. The observed velocity dependence is confirmed by geometrical construction. A simple first‐order theory qualitatively explains the behavior of zero‐offset time migration, but a more complete understanding of migration velocity dependence in a v(x, z) medium requires a higher order finite‐offset theory.

scholarly journals Imaging zero-offset 3-D P-cable data with CRS method

2019 ◽  
Vol 219 (3) ◽  
pp. 1876-1884 ◽  
Author(s):  
M Glöckner ◽  
J Walda ◽  
S Dell ◽  
D Gajewski ◽  
J Karstens ◽  
...  
Keyword(s):  
High Frequency ◽  
Small Amplitude ◽  
Kinematic Wave ◽  
Data Set ◽  
Time Migration ◽  
Seismic Acquisition ◽  
Common Reflection Surface ◽  
Frequency Source ◽  
Zero Offset ◽  
Migration Velocities

SUMMARY Standard seismic acquisition and processing require appropriate source–receiver offsets. P-cable technology represents the opposite, namely, very short source–receiver offsets at the price of increased spatial and lateral resolution with a high-frequency source. To use this advantage, a processing flow excluding offset information is required. This aim can be achieved with a processing tuned to diffractions because point diffractions scatter the same information in the offset and midpoint direction. Usually, diffractions are small amplitude events and a careful diffraction separation is required as a first step. We suggest the strategy to use a multiparameter stacking operator, for example, common-reflection surface, and stack along the midpoint direction. The obtained kinematic wave-front attributes are used to calculate time-migration velocities. A diffractivity map serves as a filter to refine the velocities. This strategy is applied to a 3-D P-cable data set to obtain a time-migrated image.

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