A method for computation of velocity profiles by inversion of large‐offset records

Geophysics ◽  
1984 ◽  
Vol 49 (8) ◽  
pp. 1249-1258 ◽  
Author(s):  
Philip M. Carrion ◽  
John T. Kuo
Keyword(s):  
Wave Field ◽  
Critical Path ◽  
Real Data ◽  
Velocity Profiles ◽  
Spatial Transformation ◽  
Lateral Velocity ◽  
Minimization Procedure ◽  
Z Domain ◽  
Minimization Technique ◽  
Lateral Extent

This paper describes a new method for recovering velocity profiles utilizing both phase and amplitude information including wide‐angle arrivals, post‐ and precritical reflections. This method is based on a double spatial transformation with a minimization procedure. The first transformation is slant stacking of the observed wave field (seismogram). The second is projecting the slant stacked wave field into the domain of horizontal slowness p and depth z. In this domain the inverse problem is reduced to finding the critical path [Formula: see text] where V(z) is the true velocity of the compressional waves. A numerical algorithm based on a minimization technique is used to find the critical path, which is equivalent to the set of turning points of the critically reflected rays. When this path is found, then the following criteria are satisfied: (1) most of the energy is concentrated away from the precritical region; (2) the computed reflection coefficients reach their maximum on this path; and (3) for horizontally stratified media or CMP data, the reflectors are aligned in the p-z domain. In tests, this method has been shown to recover the velocity profile from both synthetic and real data. It is shown that the method is able to recover accurately velocity profiles even if only part of the data are given. For example, only part of the data are available when low‐ and high‐frequency components are missing or when the data are truncated in lateral extent due to the finite length of the recording system. Moreover, the method is able to handle virtually any vertical velocity gradients in a medium; therefore, it can be applied to complicated geologic structures. The method does not require elimination of multiples, but it is not applicable to the case of a medium with a large lateral velocity gradient. It can be used even for an elastic medium when the mode‐converted energy is not small.

Post-stack depth migration in the frequency–space domain

1986 ◽  
Vol 23 (6) ◽  
pp. 839-848 ◽  
Author(s):  
Panos G. Kelamis ◽  
Einar Kjartansson ◽  
E George Marlin
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Wave Number ◽  
Lateral Velocity ◽  
Space Domain ◽  
Frequency Wave ◽  
Depth Migration ◽  
Frequency Space ◽  
Time Space ◽  
Z Domain

The 45 °monochromatic one-way wave equation, along with the thin-lens term, is used, and a depth-migration algorithm is developed in the frequency–space (ω, x) domain. Using this approach, an unmigrated stack section is directly transformed into a depth-migrated section taking into account both vertical and lateral velocity variations. In practice, the algorithm can accommodate steep events with dips of the order of 60–65°. The use of the frequency–space domain offers several advantages over the conventional time–space and frequency–wave-number domains. Time derivatives are evaluated exactly by a simple multiplication, while the use of the space (x, z) domain facilitates the handling of lateral velocity inhomogeneities. The performance of the depth-migration algorithm is tested with synthetic data from complicated models and real data from the Foothills area of western Canada.

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

Large‐scale three‐dimensional seismic models and their interpretive significance

Geophysics ◽  
1990 ◽  
Vol 55 (9) ◽  
pp. 1166-1182 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Finite Difference ◽  
Wave Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Real Data ◽  
The Real ◽  
Need To Evaluate ◽  
Zero Offset ◽  
Seismic Models

Finite‐difference seismic models are commonly set up in 2-D space. Such models must be excited by a line source which leads to different amplitudes than those in the real data commonly generated from a point source. Moreover, there is no provision for any out‐of‐plane events. These problems can be eliminated by using 3-D finite‐difference models. The fundamental strategy in designing efficient 3-D models is to minimize computational work without sacrificing accuracy. This was accomplished by using a (4,2) differencing operator which ensures the accuracy of much larger operators but requires many fewer numerical operations as well as significantly reduced manipulation of data in the computer memory. Such a choice also simplifies the problem of evaluating the wave field near the subsurface boundaries of the model where large operators cannot be used. We also exploited the fact that, unlike the real data, the synthetic data are free from ambient noise; consequently, one can retain sufficient resolution in the results by optimizing the frequency content of the source signal. Further computational efficiency was achieved by using the concept of the exploding reflector which yields zero‐offset seismic sections without the need to evaluate the wave field for individual shot locations. These considerations opened up the possibility of carrying out a complete synthetic 3-D survey on a supercomputer to investigate the seismic response of a large‐scale structure located in Oklahoma. The analysis of results done on a geophysical workstation provides new insight regarding the role of interference and diffraction in the interpretation of seismic data.

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.

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

Regression Modelling for Prediction of Construction Cost and Duration

2016 ◽  
Vol 857 ◽  
pp. 195-199 ◽  
Author(s):  
Nivea Thomas ◽  
Anu V. Thomas
Keyword(s):  
Regression Models ◽  
Critical Path ◽  
Real Data ◽  
Project Managers ◽  
Statistical Regression ◽  
Statistical Process ◽  
Project Cost ◽  
Cost Overruns ◽  
Building Projects ◽  
The Relationship

Construction investments are sensitive to time and cost overruns. Delay and cost escalation are considered two threats to project success. The project objective is to develop a model to predict project cost and duration based on historical data of similar projects. Statistical regression models are developed using real data of building projects. The methodology is adopted in 3 steps: a) Data collection b) Statistical analysis using Statistical Package for Social Sciences (SPSS) software c) Interpretation of results. The real data of cost and duration of 51 building projects have been collected. In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modelling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. The analysis is done using SPSS developed by IBM Corporation. The Regression models have been developed using the data collected from Noel Builders, Kakkanad, Ernakulam to predict the project cost and duration. The developed models are validated using split sample approach. The model outputs can be used by project managers in the planning phase to validate the scheduled critical path time and project budget.

Multimode multioffset phase analysis of surface waves, a new approach to extend MOPA to higher modes

2020 ◽  
Vol 221 (3) ◽  
pp. 1802-1819
Author(s):  
I Barone ◽  
C Strobbia ◽  
G Cassiani
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Phase Analysis ◽  
Damping Ratio ◽  
Real Data ◽  
Wave Dispersion ◽  
Spatial Period ◽  
Lateral Velocity ◽  
Surface Wave Dispersion ◽  
Surface Wave Propagation

SUMMARY Multioffset phase analysis (MOPA) is a fairly recent technique for evaluating seismic surface wave dispersion and estimating the presence of lateral variations. The main limitation of MOPA is that it is based on the assumption of one predominant mode, usually the fundamental mode, in the wave propagation. However, MOPA can be extended (at least) to the two-mode case: this new technique will be called multimode MOPA (MMMOPA). The method employs both amplitude and phase spectral information. The analysis is performed for each frequency independently. The presence of two modes causes the amplitude to have an oscillating behaviour as a function of offset (beats): the spatial period of the oscillating amplitude is identified, amplitude maxima and minima are extracted, and the local wavenumber is computed via linear regression. The resulting multimodal dispersion curve is consequently derived. Model uncertainties can be estimated by propagating the experimental phase and amplitude error variances through the different steps of the analysis all the way to the final phase velocities. An algorithm running the process in an automatic way has been implemented and tested on both synthetic and real data, with success. This is the base for future developments that, in the MOPA framework, can take into account rapid lateral velocity variations within the same acquisition window and estimate the modal absorption, for the estimation of the damping ratio, even in the presence of multimode surface wave propagation.

Q-phase compensation of seismic records in the frequency domain

1996 ◽  
Vol 86 (4) ◽  
pp. 1179-1186
Author(s):  
Maksim Bano
Keyword(s):  
Wave Field ◽  
Frequency Domain ◽  
Real Data ◽  
Processing Technique ◽  
Signal Spectrum ◽  
Variable Model ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Seismic Wavelet ◽  
Inverse Q Filtering

Abstract The attenuation process acts as a low-pass filter that attenuates the high frequencies (absorption) of the signal spectrum and also changes the phase of the seismic wavelet (dispersion). Seismic frequency losses are usually recovered according to an appropriate processing technique (such as deterministic or statistical deconvolution methods), while phase distortions are generally disregarded. Therefore, accurate processing of seismic data requires a careful investigation of the relationship between absorption and phase. In this article, a procedure is presented to accomplish this goal. To account for anelastic losses, a complex power function of frequency for the phase velocity is introduced into the one-way wave-field equation in 1D. The compensation, for both effects (absorption and dispersion) described here, is analyzed in the context of wave-field extrapolation in one dimension 1D, equivalent to that in the f-k domain as phase-shift and/or Stolt migration. The phase-only inverse Q filtering works in the frequency domain. It provides for dispersion according to a constant-Q (frequency-independent) model and is valid for any positive value of Q. The extension of this algorithm for a Q depth-variable model is also shown. The amplitude compensation is accomplished through the use of a standard statistical approach. Synthetic and real data are shown to illustrate both amplitude and phase inverse Q filtering of seismic reflection records.

Nongeometric arrivals due to highly concentrated sources adjacent to plane interfaces

1983 ◽  
Vol 73 (6A) ◽  
pp. 1655-1671
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Wave Field ◽  
High Frequency ◽  
Real Data ◽  
Synthetic Seismogram ◽  
Head Wave ◽  
Real Field ◽  
Branch Points ◽  
Good Match ◽  
Full Wave ◽  
Frequency Approximation

Abstract A high-frequency approximation for nongeometrical arrivals due to highly concentrated sources adjacent to the interfaces between two different elastic media has been developed following their detection in the real field data by Gutowski et al. (1982). In our approach, the “★” waves are associated with secondary saddle-point contributions of the contour of integration circumventing branch points in the integral representation of transmitted wave field. Our formulas are presented in a simple form suitable for an easy incorporation into any ray synthetic seismogram computation. The range of validity of our approximations is discussed and their accuracy tested by comparing the pertinent ray seismograms with their equivalents produced by the Alekseev-Mikhailenko method. A good match between both sets of seismograms suggests that our high-frequency approximations for “★” waves are well justified as are our formulas derived for the head wave-like arrivals driven by the “★” waves, and seen in the full wave field seismograms and detected in real data as well.

Numerical Prediction of Wind Flow Around Irregular Models

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
D. Y. Wang ◽  
Y. Zhou ◽  
Y. Zhu ◽  
Tim K. T. Tse
Keyword(s):  
Bluff Body ◽  
Numerical Models ◽  
Vortex Motion ◽  
Velocity Profiles ◽  
Wind Flow ◽  
Lateral Velocity ◽  
Fluctuating Pressure ◽  
Pressure Coefficients ◽  
Numerical Predictions ◽  
Building Models

This paper presents numerical predictions of flow around irregular-plan buildings (S-, R-, L- and U-shaped models) in high Reynolds number. The adopted computational approach and numerical models are described firstly. Then comparative analysis with the numerical and experimental data has been conducted to verify the reliability of the numerical predictions. Finally, characteristics of mean and fluctuating pressure distributions and vertical and lateral velocity profiles of the flow around the four models have been investigated and assessed thoroughly. The study shows that satisfactory results can be obtained by large eddy simulation (LES), especially when fluctuating wind velocity is considered in the inflow boundary. Distribution of mean pressure coefficients on front faces is relatively regular. Large fluctuating pressure coefficients are induced by strong vortex motion. Velocity profiles of wind flow are disturbed obviously among the four building models, especially in weak flow. The disturbed intensity decreases with increasing of the distance away from bluff body. The suggested MDS (Maximum Disturbance Scopes) away from bluff body are generally 0.25H in inflow zones, 0.4H in roof zones, 0.5H in both side zones and 3H in weak zones.

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