Fresnel zones in the light of broadband data

Geophysics ◽  
1991 ◽  
Vol 56 (3) ◽  
pp. 354-359 ◽  
Author(s):  
R. W. Knapp
Keyword(s):  
Seismic Response ◽  
Edge Effects ◽  
Seismic Data ◽  
Fresnel Zone ◽  
Vertical Resolution ◽  
Zone Size ◽  
Small Bodies ◽  
Lateral Offset ◽  
Zero Offset ◽  
Fresnel Zones

The investigation of zero‐offset response to circular reflectors of increasing Fresnel zone size shows that reflection response is a constant and is independent of reflector size, except when the reflector diameter is so small that the diffractions interfere with the primary reflection. The extent of this effect is dependent upon vertical resolution and the time separation of the primary reflector and the diffraction. Interference occurs for reflectors smaller in diameter than the first Fresnel zone. Migration removes this interference. For broadband data the Fresnel zone solution breaks into two parts: the primary reflector and the edge‐effects diffractor. With broadband seismic data, reflections and diffractions separate in time, except at locations near faults or very small bodies. Reflections are the seismic response to interlayer discontinuity and are independent of reflector size. Diffractions are the seismic response to lateral discontinuities and edges and depend on proximity to—and geometry of—the edge. Except in the locale of an edge, broadband reflections and diffractions are separated physically on the section and mentally by the interpreter. Furthermore, standard CMP processing attenuates diffractions, especially when CMP lateral offset is some distance from the diffractor.

scholarly journals Study on the Velocity Analysis Method of Low SNR Seismic Data

2021 ◽  
Vol 11 (1) ◽  
pp. 78
Author(s):  
Jianbo He ◽  
Zhenyu Wang ◽  
Mingdong Zhang
Keyword(s):  
Seismic Data ◽  
Fresnel Zone ◽  
Signal To Noise Ratio ◽  
Normal Wave ◽  
Curvature Radius ◽  
Velocity Spectrum ◽  
Velocity Analysis ◽  
Signal To Noise ◽  
Noise Ratio ◽  
Zero Offset

When the signal to noise ratio of seismic data is very low, velocity spectrum focusing will be poor., the velocity model obtained by conventional velocity analysis methods is not accurate enough, which results in inaccurate migration. For the low signal noise ratio (SNR) data, this paper proposes to use partial Common Reflection Surface (CRS) stack to build CRS gathers, making full use of all of the reflection information of the first Fresnel zone, and improves the signal to noise ratio of pre-stack gathers by increasing the number of folds. In consideration of the CRS parameters of the zero-offset rays emitted angle and normal wave front curvature radius are searched on zero offset profile, we use ellipse evolving stacking to improve the zero offset section quality, in order to improve the reliability of CRS parameters. After CRS gathers are obtained, we use principal component analysis (PCA) approach to do velocity analysis, which improves the noise immunity of velocity analysis. Models and actual data results demonstrate the effectiveness of this method.

Fresnel-zone binning: Fresnel-zone shape with offset and velocity function

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. T9-T14 ◽  
Author(s):  
David J. Monk
Keyword(s):  
Velocity Gradient ◽  
Constant Velocity ◽  
Fresnel Zone ◽  
Geometric Approach ◽  
Velocity Function ◽  
Zero Offset ◽  
Limiting Case ◽  
Fresnel Zones

The concept of the Fresnel zone has been explored by many workers; most commonly, their work has involved examining the Fresnel zone in the limiting case of zero offset and constant velocity. I have examined the shape of the Fresnel zone for nonzero offset and in the situation of constant velocity gradient. Finite-offset Fresnel zones are not circular but are elliptical and may be many times larger than their zero-offset equivalents. My derivation takes a largely geometric approach, and I suggest a useful approximation for the dimension of the Fresnel zone parallel to the shot-receiver azimuth. The presence of a velocity gradient (velocity increasing with depth) in the subsurface leads to an expansion of the Fresnel zone to an area that is far larger than may be determined through a more usual straight-ray determination.

Vertical resolution of a seismic survey in stratigraphic sequences less than 100 m deep in southeastern Kansas

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 423-430 ◽  
Author(s):  
Richard D. Miller ◽  
Neil L. Anderson ◽  
Howard R. Feldman ◽  
Evan K. Franseen
Keyword(s):  
Seismic Data ◽  
Fresnel Zone ◽  
Drill Hole ◽  
Seismic Profile ◽  
Dominant Frequency ◽  
Seismic Survey ◽  
Vertical Resolution ◽  
Resolution Limit ◽  
Reflection Seismic ◽  
Quarter Wavelength

A 400-m long, 12‐fold high‐resolution common depth point (CDP) reflection seismic profile was acquired across shallow converging Pennsylvanian strata in the Independence area of southeastern Kansas. One of the principal objectives was to determine practical vertical resolution limits in an excellent shallow seismic‐data area with borehole control. The dominant frequency of the CDP stacked data is in excess of 150 Hz based on peak‐to‐peak measurements. Interference phenomena observed on stacked seismic data incorporated with models derived from log and drill‐hole information suggest a practical vertical resolution limit of about 7 m, or one‐third of the dominant wavelength. This practical resolution is slightly less than the predicted (theoretical) resolution limit of 5 m based on the generally accepted one‐quarter wavelength axiom. These data suggest conventional rules of thumb describing resolution potential are not accurate when reflectors on shallow, narrow bandwidth data converge rapidly across horizontal distances less than the Fresnel Zone.

Determination of Fresnel zones from traveltime measurements

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 703-712 ◽  
Author(s):  
Peter Hubral ◽  
Jörg Schleicher ◽  
Martin Tygel ◽  
Ch. Hanitzsch
Keyword(s):  
Fresnel Zone ◽  
Three Dimensional ◽  
Earth Model ◽  
Simple Method ◽  
Interval Velocity ◽  
Stratigraphic Analysis ◽  
Zero Offset ◽  
Fresnel Zones ◽  
Key Parameter

For a horizontally stratified (isotropic) earth, the rms‐velocity of a primary reflection is a key parameter for common‐midpoint (CMP) stacking, interval‐velocity computation (by the Dix formula) and true‐amplitude processing (geometrical‐spreading compensation). As shown here, it is also a very desirable parameter to determine the Fresnel zone on the reflector from which the primary zero‐offset reflection results. Hence, the rms‐velocity can contribute to evaluating the resolution of the primary reflection. The situation that applies to a horizontally stratified earth model can be generalized to three‐dimensional (3-D) layered laterally inhomogeneous media. The theory by which Fresnel zones for zero‐offset primary reflections can then be determined purely from a traveltime analysis—without knowing the overburden above the considered reflector—is presented. The concept of a projected Fresnel zone is introduced and a simple method of its construction for zero‐offset primary reflections is described. The projected Fresnel zone provides the image on the earth’s surface (or on the traveltime surface of primary zero‐offset reflections) of that part of the subsurface reflector (i.e., the actual Fresnel zone) that influences the considered reflection. This image is often required for a seismic stratigraphic analysis. Our main aim is therefore to show the seismic interpreter how easy it is to find the projected Fresnel zone of a zero‐offset reflection using nothing more than a standard 3-D CMP traveltime analysis.

scholarly journals Model studies of shallow common‐offset seismic data

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 394-401 ◽  
Author(s):  
Thomas H. Wilson
Keyword(s):  
Seismic Response ◽  
Seismic Data ◽  
Acoustic Properties ◽  
Seismic Reflection Data ◽  
Near Surface ◽  
Model Studies ◽  
Reflection Data ◽  
Full Waveform ◽  
Geophysical Logs ◽  
Zero Offset

For simplicity, optimum‐window common‐offset data‐acquisition procedures are frequently employed to collect near‐surface, high‐resolution, seismic reflection data. However, because of large incidence angles, interpretations of the data often cannot be evaluated accurately using zero‐offset simulations alone. Common‐offset hammer seismic data collected in the central Appalachian plateau province of West Virginia are examined in this paper. Synthetic shot records using a minimum‐phase wavelet estimated from the data and subsurface acoustic properties derived from full‐waveform and other geophysical logs are used to simulate the offset seismic response of near‐surface, coal‐bearing Pennsylvanian aged rocks. Zoeppritz equations are used to model amplitudes. This study indicates that offset simulations may be required to determine the origins of events observed at a given offset. Offset simulations also help determine whether amplitude variations with offset have a significant effect on the appearance of events observed at the optimum offset. The offset seismic response is significantly different from the zero‐offset response for reflections arising from depths less than about two‐thirds of the offset distance; for greater depths, zero‐offset simulations adequately approximate the offset response.

A method of ground‐roll elimination

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 894-902 ◽  
Author(s):  
Ruhi Saatçilar ◽  
Nezihi Canitez
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Wave Motion ◽  
Frequency Interval ◽  
Vertical Resolution ◽  
Matched Filters ◽  
One Dimensional ◽  
Frequency Bands ◽  
Ground Roll ◽  
Seismic Reflections

Amplitude‐ and frequency‐modulated wave motion constitute the ground‐roll noise in seismic reflection prospecting. Hence, it is possible to eliminate ground roll by applying one‐dimensional, linear frequency‐modulated matched filters. These filters effectively attenuate the ground‐roll energy without damaging the signal wavelet inside or outside the ground roll’s frequency interval. When the frequency bands of seismic reflections and ground roll overlap, the new filters eliminate the ground roll more effectively than conventional frequency and multichannel filters without affecting the vertical resolution of the seismic data.

2-D continuation operators and their applications

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1846-1858 ◽  
Author(s):  
Claudio Bagaini ◽  
Umberto Spagnolini
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Integral Form ◽  
Amplitude Distribution ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Seismic Data Processing ◽  
Analysis Method ◽  
Standard Tool ◽  
Zero Offset

Continuation to zero offset [better known as dip moveout (DMO)] is a standard tool for seismic data processing. In this paper, the concept of DMO is extended by introducing a set of operators: the continuation operators. These operators, which are implemented in integral form with a defined amplitude distribution, perform the mapping between common shot or common offset gathers for a given velocity model. The application of the shot continuation operator for dip‐independent velocity analysis allows a direct implementation in the acquisition domain by exploiting the comparison between real data and data continued in the shot domain. Shot and offset continuation allow the restoration of missing shot or missing offset by using a velocity model provided by common shot velocity analysis or another dip‐independent velocity analysis method.

Three‐dimensional primary zero‐offset reflections

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 692-702 ◽  
Author(s):  
Peter Hubral ◽  
Jorg Schleicher ◽  
Martin Tygel
Keyword(s):  
Ray Tracing ◽  
Large Scale ◽  
Initial Conditions ◽  
Fresnel Zone ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Careful Analysis ◽  
Point Sources ◽  
Dynamic Ray Tracing ◽  
Zero Offset

Zero‐offset reflections resulting from point sources are often computed on a large scale in three‐dimensional (3-D) laterally inhomogeneous isotropic media with the help of ray theory. The geometrical‐spreading factor and the number of caustics that determine the shape of the reflected pulse are then generally obtained by integrating the so‐called dynamic ray‐tracing system down and up to the two‐way normal incidence ray. Assuming that this ray is already known, we show that one integration of the dynamic ray‐tracing system in a downward direction with only the initial condition of a point source at the earth’s surface is in fact sufficient to obtain both results. To establish the Fresnel zone of the zero‐offset reflection upon the reflector requires the same single downward integration. By performing a second downward integration (using the initial conditions of a plane wave at the earth’s surface) the complete Fresnel volume around the two‐way normal ray can be found. This should be known to ascertain the validity of the computed zero‐offset event. A careful analysis of the problem as performed here shows that round‐trip integrations of the dynamic ray‐tracing system following the actually propagating wavefront along the two‐way normal ray need never be considered. In fact some useful quantities related to the two‐way normal ray (e.g., the normal‐moveout velocity) require only one single integration in one specific direction only. Finally, a two‐point ray tracing for normal rays can be derived from one‐way dynamic ray tracing.

Transformation to zero offset for mode‐converted waves

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 474-477 ◽  
Author(s):  
Mohammed Alfaraj ◽  
Ken Larner
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Reflection Point ◽  
P Waves ◽  
S Waves ◽  
Nmo Correction ◽  
Converted Waves ◽  
Zero Offset ◽  
Correct Data

The transformation to zero offset (TZO) of prestack seismic data for a constant‐velocity medium is well understood and is readily implemented when dealing with either P‐waves or S‐waves. TZO is achieved by inserting a dip moveout (DMO) process to correct data for the influence of dip, either before or after normal moveout (NMO) correction (Hale, 1984; Forel and Gardner, 1988). The TZO process transforms prestack seismic data in such a way that common‐midpoint (CMP) gathers are closer to being common reflection point gathers after the transformation.

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