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

Geophysics ◽  
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.

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

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. N31-N50 ◽  
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.

True-amplitude, angle-domain, common-image gathers from one-way wave-equation migrations

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. S49-S58 ◽  
Author(s):  
Yu Zhang ◽  
Sheng Xu ◽  
Norman Bleistein ◽  
Guanquan Zhang
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Wave Equations ◽  
Heterogeneous Media ◽  
Image Point ◽  
Amplitude Wave ◽  
Amplitude Variation ◽  
Imaging Condition ◽  
New Methods ◽  
Amplitude Variation With Angle

True-amplitude wave-equation migration provides a quality migrated image of the earth’s interior. In addition, the amplitude of the output provides an estimate of the angular-dependent reflection coefficient, similar to the output of Kirchhoff inversion. Recently, true-amplitude wave-equation migration for common-shot data has been proposed to generate amplitude-reliable, shot-domain, common-image gathers in heterogeneous media. We present a method to directly produce angle-domain common-image gathers from both common-shot and shot-receiver wave-equation migration. Generating true-amplitude, shot-domain, common-image gathers requires a deconvolution-type imaging condition using the ratio of the upgoing and downgoing wavefield, each downward-projected to the image point. Producing true-amplitude, angle-domain, common-image gathers requires, instead, the product of the upgoing wavefield and the complexconjugate of the downgoing wavefield in the imaging condition. Since multiplication is a more stable computational process than division, the new methods proposed provide more stable ways of inverting seismic data. Furthermore, the resulting common-image gathers can be directly used for migrated amplitude-variation-with angle analysis and tomography-based velocity analysis. Shot-receiver wave-equation migration requires new true-amplitude, one-way wave equations with one depth variable and transverse variables for the coordinates corresponding to sources and receivers, hence, two transverse coordinates in 2D and four transverse coordinates in 3D. We propose a modified double-square-root one-way wave equation to produce true amplitude common-image angle gathers. We also demonstrate the new methods with some synthetic examples. Some numerical examples show that the new methods we propose give better amplitude performance on the migrated angle gathers.

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

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. N81-N92 ◽  
Author(s):  
Amir Mollajan ◽  
Hossein Memarian ◽  
Beatriz Quintal
Keyword(s):  
Synthetic Data ◽  
Imperialist Competitive Algorithm ◽  
Optimization Methods ◽  
Hydrocarbon Exploration ◽  
Inversion Method ◽  
Inversion Problem ◽  
S Wave ◽  
Amplitude Variation ◽  
Competitive Algorithm ◽  
Amplitude Variation With Angle

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.

A constrained global inversion method using an overparameterized scheme: Application to poststack seismic data

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 613-626 ◽  
Author(s):  
Xin‐Quan Ma
Keyword(s):  
Simulated Annealing ◽  
Seismic Data ◽  
A Priori ◽  
Constant Thickness ◽  
Inversion Method ◽  
Model Parameters ◽  
A Priori Information ◽  
Initial Model ◽  
Seismic Waveform ◽  
Priori Information

A global optimization algorithm using simulated annealing has advantages over local optimization approaches in that it can escape from being trapped in local minima and it does not require a good initial model and function derivatives to find a global minimum. It is therefore more attractive and suitable for seismic waveform inversion. I adopt an improved version of a simulated annealing algorithm to invert simultaneously for acoustic impedance and layer interfaces from poststack seismic data. The earth’s subsurface is overparameterized by a series of microlayers with constant thickness in two‐way traveltime. The algorithm is constrained using the low‐frequency impedance trend and has been made computationally more efficient using this a priori information as an initial model. A search bound of each parameter, derived directly from the a priori information, reduces the nonuniqueness problem. Application of this technique to synthetic and field data examples helps one recover the true model parameters and reveals good continuity of estimated impedance across a seismic section. This approach has the capability of revealing the high‐resolution detail needed for reservoir characterization when a reliable migrated image is available with good well ties.

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

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. N1-N15 ◽  
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.

1D viscoelastic waveform inversion for Q structures from the surface seismic and zero-offset VSP data

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC141-WCC148 ◽  
Author(s):  
Yushan Yang ◽  
Yuanyuan Li ◽  
Tianyou Liu
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Central China ◽  
Initial Model ◽  
Reflection And Transmission ◽  
Tomographic Inversion ◽  
Inversion Result ◽  
Transmission Data ◽  
Vsp Data ◽  
Zero Offset

Wave attenuation is an important physical property of hydrocarbon-bearing sediments that is rarely taken into account in site characterization with seismic data. We present a 1D viscoelastic waveform inversion scheme for determining the quality factor [Formula: see text] from the normal-incidence surface seismic and zero-offset vertical seismic profile (VSP) data simultaneously. The joint inversion problem is solved by the damped least-squares method, and the inversion result is successful using synthetic data. The effects of initial model thickness, [Formula: see text] value, and the existence of noise were studied through a synthetic example. By extracting all of the information contained in the waveforms, the waveform inversion of the seismic reflection and transmission data becomes a powerful tool for estimating [Formula: see text]. For a more comprehensive image of [Formula: see text], the tomographic inversion of [Formula: see text] is applied to the walkaway VSP and prestack surface seismic data, using the waveform inversion result as the initial model. Results from applying the method to a real seismic line and zero-offset VSP data from the Nanyang oilfield, central China, indicate that [Formula: see text] from the tomographic inversion of reflection and transmission data contains useful information on medium properties, which can aid in reservoir appraisal.

Double-scale supervised inversion with a data-driven forward model for low-frequency impedance recovery

Geophysics ◽  
2021 ◽  
pp. 1-102
Author(s):  
Sanyi Yuan ◽  
Shangxu Wang ◽  
Wenjing Sang ◽  
Xinqi Jiao ◽  
Yaneng Luo
Keyword(s):  
Seismic Data ◽  
Inverse Operator ◽  
Low Frequency ◽  
Data Driven ◽  
Inversion Method ◽  
Initial Model ◽  
Data Set ◽  
Model Driven ◽  
Impedance Inversion ◽  
Double Scale

Low-frequency information is important in reducing the nonuniqueness of absolute impedance inversion and for quantitative seismic interpretation. In traditional model-driven impedance inversion methods, low-frequency impedance background is from an initial model and is almost unchanged during the inversion process. Moreover, the inversion results are limited by the quality of the modeled seismic data and the extracted wavelet. To alleviate these issues, we investigate a double-scale supervised impedance inversion method based on the gated recurrent encoder-decoder network (GREDN). We first train the decoder network of GREDN called the forward operator, which can map impedance to seismic data. We then implement the well-trained decoder as a constraint to train the encoder network of GREDN called the inverse operator. Besides matching the output of the encoder with broadband pseudo-well impedance labels, data generated by inputting the encoder output into the known decoder match the observed narrowband seismic data. Both the broadband impedance information and the already-trained decoder largely limit the solution space of the encoder. Finally, after training, only the derived optimal encoder is applied to unseen seismic traces to yield broadband impedance volumes. The proposed approach is fully data-driven and does not involve the initial model, seismic wavelet and model-driven operator. Tests on the Marmousi model illustrate that the proposed double-scale supervised impedance inversion method can effectively recover low-frequency components of the impedance model, and demonstrate that low frequencies of the predicted impedance originate from well logs. Furthermore, we apply the strategy of combining the double-scale supervised impedance inversion method with a model-driven impedance inversion method to process field seismic data. Tests on a field data set show that the predicted impedance results not only reveal a classical tectonic sedimentation history, but also match the corresponding results measured at the locations of two wells.

A Solution of Imaging and Wave Impedance Inversion of Seismic Data

2013 ◽  
Vol 373-375 ◽  
pp. 569-573
Author(s):  
Rui Yang ◽  
Guang Xun Chen ◽  
Pan Ke Qin ◽  
Neng You Wu ◽  
Jia Shun Yu
Keyword(s):  
Seismic Data ◽  
Wave Impedance ◽  
Inversion Method ◽  
Reflection Coefficients ◽  
Inversion Result ◽  
Impedance Model ◽  
Impedance Inversion ◽  
High Vertical Resolution ◽  
And Inversion

In order to improve the resolution and accuracy of the inversion, this paper proposed a new inversion method. By introducing constraint sparse spike inversion, the new method can fully take the advantages of high vertical resolution of logging data and the preferable transverse continuity of the seismic data to improve the resolution of the profiles and the quality of imaging and inversion in specific areas. Experimental results showed that this solution can deduce more precise and reasonable inversion result than other inversion solution. Constraint sparse spike inversion can generate reflection coefficients with broad frequency band and solve the marking problems preferably, thereby makes the impedance model obtained from the inversion even close to the actual situation underground.

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