Synthetic full waveform acoustic logs in cased boreholes

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1051-1059 ◽  
Author(s):  
Kenneth M. Tubman ◽  
C. H. Cheng ◽  
M. Nafi Toksöz
Keyword(s):  
Rayleigh Wave ◽  
Arbitrary Number ◽  
Fluid Layer ◽  
Body Wave ◽  
Model Parameters ◽  
Combined Effects ◽  
Interface Waves ◽  
Full Waveform ◽  
Propagator Matrix ◽  
Model Geometry

A general expression is derived for the dispersion relations and the impulse response of a radially layered borehole. The model geometry consists of a central fluid cylinder surrounded by an arbitrary number of solid annuli. A Thomson‐Haskell type propagator matrix is used to relate stresses and displacements across the layers. Although the model is completely general, the geometries considered here are restricted to those of a cased hole. Layers of steel, cement, and formation surround the innermost fluid layer. Synthetic microseismograms containing all body and interface waves are calculated for a variety of model parameters. Formation body wave arrivals are relatively unaffected by the presence of a casing. They may, however, be hard to identify cement velocities are close to or larger than those of the formation. The Stoneley and pseudo‐Rayleigh wave arrivals are strongly influenced by the casing parameters. They respond to the combined effects of the steel, the cement, and the formation.

Synthetic full‐waveform acoustic logs in cased boreholes, II—Poorly bonded casing

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 902-913 ◽  
Author(s):  
Kenneth M. Tubman ◽  
C. H. Cheng ◽  
S. P. Cole ◽  
M. Nafi Toksöz
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Theoretical Study ◽  
Fluid Layer ◽  
Body Wave ◽  
P Wave ◽  
Full Waveform ◽  
Fluid Layers ◽  
First Arrival ◽  
Wave Arrival

A generalization of the technique of Tubman et al. (1984) allows the inclusion of intermediate fluid layers in the theoretical study of elastic wave propagation in a layered borehole. The number and location of fluid layers are arbitrary. The only restrictions are that the central cylinder is fluid and the outermost formation is solid. Synthetic full‐waveform microseismograms in poorly bonded cased holes can be generated, allowing investigation of free pipe and cement sheathed pipe with no bond to the formation. If there is a fluid layer between the steel and the cement, the steel is free to ring. The first arrival in this situation is from the casing, even with an extremely thin fluid layer or microannulus. The amplitude and duration of the pipe signal depend upon the thickness of the fluid layer. While the first arrival is from the casing, the formation body‐wave energy is present. The character of the waveform will vary as the formation parameters vary. If the duration of the steel arrival is small, it is possible to distinguish the formation P-wave arrival. If the fluid layer is between the cement and the formation, then the steel is well bonded to the cement but the cement is not bonded to the formation. In this case the thicknesses of the fluid and cement layers are important in determining the nature of the first arrival. If there is a large amount of cement bonded to the steel, the cement can damp out the ringing of the pipe and make it possible to distinguish formation arrivals. If there is less cement bonded to the steel, the cement does not damp out the steel ringing but the cement rings along with the steel and the first arrival is from the combination of the steel and the cement. The velocity of this wave depends upon the velocities and thicknesses of the steel and cement layers.

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.

3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R1-R11 ◽  
Author(s):  
Dmitry Borisov ◽  
Ryan Modrak ◽  
Fuchun Gao ◽  
Jeroen Tromp
Keyword(s):  
Surface Wave ◽  
Objective Function ◽  
Surface Waves ◽  
Large Scale ◽  
Body Wave ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Near Surface ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

Optimized Model Parameterization using Compact Full Waveform Inversion

2020 ◽  
Author(s):  
Linan Xu ◽  
Edgar Manukyan ◽  
Hansruedi Maurer
Keyword(s):  
Large Scale ◽  
Waveform Inversion ◽  
Gradient Methods ◽  
Significant Loss ◽  
Inverse Model ◽  
Eigenvalue Decomposition ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Model Parameterization

Summary Seismic Full Waveform Inversion (FWI) has the potential to produce high-resolution subsurface images, but the computational resources required for realistically sized problems can be prohibitively large. In terms of computational costs, Gauss-Newton algorithms are more attractive than the commonly employed conjugate gradient methods, because the former have favorable convergence properties. However, efficient implementations of Gauss-Newton algorithms require an excessive amount of computer memory for larger problems. To address this issue, we introduce Compact Full Waveform Inversion (CFWI). Here, a suitable inverse model parameterization is sought that allows representing all subsurface features, potentially resolvable by a particular source-receiver deployment, but using only a minimum number of model parameters. In principle, an inverse model parameterization, based on the Eigenvalue decomposition, would be optimal, but this is computationally not feasible for realistic problems. Instead, we present two alternative parameter transformations, namely the Haar and the Hartley transformations, with which similarly good results can be obtained. By means of a suite of numerical experiments, we demonstrate that these transformations allow the number of model parameters to be reduced to only a few percent of the original parameterization without any significant loss of spatial resolution. This facilitates efficient solutions of large-scale FWI problems with explicit Gauss-Newton algorithms.

Full-waveform inversion of salt models using shape optimization and simulated annealing

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R793-R804 ◽  
Author(s):  
Debanjan Datta ◽  
Mrinal K. Sen ◽  
Faqi Liu ◽  
Scott Morton
Keyword(s):  
Simulated Annealing ◽  
Least Squares ◽  
Level Set ◽  
Waveform Inversion ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Starting Model

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

scholarly journals Two-grid full-waveform Rayleigh-wave inversion via a genetic algorithm — Part 1: Method and synthetic examples

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R805-R814 ◽  
Author(s):  
Zhen Xing ◽  
Alfredo Mazzotti
Keyword(s):  
Genetic Algorithm ◽  
Rayleigh Wave ◽  
A Priori ◽  
Computing Time ◽  
A Priori Information ◽  
Fine Grid ◽  
Near Surface ◽  
Reference Models ◽  
Full Waveform ◽  
Priori Information

When reliable a priori information is not available, it is difficult to correctly predict near-surface S-wave velocity models from Rayleigh waves through existing techniques, especially in the case of complex geology. To tackle this issue, we have developed a new method: two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI). Adopting a two-grid parameterization of the model, the genetic algorithm inverts for unknown velocities and densities at the nodes of a coarse grid, whereas the forward modeling is performed on a fine grid to avoid numerical dispersion. A bilinear interpolation brings the coarse-grid results into the fine-grid models. The coarse inversion grid allows for a significant reduction in the computing time required by the genetic algorithm to converge. With a coarser grid, there are fewer unknowns and less required computing time, at the expense of the model resolution. To further increase efficiency, our inversion code can perform the optimization using an offset-marching strategy and/or a frequency-marching strategy that can make use of different kinds of objective functions and allows for parallel computing. We illustrate the effect of our inversion method using three synthetic examples with rather complex near-surface models. Although no a priori information was used in all three tests, the long-wavelength structures of the reference models were fairly predicted, and satisfactory matches between “observed” and predicted data were achieved. The fair predictions of the reference models suggest that the final models estimated by our genetic-algorithm FWI, which we call macromodels, would be suitable inputs to gradient-based Rayleigh-wave FWI for further refinement. We also explored other issues related to the practical use of the method in different work and explored applications of the method to field data.

Full waveform inversion with sparse structure constrained regularization

2018 ◽  
Vol 26 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Zichao Yan ◽  
Yanfei Wang
Keyword(s):  
Large Scale ◽  
Regularization Parameter ◽  
Waveform Inversion ◽  
Difference Operators ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Structure Information ◽  
Full Waveform ◽  
Ill Posed ◽  
Scale Optimization

AbstractFull waveform inversion is a large-scale nonlinear and ill-posed problem. We consider applying the regularization technique for full waveform inversion with structure constraints. The structure information was extracted with difference operators with respect to model parameters. And then we establish an {l_{p}}-{l_{q}}-norm constrained minimization model for different choices of parameters p and q. To solve this large-scale optimization problem, a fast gradient method with projection onto convex set and a multiscale inversion strategy are addressed. The regularization parameter is estimated adaptively with respect to the frequency range of the data. Numerical experiments on a layered model and a benchmark SEG/EAGE overthrust model are performed to testify the validity of this proposed regularization scheme.

Image-guided sparse-model full waveform inversion

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R189-R198 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale ◽  
Bin Gong ◽  
Zhaobo (Joe) Meng
Keyword(s):  
Waveform Inversion ◽  
Model Space ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Widespread Application ◽  
Low Frequencies ◽  
Sparse Model ◽  
Image Guided ◽  
Full Waveform ◽  
Recorded Data

Multiple problems, including high computational cost, spurious local minima, and solutions with no geologic sense, have prevented widespread application of full waveform inversion (FWI), especially FWI of seismic reflections. These problems are fundamentally related to a large number of model parameters and to the absence of low frequencies in recorded seismograms. Instead of inverting for all the parameters in a dense model, image-guided full waveform inversion inverts for a sparse model space that contains far fewer parameters. We represent a model with a sparse set of values, and from these values, we use image-guided interpolation (IGI) and its adjoint operator to compute finely and uniformly sampled models that can fit recorded data in FWI. Because of this sparse representation, image-guided FWI updates more blocky models, and this blockiness in the model space mitigates the absence of low frequencies in recorded data. Moreover, IGI honors imaged structures, so image-guided FWI built in this way yields models that are geologically sensible.

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