Imperialist competitive algorithm optimization method for nonlinear amplitude variation with angle inversion

Amplitude variation with angle (AVA) inversion is one of the most effective techniques in hydrocarbon exploration and estimating subsurface petrophysical properties. The inversion problem as a nonlinear, multiparameter, and multimodal optimization problem is conventionally solved through linearized optimization methods, but with the cost of smoothing important geologic interfaces. In addition, the results obtained by these methods are more possible to be trapped in a local minimum, while global-optimization methods can produce more accurate results and preserve the interfaces of geologic structures. A Bayesian framework is used to formulate the AVA inversion problem, which incorporates a novel prior constraint included by two regularization functions, one for sparsity of the coefficients as well as recovering discontinuities and another one for enhancing the lateral continuity. The imperialist competitive algorithm as an efficient evolutionary algorithm is then used to optimize the resulted objective function, to invert the P-and S-wave velocities as well as the density. We compare our algorithm with a commonly used Bayesian linearized inversion method by applying both methods on synthetic data and real seismic data from Gulf of Mexico. Our results reveal the practicability and stability of the presented method for the AVA inversion problem.

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Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽

10.1190/geo2017-0621.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. R669-R679 ◽

Cited By ~ 1

Author(s):

Gang Chen ◽

Xiaojun Wang ◽

Baocheng Wu ◽

Hongyan Qi ◽

Muming Xia

Keyword(s):

Reservoir Characterization ◽

Synthetic Data ◽

Pore Fluid ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Fluid Identification ◽

Fluid Property ◽

Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

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Joint anisotropic amplitude variation with offset inversion of PP and PS seismic data

Geophysics ◽

10.1190/geo2016-0516.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. N31-N50 ◽

Cited By ~ 8

Author(s):

Jun Lu ◽

Yun Wang ◽

Jingyi Chen ◽

Ying An

Keyword(s):

Seismic Data ◽

Local Minimum ◽

Synthetic Data ◽

Inversion Method ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion ◽

Time Migration ◽

Amplitude Variation With Angle ◽

Two Stages

With the increase in exploration target complexity, more parameters are required to describe subsurface properties, particularly for finely stratified reservoirs with vertical transverse isotropic (VTI) features. We have developed an anisotropic amplitude variation with offset (AVO) inversion method using joint PP and PS seismic data for VTI media. Dealing with local minimum solutions is critical when using anisotropic AVO inversion because more parameters are expected to be derived. To enhance the inversion results, we adopt a hierarchical inversion strategy to solve the local minimum solution problem in the Gauss-Newton method. We perform the isotropic and anisotropic AVO inversions in two stages; however, we only use the inversion results from the first stage to form search windows for constraining the inversion in the second stage. To improve the efficiency of our method, we built stop conditions using Euclidean distance similarities to control iteration of the anisotropic AVO inversion in noisy situations. In addition, we evaluate a time-aligned amplitude variation with angle gather generation approach for our anisotropic AVO inversion using anisotropic prestack time migration. We test the proposed method on synthetic data in ideal and noisy situations, and find that the anisotropic AVO inversion method yields reasonable inversion results. Moreover, we apply our method to field data to show that it can be used to successfully identify complex lithologic and fluid information regarding fine layers in reservoirs.

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Amplitude variation with angle inversion using the exact Zoeppritz equations — Theory and methodology

Geophysics ◽

10.1190/geo2014-0582.1 ◽

2016 ◽

Vol 81 (2) ◽

pp. N1-N15 ◽

Cited By ~ 13

Author(s):

Lixia Zhi ◽

Shuangquan Chen ◽

Xiang-yang Li

Keyword(s):

Parameter Extraction ◽

Tikhonov Regularization Method ◽

Inversion Method ◽

Data Sets ◽

Nonlinear Inversion ◽

S Wave ◽

Amplitude Variation ◽

Highly Nonlinear ◽

Amplitude Variation With Angle ◽

Dominant Frequencies

To overcome the weaknesses of conventional prestack amplitude variation with angle inversion based on various linear or quasi-linear approximations, we have conducted a nonlinear inversion method using the exact Zoeppritz matrix (EZAI). However, the inversion using the exact Zoeppritz matrix was highly nonlinear and often unstable, if not properly treated. To tackle these issues, we have used an iteratively regularizing Levenberg-Marquardt scheme (IRLM), which regularizes the inversion problem within an algorithm that minimizes the misfit between the observed and the modeled data at the same time by incorporating the Tikhonov regularization method. As a result, the new EZAI method solved using the IRLM scheme is feasible for seismic data sets with large incidence angles, even up to or beyond the critical angle as well as strong parameter contrasts. Single and multilayered synthetic examples were used to test these features. These tests also showed that EZAI is robust on noisy gathers for parameter extraction and has weak dependence on the initial model. For the influence of inaccurate amplitudes, dominant frequencies, and phase angles, we found that EZAI is less sensitive to the variation in amplitude and phase shifts than to the dominant frequencies. Specifically, the inversion results of EZAI for P- and S-wave velocities and density were reliable if the inaccurate range for the amplitude was within 20% or the angle of the phase shift was no more than 20°. The superiority of EZAI makes it a very promising method for the estimation of subsurface elastic parameters.

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Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

Interpretation ◽

10.1190/int-2016-0056.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T613-T625 ◽

Cited By ~ 1

Author(s):

Qizhen Du ◽

Bo Zhang ◽

Xianjun Meng ◽

Chengfeng Guo ◽

Gang Chen ◽

...

Keyword(s):

Reflection Coefficient ◽

Wave Reflection ◽

Coefficient Matrix ◽

P Wave ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion ◽

Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reﬂectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reﬂectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

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Frequency‐wavenumber elastic inversion of marine seismic data

Geophysics ◽

10.1190/1.1443574 ◽

1994 ◽

Vol 59 (12) ◽

pp. 1868-1881 ◽

Cited By ~ 16

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.

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Elastic envelope inversion using multicomponent seismic data without low frequency

Nonlinear Processes in Geophysics Discussions ◽

10.5194/npgd-1-1757-2014 ◽

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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Model parameterization and amplitude variation with angle and azimuthal inversion in orthotropic media

Geophysics ◽

10.1190/geo2018-0778.1 ◽

2020 ◽

Vol 86 (1) ◽

pp. R1-R14

Author(s):

Zhaoyun Zong ◽

Lixiang Ji

Keyword(s):

Parameter Estimation ◽

Seismic Data ◽

Inversion Method ◽

Initial Model ◽

Amplitude Variation ◽

Inversion Result ◽

Model Parameterization ◽

Orthotropic Media ◽

The Stability ◽

Amplitude Variation With Angle

Horizontal layered formations with a suite of vertical or near-vertical fractures are usually assumed to be an approximate orthotropic medium and are more suitable for estimating fracture properties with wide-azimuth prestack seismic data in shale reservoirs. However, the small contribution of anisotropic parameters to the reflection coefficients highly reduces the stability of anisotropic parameter estimation by using seismic inversion approaches. Therefore, a novel model parameterization approach for the reflectivity and a pragmatic inversion method are proposed to enhance the stability of the inversion for orthotropic media. Previous attempts to characterize orthotropic media properties required using four or ﬁve independent parameters. However, we have derived a novel formulation that reduces the number of parameters to three. The inversion process is better conditioned with fewer degrees of freedom. An accuracy comparison of our formula with the previous ones indicates that our approach is sufﬁciently precise for reasonable parameter estimation. Furthermore, a Bayesian inversion method is developed that uses the amplitude variation with angle and azimuth (AVAZ) of the seismic data. Smooth background constraints reduce the similarity between the inversion result and the initial model, thereby reducing the sensitivity of the initial model to the inversion result. Cauchy and Gaussian probability distributions are used as prior constraints on the model parameters and the likelihood function, respectively. These ensure that the results are within the range of plausibility. Synthetic examples demonstrate that the adopted orthotropic AVAZ inversion method is feasible for estimating the anisotropic parameters even with moderate noise. The ﬁeld data example illustrates the inversion robustness and stability of the adopted method in a fractured reservoir with a single well control.

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Joint inversion of logging-while-drilling multipole acoustic data to determine formation shear-wave transverse isotropy

Geophysics ◽

10.1190/geo2019-0611.1 ◽

2020 ◽

Vol 85 (4) ◽

pp. D121-D132

Author(s):

Yang-Hu Li ◽

Song Xu ◽

Can Jiang ◽

Yuan-Da Su ◽

Xiao-Ming Tang

Keyword(s):

Shear Wave ◽

Joint Inversion ◽

Transverse Isotropy ◽

Synthetic Data ◽

Flexural Wave ◽

Inversion Method ◽

S Wave ◽

Acoustic Data ◽

Wave Data ◽

Logging While Drilling

Seismic-wave anisotropy has long been an important topic in the exploration and development of unconventional reservoirs, especially in shales, which are commonly characterized as transversely isotropic ([TI] or vertical TI [VTI]) media. At present, the shear-wave (S-wave) TI properties have mainly been determined from monopole Stoneley- or dipole flexural-wave measurements in wireline acoustic logging, but the feasibility of those obtained from logging-while-drilling (LWD) acoustic data needs to be established. We have developed a joint inversion method for simultaneously determining formation S-wave transverse isotropy and vertical velocity from LWD multipole acoustic data. Our theoretical analysis shows that the presence of anisotropy strongly influences LWD Stoneley- and quadrupole-wave dispersion characteristics. Although the monopole Stoneley and quadrupole waves are sensitive to the formation S-wave TI parameters, they suffer from the typical nonuniqueness problem when using the individual-wave data to invert parameters alone. Thus, the respective dispersion data can be jointly used to estimate the formation S-wave TI properties. By the joint inversion, the nonuniqueness problem in the parameter inversion can also be effectively alleviated. The feasibility of the method has been verified by the processing results of theoretical synthetic data and field LWD acoustic-wave data. Therefore, the result offers an effective method for evaluating VTI formation anisotropy from acoustic LWD data.

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