Migration of seismic data by phase shift plus interpolation

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 124-131 ◽  
Author(s):  
Jeno Gazdag ◽  
Piero Sguazzero
Keyword(s):  
Phase Shift ◽  
Wave Field ◽  
Seismic Data ◽  
Three Dimensional ◽  
Reference Wave ◽  
Second Step ◽  
Lateral Velocity ◽  
Wave Fields ◽  
Shift Method ◽  
Phase Shift Method

Under the horizontally layered velocity assumption, migration is defined by a set of independent ordinary differential equations in the wavenumber‐frequency domain. The wave components are extrapolated downward by rotating their phases. This paper shows that one can generalize the concepts of the phase‐shift method to media having lateral velocity variations. The wave extrapolation procedure consists of two steps. In the first step, the wave field is extrapolated by the phase‐shift method using ℓ laterally uniform velocity fields. The intermediate result is ℓ reference wave fields. In the second step, the actual wave field is computed by interpolation from the reference wave fields. The phase shift plus interpolation (PSPI) method is unconditionally stable and lends itself conveniently to migration of three‐dimensional data. The performance of the methods is demonstrated on synthetic examples. The PSPI migration results are then compared with those obtained from a finite‐difference method.

Three‐dimensional depth migration by a generalized phase‐shift method

1986 ◽  
Author(s):  
Mickey Edwards ◽  
Chris Hsiung ◽  
David Kessler ◽  
Dan Kosloff ◽  
Moshe Reshef
Keyword(s):  
Phase Shift ◽  
Three Dimensional ◽  
Shift Method ◽  
Depth Migration ◽  
Phase Shift Method

scholarly journals Development of A Three-Dimensional Shape Measurement System Using A Phase-Shift Method

2020 ◽  
Author(s):  
Taku Sakamoto ◽  
Ichiro Oda ◽  
Takuma Okamura ◽  
Hourin Cho ◽  
Satoru Nonaka ◽  
...  
Keyword(s):  
Gastrointestinal Tract ◽  
Phase Shift ◽  
Visual Inspection ◽  
Three Dimensional ◽  
Curved Surface ◽  
Inspection System ◽  
Shift Method ◽  
Dimensional Shape ◽  
Three Dimensional Shape ◽  
Phase Shift Method

Abstract Accurate measurement of the distance between any two points under endoscopic examination of the gastrointestinal tract is difficult due to the fisheye lens currently used on endoscopes. To overcome this issue, we developed a three-dimensional visual inspection system that incorporates a phase-shift method for direct measurement of a three-dimensional shape. Projection of a striped pattern is used to enable three-dimensional renderings of a surface using an industrial camera. We evaluated the accuracy of measurement relative to that of reference measurements obtained using a measurement microscope, for three-dimensional shapes on a plane and curved surface. For 60 regions of interests, with various configurations of the reference locations relative to the camera, the measurement error for our system was <0.1 mm on the plane grid and <0.5 mm on the curved surface. The accuracy of our novel three-dimensional visual inspection system could improve determination of the size of lesions with different shapes, flat or depressed, regardless of the curved surface of the gastrointestinal tract.

Recursive wavenumber‐frequency migration

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 319-329 ◽  
Author(s):  
Y. C. Kim ◽  
R. Gonzalez ◽  
J. R. Berryhill
Keyword(s):  
Phase Shift ◽  
Seismic Data ◽  
Computational Effort ◽  
Velocity Estimation ◽  
Velocity Variation ◽  
Resolution Limit ◽  
Step Size ◽  
Shift Method ◽  
Phase Shift Method ◽  
Depth Curve

There are many approaches for migrating seismic data using velocities varying only with depth. These methods are capable of accommodating quasi‐continuous vertical velocity variation at the expense of a considerably larger amount of computation than with the Stolt method, which assumes a constant velocity for the subsurface of the earth. However, the errors involved in estimating migration velocities from seismic data are often too large to justify such a large amount of computational effort. Furthermore, because there is a resolution limit in velocity estimation, a time‐depth curve based on the velocity estimates may be represented by a series of line segments that typically are much larger than the migration step size. For a time‐depth curve segmented in this way, we may successively apply the fast Stolt method interleaved with phase shift for downward continuation. This approach, recursive wavenumber‐frequency (k-f ) migration, retains the speed of the Stolt method and produces from seismic data a subsurface image as good as that from the phase‐shift method. The recursive k-f method is a powerful tool, particularly for the migration of 3-D data.

Suppressing the unwanted reflections of the full wave equation

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 1007-1012 ◽  
Author(s):  
Dan Loewenthal ◽  
Paul L. Stoffa ◽  
Eduardo L. Faria
Keyword(s):  
Wave Equation ◽  
Phase Shift ◽  
Wave Fields ◽  
Shift Method ◽  
Depth Direction ◽  
Full Wave ◽  
And Migration ◽  
The One ◽  
Phase Shift Method ◽  
Natural Way

In many instances in exploration geophysics we are interested in the so‐called one‐way wave equation. This equation allows the wave fields to propagate in the positive depth direction, but not in the reverse (−Z) direction. Some modeling and migration methods, such as the f-k method (Stolt, 1978) and the phase‐shift method (Gazdag, 1978), produce in a natural way the one‐way wave equation. The main advantage of the one‐way wave equation is that it does not give rise to multiples or interlayer reverberations and enables the observation of primary events only.

A HIGHLY ACCURATE ULTRASONIC MEASUREMENT SYSTEM FOR TREMOR USING BINARY AMPLITUDE-SHIFT-KEYING AND PHASE-SHIFT METHOD

2003 ◽  
Vol 15 (02) ◽  
pp. 61-67 ◽  
Author(s):  
MENG-HSIANG YANG ◽  
K. N. HUANG ◽  
C. F. HUANG ◽  
S. S. HUANG ◽  
M. S. YOUNG
Keyword(s):  
Phase Shift ◽  
Measurement System ◽  
Low Cost ◽  
Phase Shifts ◽  
Ultrasonic Waves ◽  
Shift Method ◽  
Narrow Bandwidth ◽  
Shift Keying ◽  
Modulation Signal ◽  
Phase Shift Method

A highly accurate Binary Amplitude-Shift-Keyed (BASK) ultrasonic tremor measurement system for use in isothermal air is developed. In this paper, we present a simple but efficient algorithm based upon phase shifts generated by three ultrasonic waves of different frequencies. By the proposed method, we can conduct larger range measurement than the phase-shift method and also get higher accuracy compared with the time-of-flight (TOF) method. Our microcomputer-based system includes two important parts. One of which is BASK modulation signal generator. The other is a phase meter designed to record and compute the phase shifts of the three different frequencies and the result motion is then sent to either an LCD for display or a PC for calibration. Experiments are done in the laboratory using BASK modulation for the frequencies of 200 Hz and 1 kHz with a 40 kHz carrier. The measurement accuracy of this measurement system in the reported experiments is within +/- 0.98 mm. The main advantages of this ultrasonic tremor measurement system are high resolution, narrow bandwidth requirement, low cost, and easy to be implemented.

A digital phase shift method for phase compensation of electronic transformer

2017 ◽  
Vol 40 (13) ◽  
pp. 3690-3695 ◽  
Author(s):  
Wei Wei ◽  
Han-miao Cheng ◽  
Fan Li ◽  
Deng-ping Tang ◽  
Shui-bin Xia
Keyword(s):  
Phase Shift ◽  
Phase Error ◽  
Recursion Formula ◽  
Rogowski Coil ◽  
Shift Method ◽  
Electronic Transformer ◽  
Digital Phase ◽  
Fitting Algorithm ◽  
Fixed Phase ◽  
Phase Shift Method

When sampling analog signal, the electronic transformer generally produces a fixed phase error that will compromise the measurement accuracy and require a phase shift method for correction. In this paper, we propose a digital phase shift method based on least squares fitting algorithm and derive the recursion formula of digital phase shift. The simulation has also been done to analysis its performance. The result shows that the method has high phase shift resolution and precision. By applying the method to an electronic transformer based on Rogowski coil, we have experimentally verified the feasibility and validity of the method.

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