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.

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.

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.

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.

t-x reflection curves for arbitrary three‐dimensional media in terms of geometry of a reflector and a near‐reflector wavefront

Geophysics ◽  
1986 ◽  
Vol 51 (10) ◽  
pp. 1912-1922
Author(s):  
G. Nedlin
Keyword(s):  
General Relation ◽  
Three Dimensional ◽  
Earth Model ◽  
Arrival Times ◽  
Geometrical Properties ◽  
Parametric Description ◽  
Time Offset ◽  
Zero Offset ◽  
New Formulation ◽  
Reflecting Surface

A general relation between a normal‐moveout velocity (NMOV) for t-x (time‐offset) reflection curves and the geometrical properties of a reflector and a wavefront in the vicinity of the reflector has been found. Furthermore, by considering the reflector as a set of zero‐offset reflecting points for different shot locations on the earth’s surface, a new formulation of the special “seismic” parametric description of a reflecting surface allows the arrival times to be related directly to the wavefront equation, without introducing any earth model above the reflector. The NMOV is expressed in terms of the local velocity near the reflector and the curvatures of the reflector and of the near‐reflector wavefront. New equations for geometrical migration make it possible to do direct wavefront modeling without earth modeling (above the reflector). If t-x curves are approximated by hyperbolas (i.e., terms higher than those quadratic in the offsets are neglected), all rays in a common‐midpoint (CMP) panel with a fixed midpoint have the same reflecting point, for any earth model.

The nonuniqueness of the determination of interval velocities from moveout velocities

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1209-1211 ◽  
Author(s):  
Theodor C. Krey
Keyword(s):  
Seismic Profile ◽  
Layered Earth ◽  
Interval Velocity ◽  
Offset Time ◽  
Zero Offset ◽  
Interval Velocities

In earlier papers (Krey, 1976; Hubral and Krey, 1980) I described how to obtain an equation for [Formula: see text], the nth interval velocity in an isovelocity layered earth having interfaces with arbitrary dips and curvatures, provided the velocities [Formula: see text], [Formula: see text], … to [Formula: see text] for the first n − 1 layers and the depths of the first n − 1 interfaces [Formula: see text], K = 1, 2, …, n − 1, are known and have continuous derivatives. Moreover, we assume that the zero‐offset time for the reflection from the base of the nth layer and gradient of the traveltime with respect to the horizontal coordinates are known. Finally, the normal moveout (NMO) velocity [Formula: see text] for the nth interface is observed in one arbitrary azimuth (one only), defined by ϕ, the angle between the x‐axis and the seismic profile.

Geometrical spreading corrections of offset reflections in a laterally inhomogeneous earth

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 1054-1063 ◽  
Author(s):  
M. Tygel ◽  
J. Schleicher ◽  
P. Hubral
Keyword(s):  
Three Dimensional ◽  
Velocity Model ◽  
Earth Model ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Depth Migration ◽  
Avo Analysis ◽  
Amplitude Versus Offset ◽  
One Step

Compressional primary seismic nonzero offset reflections are the most essential wavefield attributes used in seismic parameter estimation and imaging. We show how the determination of angle‐dependent reflection coefficients can be addressed from identifying such events for arbitrarily curved three‐dimensional (3-D) subsurface reflectors below a laterally inhomogeneous layered overburden. More explicitly, we show how the geometrical‐spreading factor along a reflected primary ray with offset can be calculated from the identified (i.e., picked) traveltimes of offset primary reflections. Seismic traces in which all primary reflections are corrected with the geometrical‐spreading factor are, as is well‐known, referred to as true‐amplitude traces. They can be constructed without any knowledge of the velocity distribution in the earth model. Apart from possibly finding a direct application in an amplitude‐versus‐offset (AVO) analysis, the theory developed here can be of use to derive true‐amplitude time‐ and depth‐migration methods for various seismic data acquisition configurations, which pursue the aim of performing the wavefield migration (based upon the use of a macro‐velocity model) and the AVO analysis in one step.

scholarly journals The use of the model for determining potato (Solanum tuberosum L.) tuber distribution in the soil

2017 ◽  
Vol 109 (2) ◽  
pp. 425
Author(s):  
Jošt Potrpin ◽  
Uroš Benec ◽  
Rajko Bernik ◽  
Bojan Gospodarič
Keyword(s):  
Laboratory Testing ◽  
Solanum Tuberosum L ◽  
Accurate Determination ◽  
Three Dimensional ◽  
Calculated Data ◽  
Field Measurements ◽  
Potato Tubers ◽  
Left And Right ◽  
Key Parameter

<span lang="EN-US">The paper focuses on the testing of a model for determining the distribution of potato tubers in the soil. Analytical testing of the model was performed at the laboratory of the Biotechnological Faculty (University in Ljubljana) in 2015 and in the same year, the model was tested in practice on a field owned by the company Zeleni Hit d.o.o. in Ljubljana. After the laboratory testing, the results were analyzed and additional steps were taken to expedite field measurements. To optimize the determination of the distribution of potato tubers in the soil, the program was upgraded to include three-dimensional data acquisition. This allows accurate determination of the horizontal, vertical and longitudinal spans of the distribution of tubers in the soil. Specifically, the program calculates the shape of the tubers, vertical cover of tubers with soil and their minimum distance from the left and right edges of the ridge. The program also locates the center of the tubers, which is a key parameter (along with tuber mass) for determining the area of the tuber cluster. The laboratory testing of the model revealed successful data processing of the program and adequate precision analytics. The testing of the model in the field on Arizona potato variety revealed that the model includes all the data necessary for further processing. Based on the calculated data, it can be assumed with great certainty that the model enables the acquisition of all necessary data and accurately determines the distribution of potato tubers in the soil, ideal shape of the ridge and the minimum necessary depth and distance for the planting of Arizona seed potatoes.</span>

Minimum apertures and Fresnel zones in migration and demigration

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 183-194 ◽  
Author(s):  
Jörg Schleicher ◽  
Peter Hubral ◽  
Martin Tygel ◽  
Makky S. Jaya
Keyword(s):  
Fresnel Zone ◽  
Prestack Migration ◽  
Common Opinion ◽  
Correct Determination ◽  
The Common ◽  
The Cost ◽  
Fresnel Zones ◽  
Selection Of

The size of the aperture has an important influence on the results of (Kirchhoff‐type) migration and demigration. For true‐amplitude imaging, it is crucial not to have apertures below a certain size. For both the minimum migration and demigration apertures, theoretical expressions are established. Both minimum apertures depend on each other and, although a time‐domain concept, are closely related to the frequency‐dependent Fresnel zone on the searched‐for subsurface reflector. This relationship sheds new light on the role of Fresnel zones in the seismic imaging of subsurface reflectors by showing that Fresnel zones are not only important in resolution studies but also for the correct determination of migration amplitudes. It further helps to better understand the intrinsic interconnection between prestack migration and demigration as inverse procedures of the same type. In contrast to the common opinion that it is always the greatest possible aperture that yields the best signal‐to‐noise enhancement, it is in fact the selection of a minimum aperture that should be desired in order to (a) enhance the computational efficiency and reduce the cost of the summation, (b) improve the image quality by minimizing the noise on account of summing the smallest number of traces, and (c) to have a better control over boundary effects. This paper demonstrates these features rather than addressing the question of how to achieve them technically.

Three‐dimensional true‐amplitude zero‐offset migration

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Peter Hubral ◽  
Martin Tygel ◽  
Holger Zien
Keyword(s):  
Time Derivative ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Earth Model ◽  
Ray Theory ◽  
Transmission Losses ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Time Migration ◽  
Zero Offset

The primary zero‐offset reflection of a point source from a smooth reflector within a laterally inhomogeneous velocity earth model is (within the framework of ray theory) defined by parameters pertaining to the normal‐incidence ray. The geometrical‐spreading factor—usually computed along the ray by dynamic‐ray tracing in a forward‐modeling approach—can, in this case, be recovered from traveltime measurements at the surface. As a consequence, zero‐offset reflections can be time migrated such that the geometrical‐spreading factor for the normal‐incidence ray is removed. This leads to a so‐called “true‐amplitude time migration.” In this work, true‐amplitude time‐migrated reflections are obtained by nothing more than a simple diffraction stack essentially followed by a time derivative of the diffraction‐stack traces. For small transmission losses of primary zero‐offset reflections through intermediate‐layer boundaries, the true‐amplitude time‐migrated reflection provides a direct measure of the reflection coefficient at the reflecting lower end of the normal‐incidence ray. The time‐migrated field can be easily transformed into a depth‐migrated field with the help of image rays.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

Sign in / Sign up

Export Citation Format

Share Document