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.

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.

A convenient approach for the determination of multiple trace BPs using an in-syringe-assisted solid phase microextraction system packed with elastic spongy graphene rods coupled with HPLC

2017 ◽  
Vol 9 (18) ◽  
pp. 2673-2681 ◽  
Author(s):  
Lingling Wang ◽  
Qi Li ◽  
Lei Zhang
Keyword(s):  
Hydrothermal Method ◽  
Environmental Samples ◽  
Solid Phase Microextraction ◽  
Solid Phase ◽  
Three Dimensional ◽  
Convenient Approach ◽  
One Step

An elastic cylindrical three-dimensional porous spongy graphene rod (3D-PSGR) was synthesized by a facile one-step hydrothermal method and applied in a syringe system as a solid phase adsorbent for the extraction of nine trace bisphenol analogs (BPs) from environmental samples.

3-D true‐amplitude finite‐offset migration

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1112-1126 ◽  
Author(s):  
Jorg Schleicher ◽  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Weight Function ◽  
A Priori ◽  
Three Dimensional ◽  
Reflection Coefficients ◽  
Ray Theory ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Prestack Migration ◽  
The One ◽  
Paraxial Ray

Compressional primary nonzero offset reflections can be imaged into three‐dimensional (3-D) time or depth‐migrated reflections so that the migrated wavefield amplitudes are a measure of angle‐dependent reflection coefficients. Various migration/inversion algorithms involving weighted diffraction stacks recently proposed are based on Born or Kirchhoff approximations. Here a 3-D Kirchhoff‐type prestack migration approach is proposed where the primary reflections of the wavefields to be imaged are a priori described by the zero‐order ray approximation. As a result, the principal issue in the attempt to recover angle‐dependent reflection coefficients becomes the removal of the geometrical spreading factor of the primary reflections. The weight function that achieves this aim is independent of the unknown reflector and correctly accounts for the recovery of the source pulse in the migrated image irrespective of the source‐receiver configurations employed and the caustics occurring in the wavefield. Our weight function, which is computed using paraxial ray theory, is compared with the one of the inversion integral based on the Beylkin determinant. It differs by a factor that can be easily explained.

Fast and accurate dynamic raytracing in heterogeneous media

1990 ◽  
Vol 80 (5) ◽  
pp. 1284-1296
Author(s):  
Claude F. Lafond ◽  
Alan R. Levander
Keyword(s):  
Shooting Method ◽  
Heterogeneous Media ◽  
Velocity Model ◽  
Travel Times ◽  
Complex Velocity ◽  
Geometrical Spreading ◽  
Imaging Condition ◽  
Depth Migration ◽  
Velocity Models ◽  
Complex Velocity Model

Abstract We have developed a fast and accurate dynamic raytracing method for 2.5-D heterogeneous media based on the kinematic algorithm proposed by Langan et al. (1985). This algorithm divides the model into cells of constant slowness gradient, and the positions, directions, and travel times of the rays are expressed as polynomials of the travel path length, accurate to the second other in the gradient. This method is efficient because of the use of simple polynomials at each raytracing step. We derived similar polynomial expressions for the dynamic raytracing quantities by integrating the raytracing system and expanding the solutions to the second order in the gradient. This new algorithm efficiently computes the geometrical spreading, amplitude, and wavefront curvature on individual rays. The two-point raytracing problem is solved by the shooting method using the geometrical spreading. Paraxial corrections based on the wavefront curvature improve the accuracy of the travel time and amplitude at a given receiver. The computational results for two simple velocity models are compared with those obtained with the SEIS83 seismic modeling package (Cerveny and Psencik, 1984); this new method is accurate for both travel times and amplitudes while being significantly faster. We present a complex velocity model that shows that the algorithm allows for realistic models and easily computes rays in structures that pose difficulties for conventional methods. The method can be extended to raytracing in 3-D heterogeneous media and can be used as a support for a Gaussian beam algorithm. It is also suitable for computing the Green's function and imaging condition needed for prestack depth migration.

One-step synthesis of isoreticular metal–organic framework-8 derived hierarchical porous carbon and its application in differential pulse anodic stripping voltammetric determination of Pb(ii)

RSC Advances ◽  
2015 ◽  
Vol 5 (94) ◽  
pp. 77159-77167 ◽  
Author(s):  
Lili Xiao ◽  
Shenghai Zhou ◽  
Guangzhi Hu ◽  
Hongbo Xu ◽  
Yi Wang ◽  
...  
Keyword(s):  
Metal Organic Framework ◽  
Three Dimensional ◽  
Differential Pulse ◽  
Bet Surface Area ◽  
Hierarchical Porous Carbon ◽  
Hierarchical Porous ◽  
Anodic Stripping ◽  
Metal Organic ◽  
One Step

A novel electrochemical sensor for Pb(ii) was constructed based on an IRMOF-8-derived NPC with three-dimensional hierarchy of micro-, meso-, and macropores (BET surface area = 1715 m2 g−1).

2.5-D true‐amplitude Kirchhoff migration to zero offset in laterally inhomogeneous media

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 557-573 ◽  
Author(s):  
Martin Tygel ◽  
Jörg Schleicher ◽  
Peter Hubral ◽  
Lúcio T. Santos
Keyword(s):  
Seismic Source ◽  
Velocity Model ◽  
Dynamic Effects ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Seismic Section ◽  
Kirchhoff Migration ◽  
Reflection Angle ◽  
Earth Models ◽  
Zero Offset

The proposed new Kirchhoff‐type true‐amplitude migration to zero offset (MZO) for 2.5-D common‐offset reflections in 2-D laterally inhomogeneous layered isotropic earth models does not depend on the reflector curvature. It provides a transformation of a common‐offset seismic section to a simulated zero‐offset section in which both the kinematic and main dynamic effects are accounted for correctly. The process transforms primary common‐offset reflections from arbitrary curved interfaces into their corresponding zero‐offset reflections automatically replacing the geometrical‐spreading factor. In analogy to a weighted Kirchhoff migration scheme, the stacking curve and weight function can be computed by dynamic ray tracing in the macro‐velocity model that is supposed to be available. In addition, we show that an MZO stretches the seismic source pulse by the cosine of the reflection angle of the original offset reflections. The proposed approach quantitatively extends the previous MZO or dip moveout (DMO) schemes to the 2.5-D situation.

scholarly journals Advanced Seismic Data Interpretation for Carbonate Targets Based on Optimized Processing Techniques

GeoArabia ◽  
1996 ◽  
Vol 1 (2) ◽  
pp. 285-296
Author(s):  
Klaus C. Fischer ◽  
Ulrich Möller ◽  
Roland Marschall
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Data Interpretation ◽  
Second Phase ◽  
Shelf Area ◽  
Depth Migration ◽  
Amplitude Versus Offset ◽  
And Migration ◽  
Processing Techniques ◽  
Seismic Anomalies

ABSTRACT Seismic data from the shelf area of the Cretaceous Shu’aiba Formation in Abu Dhabi is used to investigate stratigraphic and structural seismic anomalies. The data consists of a 2-D grid of seismic lines, acquired in the late 1980s and 1993. The data was reprocessed in several phases. The first phase consists of standard time domain processing upto final Dip Move Out stack and migration. In the second phase, a macro-velocity model for post-stack depth migration is generated and tested by the interpreters. The third phase is the interpretation of the pre-stack depth migration stack. Due to the structural irregularity of the Shu’aiba Formation, the pre-stack depth migrated data is considered the most reliable for Amplitude Versus Offset analysis. Further steps are L-1 deconvolution followed by Born Inversion. These last steps are required before the lithology can be modeled with high-resolution. The final lithological model is verified by applying forward modeling. The lithological model forms the basis for reservoir and geostatistical evaluations which account for heterogeneities.

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.

True‐amplitude frequency‐wavenumber constant‐offset migration

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 915-924 ◽  
Author(s):  
B. O. Ekren ◽  
Bjørn Ursin
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Earth Model ◽  
Geometrical Spreading ◽  
Amplitude Analysis ◽  
Time Migration ◽  
Amplitude Versus Offset ◽  
Out Of Plane ◽  
Nmo Correction ◽  
Prestack Time Migration

Low S/N ratios, interfering diffractions, and dip‐related problems (e.g., reflector point dispersal, dip‐dependent NMO, and reflection angle) make reliable amplitude versus offset (AVO) analysis a difficult task. Prestack time migration (PSTM) collapses diffractions, increases the S/N ratio, and reduces dip‐related problems. Therefore, PSTM is usually required before offset dependent information can be extracted from seismic data, and PSTM is mandatory before comparing real seismic data with 1-D earth model synthetic data. We present a 2-D frequency‐wavenumber common‐offset prestack time migration algorithm. To treat the amplitudes correctly, a 3-D to 2-D transform of the data is required before doing the migration. This is done by correcting the data for out‐of‐plane geometrical spreading. Migration artifacts are attenuated, exploiting the fact that the maximum dip to be migrated decreases with increasing traveltime and offset. The final processing steps before further processing are 2-D geometrical spreading correction and removal of the implicit NMO correction inherent in the migration. Two marine data examples show improved data quality after prestack time migration, making subsequent amplitude analysis more reliable.

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