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.

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.

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.

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.

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.

Numerical and Theoretical Investigation on the Origin of the Multiple Peaks of the H/V Ratio Curve

2021 ◽  
Author(s):  
Wanbo Xiao ◽  
Siqi Lu ◽  
Yanbin Wang
Keyword(s):  
Rayleigh Wave ◽  
Wave Velocity ◽  
Subsurface Layer ◽  
P Wave ◽  
Theoretical Formula ◽  
S Wave ◽  
Multiple Peaks ◽  
Ratio Curve ◽  
Multiple Layer ◽  
Wave Resonance

<p>Despite the popularity of the horizontal to vertical spectral ratio (HVSR) method in site effect studies, the origin of the H/V peaks has been controversial since this method was proposed. Many previous studies mainly focused on the explanation of the first or single peak of the H/V ratio, trying to distinguish between the two hypotheses — the S-wave resonance and ellipticity of Rayleigh wave. However, it is common both in numerical simulations and practical experiments that the H/V ratio exhibits multiple peaks, which is essential to explore the origin of the H/V peaks.</p><p>The cause for the multiple H/V peaks has not been clearly figured out, and once was simply explained as the result of multi subsurface layers. Therefore, we adopted numerical method to simulate the ambient noise in various layered half-space models and calculated the H/V ratio curves for further comparisons. The peak frequencies of the H/V curves accord well with the theoretical frequencies of S-wave resonance in two-layer models, whose frequencies only depend on the S wave velocity and the thickness of the subsurface layer. The same is true for models with varying model parameters. Besides, the theoretical formula of the S-wave resonance in multiple-layer models is proposed and then supported by numerical investigations as in the cases of two-layer models. We also extended the S-wave resonance to P-wave resonance and found that its theoretical frequencies fit well with the V/H peaks, which could be an evidence to support the S-wave resonance theory from a new perspective. By contrast, there are obvious differences between the higher orders of the H/V ratio peaks and the higher orders of Rayleigh wave ellipticity curves both in two-layer and multiple-layer models. The Rayleigh wave ellipticity curves are found to be sensitive to the Poisson’s ratio and the thickness of the subsurface layer, so the variation of the P wave velocity can affect the peak frequencies of the Rayleigh wave ellipticity curves while the H/V peaks show slight change. The Rayleigh wave ellipticity theory is thus proved to be inappropriate for the explanation of the multiple H/V peaks, while the possible effects of the Rayleigh wave on the fundamental H/V peak still cannot be excluded.</p><p>Based on the analyses above, we proposed a new evidence to support the claim that the peak frequencies of the H/V ratio curve, except the fundamental peaks, are caused by S-wave resonance. The relationship between the P-wave resonance and the V/H peaks may also find further application.</p>

Using Seismic Data to Predict Shale Pore Pressure and Overpressure Sweet Spots: A Case Study from the Lower Silurian Longmaxi Formation in Sichuan Basin, China

2021 ◽  
Author(s):  
Sheng Chen ◽  
Qingcai Zeng ◽  
Xiujiao Wang ◽  
Qing Yang ◽  
Chunmeng Dai ◽  
...  
Keyword(s):  
Prediction Model ◽  
Wave Velocity ◽  
Shale Gas ◽  
Seismic Data ◽  
P Wave ◽  
Formation Pressure ◽  
S Wave ◽  
P Wave Velocity ◽  
New Formation ◽  
Sweet Spots

Abstract Practices of marine shale gas exploration and development in south China have proved that formation overpressure is the main controlling factor of shale gas enrichment and an indicator of good preservation condition. Accurate prediction of formation pressure before drilling is necessary for drilling safety and important for sweet spots predicting and horizontal wells deploying. However, the existing prediction methods of formation pore pressures all have defects, the prediction accuracy unsatisfactory for shale gas development. By means of rock mechanics analysis and related formulas, we derived a formula for calculating formation pore pressures. Through regional rock physical analysis, we determined and optimized the relevant parameters in the formula, and established a new formation pressure prediction model considering P-wave velocity, S-wave velocity and density. Based on regional exploration wells and 3D seismic data, we carried out pre-stack seismic inversion to obtain high-precision P-wave velocity, S-wave velocity and density data volumes. We utilized the new formation pressure prediction model to predict the pressure and the spatial distribution of overpressure sweet spots. Then, we applied the measured pressure data of three new wells to verify the predicted formation pressure by seismic data. The result shows that the new method has a higher accuracy. This method is qualified for safe drilling and prediction of overpressure sweet spots for shale gas development, so it is worthy of promotion.

Constraints on the composition of the crust and uppermost mantle in northwestern Canada: Vp/Vs variations along Lithoprobe's SNorCLE transect

2005 ◽  
Vol 42 (6) ◽  
pp. 1205-1222 ◽  
Author(s):  
Gabriela Fernández-Viejo ◽  
Ron M Clowes ◽  
J Kim Welford
Keyword(s):  
Wave Velocity ◽  
Upper Mantle ◽  
Laboratory Data ◽  
High Ratio ◽  
P Wave ◽  
S Wave ◽  
Uppermost Mantle ◽  
Crust And Upper Mantle ◽  
Slave Craton ◽  
Crustal Composition

Shear-wave seismic data recorded along four profiles during the SNoRE 97 (1997 Slave – Northern Cordillera Refraction Experiment) refraction – wide-angle reflection experiment in northwestern Canada are analyzed to provide S-wave velocity (Vs) models. These are combined with previous P-wave velocity (Vp) models to produce cross sections of the ratio Vp/Vs for the crust and upper mantle. The Vp/Vs values are related to rock types through comparisons with published laboratory data. The Slave craton has low Vp/Vs values of 1.68–1.72, indicating a predominantly silicic crustal composition. Higher values (1.78) for the Great Bear and eastern Hottah domains of the Wopmay orogen imply a more mafic than average crustal composition. In the western Hottah and Fort Simpson arc, values of Vp/Vs drop to ∼1.69. These low values continue westward for 700 km into the Foreland and Omineca belts of the Cordillera, providing support for the interpretation from coincident seismic reflection studies that much of the crust from east of the Cordilleran deformation front to the Stikinia terrane of the Intermontane Belt consists of quartzose metasedimentary rocks. Stikinia shows values of 1.78–1.73, consistent with its derivation as a volcanic arc terrane. Upper mantle velocity and ratio values beneath the Slave craton indicate an ultramafic peridotitic composition. In the Wopmay orogen, the presence of low Vp/Vs ratios beneath the Hottah – Fort Simpson transition indicates the presence of pyroxenite in the upper mantle. Across the northern Cordillera, low Vp values and a moderate-to-high ratio in the uppermost mantle are consistent with the region's high heat flow and the possible presence of partial melt.

Nonlinear two‐dimensional elastic inversion of multioffset seismic data

Geophysics ◽  
1987 ◽  
Vol 52 (9) ◽  
pp. 1211-1228 ◽  
Author(s):  
Peter Mora
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
A Priori ◽  
Gaussian Model ◽  
Wave Impedance ◽  
P Wave ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Gradient Direction ◽  
P Wave Velocity

The treatment of multioffset seismic data as an acoustic wave field is becoming increasingly disturbing to many geophysicists who see a multitude of wave phenomena, such as amplitude‐offset variations and shearwave events, which can only be explained by using the more correct elastic wave equation. Not only are such phenomena ignored by acoustic theory, but they are also treated as undesirable noise when they should be used to provide extra information, such as S‐wave velocity, about the subsurface. The problems of using the conventional acoustic wave equation approach can be eliminated via an elastic approach. In this paper, equations have been derived to perform an inversion for P‐wave velocity, S‐wave velocity, and density as well as the P‐wave impedance, S‐wave impedance, and density. These are better resolved than the Lamé parameters. The inversion is based on nonlinear least squares and proceeds by iteratively updating the earth parameters until a good fit is achieved between the observed data and the modeled data corresponding to these earth parameters. The iterations are based on the preconditioned conjugate gradient algorithm. The fundamental requirement of such a least‐squares algorithm is the gradient direction which tells how to update the model parameters. The gradient direction can be derived directly from the wave equation and it may be computed by several wave propagations. Although in principle any scheme could be chosen to perform the wave propagations, the elastic finite‐ difference method is used because it directly simulates the elastic wave equation and can handle complex, and thus realistic, distributions of elastic parameters. This method of inversion is costly since it is similar to an iterative prestack shot‐profile migration. However, it has greater power than any migration since it solves for the P‐wave velocity, S‐wave velocity, and density and can handle very general situations including transmission problems. Three main weaknesses of this technique are that it requires fairly accurate a priori knowledge of the low‐ wavenumber velocity model, it assumes Gaussian model statistics, and it is very computer‐intensive. All these problems seem surmountable. The low‐wavenumber information can be obtained either by a prior tomographic step, by the conventional normal‐moveout method, by a priori knowledge and empirical relationships, or by adding an additional inversion step for low wavenumbers to each iteration. The Gaussian statistics can be altered by preconditioning the gradient direction, perhaps to make the solution blocky in appearance like well logs, or by using large model variances in the inversion to reduce the effect of the Gaussian model constraints. Moreover, with some improvements to the algorithm and more parallel computers, it is hoped the technique will soon become routinely feasible.

Shear‐wave velocity and density estimation from PS-wave AVO analysis: Application to an OBS dataset from the North Sea

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1446-1454 ◽  
Author(s):  
Side Jin ◽  
G. Cambois ◽  
C. Vuillermoz
Keyword(s):  
Wave Velocity ◽  
North Sea ◽  
Random Noise ◽  
P Wave ◽  
S Wave ◽  
Data Set ◽  
Avo Analysis ◽  
The North ◽  
Avo Inversion ◽  
The North Sea

S-wave velocity and density information is crucial for hydrocarbon detection, because they help in the discrimination of pore filling fluids. Unfortunately, these two parameters cannot be accurately resolved from conventional P-wave marine data. Recent developments in ocean‐bottom seismic (OBS) technology make it possible to acquire high quality S-wave data in marine environments. The use of (S)-waves for amplitude variation with offset (AVO) analysis can give better estimates of S-wave velocity and density contrasts. Like P-wave AVO, S-wave AVO is sensitive to various types of noise. We investigate numerically and analytically the sensitivity of AVO inversion to random noise and errors in angles of incidence. Synthetic examples show that random noise and angle errors can strongly bias the parameter estimation. The use of singular value decomposition offers a simple stabilization scheme to solve for the elastic parameters. The AVO inversion is applied to an OBS data set from the North Sea. Special prestack processing techniques are required for the success of S-wave AVO inversion. The derived S-wave velocity and density contrasts help in detecting the fluid contacts and delineating the extent of the reservoir sand.

scholarly journals Discussion on the Theoretical Basis for Cross-Over Method Applied to Downhole Wave Velocity Test

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qing Dong ◽  
Zheng-hua Zhou ◽  
Su Jie ◽  
Bing Hao ◽  
Yuan-dong Li
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Wave Velocity ◽  
Theoretical Basis ◽  
Influence Factors ◽  
P Wave ◽  
Engineering Practice ◽  
S Wave ◽  
Simulation Results ◽  
The Cross

At engineering practice, the theoretical basis for the cross-over method, used to obtain shear wave arrival time in the downhole method of the wave velocity test by surface forward and backward strike, is that the polarity of P-wave keeps the same, while the polarity of S-wave transforms when the direction of strike inverted. However, the characteristics of signals recorded in tests are often found to conflict with this theoretical basis for the cross-over method, namely, the polarity of the P-wave also transforms under the action of surface forward and backward strike. Therefore, 3D finite element numerical simulations were conducted to study the validity of the theoretical basis for the cross-over method. The results show that both shear and compression waves are observed to be in 180° phase difference between horizontal signal traces, consistent with the direction of excitation generated by reversed impulse. Furthermore, numerical simulation results prove to be reliable by the analytic solution; it shows that the theoretical basis for the cross-over method applied to the downhole wave velocity test is improper. In meanwhile, numerical simulations reveal the factors (inclining excitation, geophone deflection, inclination, and background noise) that may cause the polarity of the P-wave not to reverse under surface forward and backward strike. Then, as to reduce the influence factors, we propose a method for the downhole wave velocity test under surface strike, the time difference of arrival is based between source peak and response peak, and numerical simulation results show that the S-wave velocity by this method is close to the theoretical S-wave velocity of soil.

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