Including lateral velocity variations into true-amplitude common-shot wave-equation migration

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. S175-S186 ◽  
Author(s):  
Daniela Amazonas ◽  
Rafael Aleixo ◽  
Gabriela Melo ◽  
Jörg Schleicher ◽  
Amélia Novais ◽  
...  
Keyword(s):  
Wave Equations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Approximate Solutions ◽  
Vertical Gradient ◽  
Correct Description ◽  
Lateral Velocity ◽  
One Dimensional ◽  
Velocity Variations ◽  
The One

In heterogeneous media, standard one-way wave equations describe only the kinematic part of one-way wave propagation correctly. For a correct description of amplitudes, the one-way wave equations must be modified. In media with vertical velocity variations only, the resulting true-amplitude one-way wave equations can be solved analytically. In media with lateral velocity variations, these equations are much harder to solve and require sophisticated numerical techniques. We present an approach to circumvent these problems by implementing approximate solutions based on the one-dimensional analytic amplitude modifications. We use these approximations to show how to modify conventional migration methods such as split-step and Fourier finite-difference migrations in such a way that they more accurately handle migration amplitudes. Simple synthetic data examples in media with a constant vertical gradient demonstrate that the correction achieves the recovery of true migration amplitudes. Applications to the SEG/EAGE salt model and the Marmousi data show that the technique improves amplitude recovery in the migrated images in more realistic situations.

One-way true-amplitude migration using matrix decomposition

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. S387-S398 ◽  
Author(s):  
Jiachun You ◽  
Ru-Shan Wu ◽  
Xuewei Liu
Keyword(s):  
Wave Equations ◽  
Matrix Decomposition ◽  
Dynamic Imaging ◽  
Velocity Variation ◽  
Lateral Velocity ◽  
Amplitude Wave ◽  
Contrast Model ◽  
Migration Method ◽  
The One ◽  
Imaging Performance

To meet the requirement of true-amplitude migration and address the shortcomings of the classic one-way wave equations on the dynamic imaging, one-way true-amplitude wave equations were developed. Migration methods, based on the Taylor or other series approximation theory, are introduced to solve the one-way true-amplitude wave equations. This leads to the main weakness of one-way true-amplitude migration for imaging the complex or strong velocity — contrast media — the limited imaging angles. To deal with this issue, we apply a matrix decomposition method to accurately calculate the square-root operator and impose the boundary conditions of the one-way true-amplitude wave equations. Our migration method and the conventional one-way true-amplitude Fourier finite-difference (FFD) migration method are used by us to test and compare the imaging performance. The impulse responses in a strong velocity-contrast model prove that our migration method works for larger imaging angles than the one-way true-amplitude FFD method. The amplitude calculations in a strong-lateral velocity variation media with one reflector and in the Marmousi model demonstrate that our migration method provides better amplitude-preserving performance and offers higher structural imaging quality than the one-way true-amplitude FFD method. We also use field data to indicate the imaging enhancement and the feasibility of our method compared with the one-way true-amplitude FFD method. Our one-way true-amplitude migration method using matrix decomposition fully exploits the features of one-way true-amplitude wave equations with less approximation, and it is capable of producing more accurate amplitude estimations and potentially wider imaging angles.

scholarly journals Analysis of temporal correlation in heart rate variability through maximum entropy principle in a minimal pairwise glassy model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Elena Agliari ◽  
Francesco Alemanno ◽  
Adriano Barra ◽  
Orazio Antonio Barra ◽  
Alberto Fachechi ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Maximum Entropy ◽  
Clinical Status ◽  
Synthetic Data ◽  
Maximum Entropy Principle ◽  
Temporal Correlation ◽  
One Dimensional ◽  
Entropy Principle ◽  
The One

Abstract In this work we apply statistical mechanics tools to infer cardiac pathologies over a sample of M patients whose heart rate variability has been recorded via 24 h Holter device and that are divided in different classes according to their clinical status (providing a repository of labelled data). Considering the set of inter-beat interval sequences $$\{\mathbf {r}(i) \} = \{ r_1(i), r_2(i), \ldots , \}$$ { r ( i ) } = { r 1 ( i ) , r 2 ( i ) , … , } , with $$i=1,\ldots ,M$$ i = 1 , … , M , we estimate their probability distribution $$P(\mathbf {r})$$ P ( r ) exploiting the maximum entropy principle. By setting constraints on the first and on the second moment we obtain an effective pairwise $$(r_n,r_m)$$ ( r n , r m ) model, whose parameters are shown to depend on the clinical status of the patient. In order to check this framework, we generate synthetic data from our model and we show that their distribution is in excellent agreement with the one obtained from experimental data. Further, our model can be related to a one-dimensional spin-glass with quenched long-range couplings decaying with the spin–spin distance as a power-law. This allows us to speculate that the 1/f noise typical of heart-rate variability may stem from the interplay between the parasympathetic and orthosympathetic systems.

Improving plane‐wave decomposition and migration

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 195-205 ◽  
Author(s):  
Hans J. Tieman
Keyword(s):  
Plane Wave ◽  
Computer Time ◽  
Lateral Velocity ◽  
High Quality ◽  
Depth Migration ◽  
Wave Data ◽  
Velocity Variations ◽  
And Migration ◽  
The One ◽  
Slant Stacking

Plane‐wave data can be produced by slant stacking common geophone gathers over source locations. Practical difficulties arise with slant stacks over common receiver gathers that do not arise with slant stacks over common‐midpoint gathers. New techniques such as hyperbolic velocity filtering allow the production of high‐quality slant stacks of common‐midpoint data that are relatively free of artifacts. These techniques can not be used on common geophone data because of the less predictive nature of data in this domain. However, unlike plane‐wave data, slant stacks over midpoint gathers cannot be migrated accurately using depth migration. A new transformation that links common‐midpoint slant stacks to common geophone slant stacks allows the use together of optimized methods of slant stacking and accurate depth migration in data processing. Accurate depth migration algorithms are needed to migrate plane‐wave data because of the potentially high angles of propagation exhibited by the data and because of any lateral velocity variations in the subsurface. Splitting the one‐way wave continuation operator into two components (one that is a function of a laterally independent velocity, and a residual term that handles lateral variations in subsurface velocities) results in a good approximation. The first component is applied in the wavenumber domain, the other is applied in the space domain. The approximation is accurate for any angle of propagation in the absence of lateral velocity variations, although with severe lateral velocity variations the accuracy is reduced to 50°. High‐quality plane‐wave data migrated using accurate wave continuation operators results in a high‐quality image of the subsurface. Because of the signal‐to‐noise content of this data the number of sections that need to be migrated can be reduced considerably. This not only saves computer time, more importantly it makes computer‐intensive tasks such as migration velocity analysis based on maximizing stack power more feasible.

scholarly journals Optimal Polynomial Decay to Coupled Wave Equations and Its Numerical Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. F. C. Lobato ◽  
S. M. S. Cordeiro ◽  
M. L. Santos ◽  
D. S. Almeida Júnior
Keyword(s):  
Decay Rate ◽  
Spectral Methods ◽  
Finite Differences ◽  
Wave Equations ◽  
Coupled System ◽  
Polynomial Decay ◽  
One Dimensional ◽  
Coupled Wave Equations ◽  
Optimal Polynomial ◽  
The One

In this work we consider a coupled system of two weakly dissipative wave equations. We show that the solution of this system decays polynomially and the decay rate is optimal. Computational experiments are conducted in the one-dimensional case in order to show that the energies properties are preserved. In particular, we use finite differences and also spectral methods.

scholarly journals Estimation of in Vivo Pulses in Medical Ultrasound

1994 ◽  
Vol 16 (3) ◽  
pp. 190-203 ◽  
Author(s):  
Jørgen Arendt Jensen
Keyword(s):  
Local Minimum ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Medical Ultrasound ◽  
One Dimensional ◽  
Main Application ◽  
Estimated Parameters ◽  
Ultrasound Field ◽  
The One

An algorithm for the estimation of one-dimensional in-vivo ultrasound pulses is derived. The routine estimates a set of ARMA parameters describing the pulse and uses data from a number of adjacent rf lines. Using multiple lines results in a decrease in variance on the estimated parameters and significantly reduces the risk of terminating the algorithm at a local minimum. Examples from use on synthetic data confirms the reduction in variance and increased chance of successful minimization termination. Simulations are also reported indicating the relation between the one-dimensional pulse and the three-dimensional, attenuated ultrasound field for a concave transducer. Pulses are estimated from in-vivo liver data showing good resemblance to a pulse measured as the response from a planar reflector and then properly attenuated. The main application for the algorithm is to function as a preprocessing stage for deconvolution algorithms using parametric pulses.

Anisotropic Helmholtz and wave–vortex decomposition of one-dimensional spectra

2017 ◽  
Vol 815 ◽  
pp. 361-387 ◽  
Author(s):  
Oliver Bühler ◽  
Max Kuang ◽  
Esteban G. Tabak
Keyword(s):  
Synthetic Data ◽  
Power Spectra ◽  
Statistical Correlation ◽  
Original Method ◽  
Anisotropic Flow ◽  
One Dimensional ◽  
Divergent Flow ◽  
Consistent Manner ◽  
Flow Components ◽  
The One

We present an extension to anisotropic flows of the recently developed Helmholtz and wave–vortex decomposition method for one-dimensional spectra measured along ship or aircraft tracks in Bühler et al. (J. Fluid Mech., vol. 756, 2014, pp. 1007–1026). Here, anisotropy refers to the statistical properties of the underlying flow field, which in the original method was assumed to be homogeneous and isotropic in the horizontal plane. Now, the flow is allowed to have a simple kind of horizontal anisotropy that is chosen in a self-consistent manner and can be deduced from the one-dimensional power spectra of the horizontal velocity fields and their cross-correlation. The key result is that an exact and robust Helmholtz decomposition of the horizontal kinetic energy spectrum can be achieved in this anisotropic flow setting, which then also allows the subsequent wave–vortex decomposition step. The anisotropic method is as easy to use as its isotropic counterpart and it robustly converges back to it if the observed anisotropy tends to zero. As a by-product of our analysis we also found a simple test for statistical correlation between rotational and divergent flow components. The new method is developed theoretically and tested with encouraging results on challenging synthetic data as well as on ocean data from the Gulf Stream.

Sign in / Sign up

Export Citation Format

Share Document