Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1868-1881 ◽  
Author(s):  
Huasheng Zhao ◽  
Bjørn Ursin ◽  
Lasse Amundsen
Keyword(s):  
Wave Velocity ◽  
Reference Data ◽  
Jacobian Matrix ◽  
Synthetic Data ◽  
Velocity Model ◽  
P Wave ◽  
Stratified Medium ◽  
Inversion Method ◽  
S Wave ◽  
Time Space

We present an inversion method for determining the velocities, densities, and layer thicknesses of a horizontally stratified medium with an acoustic layer at the top and a stack of elastic layers below. The multioffset reflection response of the medium generated by a compressional point source is transformed from the time‐space domain into the frequency‐wavenumber domain where the inversion is performed by minimizing the difference between the reference data and the modeled data using a least‐squares technique. The forward modeling is based on the reflectivity method where the solution for each frequency‐wavenumber component is found by computing the generalized reflection and transmission matrices recursively. The gradient of the objective function is computed from analytical expressions of the Jacobian matrix derived directly from the recursive modeling equations. The partial derivatives of the reflection response of the stratified medium are then computed simultaneously with the reflection response by layer‐recursive formulas. The limited‐aperture and discretization effects in time and space of the reference data are included by applying a pair of frequency and wavenumber dependent filters to the predicted data and to the Jacobian matrix at each iteration. Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorily reconstructs the elastic parameters of a stratified medium. The low‐frequency trends of the S‐wave velocity and density are found when the initial P‐wave velocity model gives approximately correct traveltimes. The convergence of the iterative minimization algorithm is fast.

Nonlinear waveform inversion of plane‐wave seismograms in stratified elastic media

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 664-674 ◽  
Author(s):  
F. Kormendi ◽  
M. Dietrich
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Wave Velocity ◽  
Generalized Least Squares ◽  
P Wave ◽  
Gradient Algorithm ◽  
Stratified Medium ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Frequency Wave

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane‐wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least‐squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency‐wave slowness domain and can be readily adapted to various source‐receiver configurations. The behavior of the algorithm conforms to the predictions of generalized least‐squares inverse theory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P‐wave velocity (or P‐wave impedance) by considering plane waves in the low slowness region (near‐normal angles of incidence), then in optimizing for the S‐wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorialy reconstructs the elastic properties of a stratified medium from a limited set of plane‐wave components, at a reasonable computing cost.

scholarly journals The potential of seismic cross-hole tomography for geotechnical site investigation

2019 ◽  
Vol 92 ◽  
pp. 18006
Author(s):  
Yannick Choy Hing Ng ◽  
William Danovan ◽  
Taeseo Ku
Keyword(s):  
Wave Velocity ◽  
Site Investigation ◽  
Velocity Model ◽  
P Wave ◽  
Reconstruction Technique ◽  
Sufficient Information ◽  
Eastern Region ◽  
S Wave ◽  
Near Surface ◽  
Soil Layers

Seismic cross-hole tomography has been commonly used in oil and gas exploration and the mining industry for the detection of precious resources. For near-surface geotechnical site investigation, this geophysical method is relatively new and can be used to supplement traditional methods such as the standard penetration test, coring and sampling, thus improving the effectiveness of site characterization. This paper presents a case study which was carried out on a reclaimed land in the Eastern region of Singapore. A seismic cross-hole test was performed by generating both compressional waves and shear waves into the ground. The signals were interpreted by using first-arrival travel time wave tomography and the arrival times were subsequently inverted using Simultaneous Iterative Reconstruction Technique (SIRT). A comparison with the borehole logging data indicated that P-wave velocity model cannot provide sufficient information about the soil layers, especially when the ground water table is near the surface. The S-wave velocity model seemed to agree quite well with the variation in the SPT-N value and could identify to a certain extent the interface between the different soil layers. Finally, P-wave and S-wave velocities are used to compute the Poisson's ratio distribution which gave a good indication of the degree of saturation of the soil.

scholarly journals Travel-Time Inversion Method of Converted Shear Waves Using RayInvr Algorithm

2021 ◽  
Vol 11 (8) ◽  
pp. 3571
Author(s):  
Genggeng Wen ◽  
Kuiyuan Wan ◽  
Shaohong Xia ◽  
Huilong Xu ◽  
Chaoyan Fan ◽  
...  
Keyword(s):  
Travel Time ◽  
Wave Velocity ◽  
P Wave ◽  
Inversion Method ◽  
Time Inversion ◽  
Ocean Bottom Seismometer ◽  
S Wave ◽  
S Waves ◽  
Inversion Model ◽  
Travel Time Inversion

The detailed studies of converted S-waves recorded on the Ocean Bottom Seismometer (OBS) can provide evidence for constraining lithology and geophysical properties. However, the research of converted S-waves remains a weakness, especially the S-waves’ inversion. In this study, we applied a travel-time inversion method of converted S-waves to obtain the crustal S-wave velocity along the profile NS5. The velocities of the crust are determined by the following four aspects: (1) modelling the P-wave velocity, (2) constrained sediments Vp/Vs ratios and S-wave velocity using PPS phases, (3) the correction of PSS phases’ travel-time, and (4) appropriate parameters and initial model are selected for inversion. Our results show that the vs. and Vp/Vs of the crust are 3.0–4.4 km/s and 1.71–1.80, respectively. The inversion model has a similar trend in velocity and Vp/Vs ratios with the forward model, due to a small difference with ∆Vs of 0.1 km/s and ∆Vp/Vs of 0.03 between two models. In addition, the high-resolution inversion model has revealed many details of the crustal structures, including magma conduits, which further supports our method as feasible.

Guidelines for building a detailed elastic depth model

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 35-45
Author(s):  
Jarrod C. Dunne ◽  
Greg Beresford ◽  
Brian L. N Kennett
Keyword(s):  
Wave Velocity ◽  
Mode Conversion ◽  
Poisson Ratio ◽  
Velocity Model ◽  
P Wave ◽  
Time Interval ◽  
S Wave ◽  
Sea Floor ◽  
P Wave Velocity ◽  
Inelastic Attenuation

We developed guidelines for building a detailed elastic depth model by using an elastic synthetic seismogram that matched both prestack and stacked marine seismic data from the Gippsland Basin (Australia). Recomputing this synthetic for systematic variations upon the depth model provided insight into how each part of the model affected the synthetic. This led to the identification of parameters in the depth model that have only a minor influence upon the synthetic and suggested methods for estimating the parameters that are important. The depth coverage of the logging run is of prime importance because highly reflective layering in the overburden can generate noise events that interfere with deeper events. A depth sampling interval of 1 m for the P-wave velocity model is a useful lower limit for modeling the transmission response and thus maintaining accuracy in the tie over a large time interval. The sea‐floor model has a strong influence on mode conversion and surface multiples and can be built using a checkshot survey or by testing different trend curves. When an S-wave velocity log is unavailable, it can be replaced using the P-wave velocity model and estimates of the Poisson ratio for each significant geological formation. Missing densities can be replaced using Gardner’s equation, although separate substitutions are required for layers known to have exceptionally high or low densities. Linear events in the elastic synthetic are sensitive to the choice of inelastic attenuation values in the water layer and sea‐floor sediments, while a simple inelastic attenuation model for the consolidated sediments is often adequate. The usefulness of a 1-D depth model is limited by misties resulting from complex 3-D structures and the validity of the measurements obtained in the logging run. The importance of such mis‐ties can be judged, and allowed for in an interpretation, by recomputing the elastic synthetic after perturbing the depth model to simulate the key uncertainties. Taking the next step beyond using simplistic modeling techniques requires extra effort to achieve a satisfactory tie to each part of a prestack seismic record. This is rewarded by the greater confidence that can then be held in the stacked synthetic tie and applications such as noise identification, data processing benchmarking, AVO analysis, and inversion.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

Direct nonlinear inversion of multiparameter 1D elastic media using the inverse scattering series

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCD15-WCD27 ◽  
Author(s):  
Haiyan Zhang ◽  
Arthur B. Weglein
Keyword(s):  
Wave Velocity ◽  
Material Properties ◽  
Value Added ◽  
P Wave ◽  
Added Value ◽  
Inversion Method ◽  
Elastic Media ◽  
Nonlinear Inversion ◽  
Model Matching ◽  
S Wave

In the direct nonlinear inversion method and in algorithms for 1D elastic media, P-wave velocity, S-wave velocity, and density are depth dependent. “Direct nonlinear” means that the method uses explicit formulas that (1) input data and directly output changes in material properties without the need for indirect procedures such as model matching, searching, optimization, or other assumed aligned objectives or proxies and that (2) the algorithms recognize and directly invert the intrinsic nonlinear relationship between changes in material properties and the recorded reflection wavefields. To achieve full elastic inversion, all components of data (such as PP, SP, and SS data) are needed. The method assumes that only data and reference medium propertiesare input, and terms in the inverse series for moving mislocated reflectors resulting from the linear inverse term are separated from amplitude correction terms. Although in principle this direct inversion approach requires all components of elastic data, synthetic tests indicate that a consistent value-added result may be achieved given only PP data measurements, as long as the PP data are used to approximately synthesize the PS and SP components. Further value would be derived from measuring all components of the data as the method requires. If all components of data are available, one consistent method can solve for all of the second terms (the first terms beyond linear). The explicit nonlinear inversion formulas provide an unambiguous data requirement message as well as conceptual and practical added value beyond both linear approaches and all indirect methods.

Inversion of the shear velocity of the cement in cased borehole through ultrasonic flexural waves

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. D57-D68 ◽  
Author(s):  
Feilong Xu ◽  
Hengshan Hu
Keyword(s):  
Wave Velocity ◽  
Error Rate ◽  
Shear Velocity ◽  
P Wave ◽  
Inversion Method ◽  
Flexural Waves ◽  
S Wave ◽  
Additional Time ◽  
Full Waveforms ◽  
Cased Borehole

Young’s elastic modulus and Poisson’s ratio of the cement in a cased borehole are important in the prediction of the cement sheath integrity under hydraulic fracturing. Although these mechanical properties can be derived in principle from the bulk velocities, the inversion of these velocities of the cement from the received full waveforms remains a challenging problem, especially the S-wave velocity. We have developed an inversion method based on the round-trip traveltimes of the leaked flexural waves (TTL) to invert the bulk velocities of the medium behind the casing. The traveltime difference between the casing wave and the delayed casing wave is the additional time for the leaked wave to travel in the interlayer to the formation and back to the casing. To demonstrate the effectiveness of this method, synthetic full waveforms with a changing interlayer are calculated when an ultrasonic acoustic beam is incident obliquely on the casing. The traveltimes of the wave packets are picked from the envelope curve of the full waveform and then used to invert the bulk velocities in the TTL method. The inverted S-wave velocity of cement is quite accurate with an error rate smaller than 3%, no matter whether the cement is of the ordinary, heavy, or light type. When the interlayer is mud, the P-wave is inverted with an error rate of less than 2%. The P-wave velocity is inverted roughly with an error rate of approximately 10% when the medium behind the casing is light cement.

Bayesian linearized AVO inversion

Geophysics ◽  
2003 ◽  
Vol 68 (1) ◽  
pp. 185-198 ◽  
Author(s):  
Arild Buland ◽  
Henning Omre
Keyword(s):  
Wave Velocity ◽  
Posterior Distribution ◽  
Acoustic Impedance ◽  
Velocity Ratio ◽  
P Wave ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
S Wave ◽  
Data Set ◽  
Avo Inversion

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

Time-reverse imaging with limited S-wave velocity model information

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. MA33-MA40 ◽  
Author(s):  
Brian Steiner ◽  
Erik H. Saenger ◽  
Stefan M. Schmalholz
Keyword(s):  
Energy Density ◽  
Wave Velocity ◽  
Wave Energy ◽  
Velocity Model ◽  
Body Waves ◽  
P Wave ◽  
S Wave ◽  
Velocity Models ◽  
Wave Energy Density ◽  
Wavefield Extrapolation

Time-reverse imaging is a wave propagation algorithm for locating sources. Signals recorded by synchronized receivers are reversed in time and propagated back to the source location by elastic wavefield extrapolation. Elastic wavefield extrapolation requires a P-wave as well as an S-wave velocity model. The velocity models available from standard reflection seismic methods are usually restricted to only P-waves. In this study, we use synthetically produced time signals to investigate the accuracy of seismic source localization by means of time-reverse imaging with the correct P-wave and a perturbed S-wave velocity model. The studies reveal that perturbed S-wave velocity models strongly influence the intensity and position of the focus. Imaging the results with the individual maximum energy density for both body wave types instead of mixed modes allows individual analysis of the two body waves. P-wave energy density images render stable focuses in case of a correct P-wave and incorrect S-wave velocity model. Thus, P-wave energy density seems to be a more suitable imaging condition in case of a high degree of uncertainty in the S-wave velocity model.

scholarly journals Elastic envelope inversion using multicomponent seismic data without low frequency

2014 ◽  
Vol 1 (2) ◽  
pp. 1757-1802
Author(s):  
C. Huang ◽  
L. Dong ◽  
Y. Liu ◽  
B. Chi
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

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