Simultaneous determination of time delays and stacking weights in seismic array beamforming

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 491-502 ◽  
Author(s):  
Weijian Mao ◽  
David Gubbins
Keyword(s):  
Conjugate Gradient ◽  
Time Delays ◽  
Random Noise ◽  
Waveform Inversion ◽  
Real Data ◽  
Seismic Array ◽  
Model Parameters ◽  
Static Corrections ◽  
Array Beamforming ◽  
Value Decomposition

An algorithm for the estimation of time delays and weights in an arbitrary‐single or three‐component seismic array is developed by the use of a linearized waveform inversion technique. This algorithm differs from conventional crosscorrelation methods in its ability to simultaneously obtain time delays and weights by minimizing residuals of all possible waveform fittings, and by its robustness in the presence of high random noise levels and local geological scattering. There are N stations in an array, and for each station, a beam is formed by a weighted linear combination of the remaining (N − 1) seismic traces. The time delays and weights are model parameters to be found by minimizing the sum of N objective functions. Two optimization algorithms for solving the least‐squares problem, singular‐value decomposition and conjugate gradient, are compared, and the conjugate gradient method is found to be satisfactory and faster for large arrays. The algorithm was tested using synthetic array data with high noise, real data from shots in a borehole to a linear array on land, and Ms 6.7 earthquake data recorded with a broadband three‐component array. The success with synthetic and real data shows the algorithm to be useful for seismic data stacking, residual static corrections, and phase picking when the data quality is poor.

Accelerating Hessian-free Gauss-Newton full-waveform inversion via l-BFGS preconditioned conjugate-gradient algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. R49-R64 ◽  
Author(s):  
Wenyong Pan ◽  
Kristopher A. Innanen ◽  
Wenyuan Liao
Keyword(s):  
Conjugate Gradient ◽  
Random Noise ◽  
Waveform Inversion ◽  
Initial Guess ◽  
Gradient Algorithm ◽  
Preconditioned Conjugate Gradient ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Numerical Examples ◽  
Full Waveform

Full-waveform inversion (FWI) has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data. The Hessian-free (HF) optimization method represents an attractive alternative to Newton-type and gradient-based optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a matrix-free conjugate-gradient (CG) algorithm. The main drawback with HF optimization is that the CG algorithm requires many iterations. In our research, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton (GN) method. Traditionally, preconditioners are designed as diagonal Hessian approximations. We additionally use a new pseudo diagonal GN Hessian as a preconditioner, making use of the reciprocal property of Green’s function. Furthermore, we have developed an [Formula: see text]-BFGS inverse Hessian preconditioning strategy with the diagonal Hessian approximations as an initial guess. Several numerical examples are carried out. We determine that the quasi-Newton [Formula: see text]-BFGS preconditioning scheme with the pseudo diagonal GN Hessian as the initial guess is most effective in speeding up the HF GN FWI. We examine the sensitivity of this preconditioning strategy to random noise with numerical examples. Finally, in the case of multiparameter acoustic FWI, we find that the [Formula: see text]-BFGS preconditioned HF GN method can reconstruct velocity and density models better and more efficiently compared with the nonpreconditioned method.

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. U25-U38 ◽  
Author(s):  
Nuno V. da Silva ◽  
Andrew Ratcliffe ◽  
Vetle Vinje ◽  
Graham Conroy
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Radiation Patterns ◽  
Data Set ◽  
Full Waveform ◽  
Seismic Image ◽  
Central North Sea

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

scholarly journals Near-surface attenuation estimation using wave-propagation modeling

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. U27-U37 ◽  
Author(s):  
Nizare El Yadari ◽  
Fabian Ernst ◽  
Wim Mulder
Keyword(s):  
Wave Attenuation ◽  
Waveform Inversion ◽  
Real Data ◽  
P Wave ◽  
Surface Model ◽  
Near Surface ◽  
Propagation Modeling ◽  
Static Corrections ◽  
Starting Model ◽  
Wave Propagation Modeling

The effect of the near surface on seismic land data can be so severe that static corrections are insufficient. Full-waveform inversion followed by redatuming may be an alternative, but inversion will work only if the starting model is sufficiently close to the true model. As a first step toward determining a viscoelastic near-surface model, we assume that existing methods can provide a horizontally layered velocity and density model. Because near-surface attenuation is strongest, we propose a method to estimate the P-wave attenuation based on viscoacoustic finite-difference modeling. We compare energy decay along traveltime curves of reflection and refraction events in the modeled and observed seismic data for a range of attenuation parameters. The best match provides an estimate of the attenuation. First, we estimate only the attenuation of the top layer and study the sensitivity to depth and velocity perturbations. Then, we consider multiple layers. We apply the method to synthetic and real data and investigate the effect of source wavelet and topography. The method is robust against depth and velocity perturbations smaller than 10%. The results are sensitive to the source wavelet. Incorporating the surface topography in the computed traveltimes reduces the uncertainty of the attenuation estimates, especially for deeper layers.

Multiparameter estimation with acoustic vertical transverse isotropic full-waveform inversion of surface seismic data

2016 ◽  
Vol 4 (4) ◽  
pp. SU1-SU16 ◽  
Author(s):  
Xin Cheng ◽  
Kun Jiao ◽  
Dong Sun ◽  
Denes Vigh
Keyword(s):  
Vertical Velocity ◽  
Seismic Data ◽  
Joint Inversion ◽  
Waveform Inversion ◽  
Real Data ◽  
Vertical Axis ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Wavefield Simulation

Obtaining accurate depth-migrated images demands an anisotropic representation of the earth. As a prominent tool for building high-resolution earth models, full-waveform inversion (FWI) therefore must not only account for anisotropy during wavefield simulation but also reconstruct the anisotropy fields. We have developed an inversion strategy to perform acoustic multiparameter FWI of surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI). During the early era of FWI practice, most studies only invert for the most dominant parameter, that is, the vertical velocity, and the rest of the model parameters are either ignored or kept constant. Recently, more and more emphases focus on inverting for more parameters, such as for the vertical velocity and the anisotropy fields; these are referred to as multiparameter inversion. Due to the dominant influence of the vertical velocity on the kinematics of surface seismic data, we have developed a hierarchical approach to invert for the vertical velocity first, but we kept the anisotropy fields unchanged and only switched to joint inversion of the vertical velocity and the anisotropy fields when the inversion for the vertical velocity approaches convergence. In addition, we have illustrated the necessity of incorporating the diving and reflection energy during inversion to mitigate the nonuniqueness of the solutions caused by the coupling between the vertical velocity and the anisotropy fields. We also demonstrate the success of our method for VTI FWI using synthetic and real data examples based on marine surface seismic acquisition. Our results show that incorporation of multiparameter anisotropy inversion produced better focused migration images.

Multicomponent f-x seismic random noise attenuation via vector autoregressive operators

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. V91-V99 ◽  
Author(s):  
Mostafa Naghizadeh ◽  
Mauricio Sacchi
Keyword(s):  
Temporal Frequency ◽  
Random Noise ◽  
Real Data ◽  
Var Model ◽  
Model Parameters ◽  
Prediction Errors ◽  
Noise Attenuation ◽  
Vector Autoregressive ◽  
Random Noise Attenuation ◽  
Frequency Space

We propose an extension of the traditional frequency-space ([Formula: see text]) random noise attenuation method to three-component seismic records. For this purpose, we develop a three-component vector autoregressive (VAR) model in the [Formula: see text] domain that is applied to the multicomponent spatial samples of each individual temporal frequency. VAR model parameters are estimated using the least-squares minimization of forward and backward prediction errors. VAR modeling effectively identifies the potential coherencies between various components of a multicomponent signal. We use the squared coherence spectrum of VAR models as an indicator to determine these coherencies. Synthetic and real data examples are provided to show the effectiveness of the proposed method.

scholarly journals 2D dipping dike magnetic data interpretation using a robust particle swarm optimization

2017 ◽  
Author(s):  
Khalid S. Essa ◽  
Mahmoud El-Hussein
Keyword(s):  
Particle Swarm Optimization ◽  
Mineral Exploration ◽  
Random Noise ◽  
Particle Swarm ◽  
Real Data ◽  
Data Interpretation ◽  
Magnetic Data ◽  
Model Parameters ◽  
Swarm Optimization ◽  
Ore Bodies

Abstract. A robust Particle Swarm Optimization (PSO) investigation for magnetic data by a 2D dipping dike has been presented. The interpretive model parameters are: the amplitude coefficient (K), the depth to the top of the dipping dike (z), exact origin of the dipping dike (x0), and the width of dipping dike (w). The inversion procedure is actualized to gauge the parameters of a 2D dipping dike structures where it has been confirmed first on synthetic models without and with different level of random noise. The results of the inversion demonstrate that the parameters derived from the inversion concur well with the true ones. The root mean square (RMS) is figured by the strategy which is considered as the misfit between the measured and computed anomalies. The technique has been warily and effectively applied to real data examples from China and UK with the presence of ore bodies. The present technique can be applicable for mineral exploration and ore bodies of dike-like structure embedded in the shallow and deeper subsurface.

Seismic waveform modelling and inversion with velocity-deviatoric stress-isotropic pressure formulation

2021 ◽  
Author(s):  
Yi Zhang ◽  
Luca de Siena ◽  
Alexey Stovas
Keyword(s):  
Waveform Inversion ◽  
Real Data ◽  
Deviatoric Stress ◽  
Model Parameters ◽  
Perfectly Matched Layers ◽  
Current Form ◽  
Anisotropic Models ◽  
Seismic Waveform ◽  
Adjoint State ◽  
Isotropic Pressure

<p>In waveform inversion, most of the existing adjoint-state methods are based on the second-order elastic wave equations subject to displacement. The implementation of the acoustic-elastic coupling problem and free-surface in this formulation is not explicit, especially for arbitrary boundaries. The formulation of velocity-deviatoric stress-isotropic pressure can tackle the above issue. We firstly review the difference between velocity stress equations and velocity-deviatoric stress-isotropic pressure equations. Then the adjoint state of the velocity-stress equations are derived, decomposing stresses into their deviatoric and isotropic parts. To simulate the unbounded wavefield, perfectly matched layers (PML) are embedded into the system of equations. It is modified for cheap computation, which avoids PML-related memory variables by applying complex coordinate stretch to three Cartesian axes in parallel.</p><p>A 3D velocity-deviatoric stress-isotropic stress formulation is implemented with the staggered finite-difference method for several synthetic models (including anisotropic models). And inversions are then performed to reconstruct the model parameters, which is followed by a sensitivity analysis.</p><p>This method has the potential to be used with real data, both for active and passive seismics. However, in its current form, since it does not treat fluid/anisotropic solid interfaces correctly, it is limited to fluid or isotropic solid problems.</p>

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

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