scholarly journals Multiparameter Inversion: Cramer's Rule for Pseudodifferential Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Rami Nammour ◽  
William W. Symes
Keyword(s):  
Iterative Methods ◽  
Pseudodifferential Operators ◽  
Normal Operator ◽  
Model Parameters ◽  
Model Driven ◽  
Amplitude Versus Offset ◽  
Multiparameter Problem ◽  
Cramer’S Rule ◽  
Large Linear Systems ◽  
Amplitude Versus

Linearized multiparameter inversion is a model-driven variant of amplitude-versus-offset analysis, which seeks to separately account for the influences of several model parameters on the seismic response. Previous approaches to this class of problems have included geometric optics-based (Kirchhoff, GRT) inversion and iterative methods suitable for large linear systems. In this paper, we suggest an approach based on the mathematical nature of the normal operator of linearized inversion—it is a scaling operator in phase space—and on a very old idea from linear algebra, namely, Cramer's rule for computing the inverse of a matrix. The approximate solution of the linearized multiparameter problem so produced involves no ray theory computations. It may be sufficiently accurate for some purposes; for others, it can serve as a preconditioner to enhance the convergence of standard iterative methods.

Simultaneous joint inversion of amplitude-versus-offset and controlled-source electromagnetic data by implicit representation of common parameter structure

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. ID15-ID27 ◽  
Author(s):  
Martha Lien
Keyword(s):  
Joint Inversion ◽  
P Wave ◽  
Fluid Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
Controlled Source ◽  
Flow Monitoring ◽  
Fluid Saturation ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

I evaluated a simultaneous joint inversion of seismic amplitude-versus-offset (AVO) and controlled-source electromagnetic (CSEM) data for fluid-flow monitoring. A new approach for structure-coupled joint inversion was presented, in which the coupling of the two data types was obtained by allowing for the direct identification of parameter structure that is shared by the different geophysical model parameters. The main idea was to use a composite parameter representation, which enables inversion with respect to the parameter magnitude and parameter structure. In the current application, parameter structure refers to transitions between dominating property values and is represented by the position and shape of the flooding front. Hence, with this approach, the position and shape of the flooding front are inverted for directly, and the coupling between the different data sets is obtained without the inclusion of an additional penalizing term in the objective function. Regularization of the inverse problem is obtained by using a flexible parameterization grid adapted to the resolution power of the available data. This approach is especially suited for problems in which the prior information is limited or highly uncertain. The solution approach is illustrated for two types of coupling: (1) identification of fluid saturation using rock-physics modeling and (2) for structure-coupled joint inversion with respect to P-wave velocity and electric conductivity. Through various synthetic examples in 2D, the proposed approach showed its efficiency for identifying the main features of the fluid distribution within the reservoir. Simultaneously inverting AVO and CSEM data was further seen to give results that were more robust with respect to certain random and more systematic (modeling) errors compared with inverting the data sets separately.

High-order sparse Radon transform for AVO-preserving data reconstruction

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. V13-V22 ◽  
Author(s):  
Yaru Xue ◽  
Jitao Ma ◽  
Xiaohong Chen
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Field Data ◽  
High Order ◽  
Data Reconstruction ◽  
Model Parameters ◽  
Data Interpolation ◽  
Constant Amplitude ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

The sparse Radon transform (RT) represents seismic data by the superposition of a few constant amplitude events, and thus it has trouble dealing with amplitude-versus-offset (AVO) variations. We integrated the gradient and curvature parameters of AVO into the RT. With these additional properties, the lateral continuity of the events’ amplitude was modeled in the transformation and it could be fitted with orthogonal polynomials. This resulted in a higher order RT, which included AVO terms. The high-order RT is a highly underdetermined problem, which was solved by extracting the major model parameters from energy distribution in a high-order Radon domain and by decreasing the number of inversion parameters. Thus, a high-order sparse RT was achieved. The proposed method can be used for data interpolation as well as extrapolation. The AVO-preservation performance of the proposed algorithm in data reconstruction was illustrated using both synthetic and field data examples, and the results showed the feasibility of the method.

Incomplete AVO near salt structures

Geophysics ◽  
1992 ◽  
Vol 57 (4) ◽  
pp. 543-553 ◽  
Author(s):  
Christopher P. Ross
Keyword(s):  
Seismic Profiles ◽  
Spectral Modeling ◽  
Signal Degradation ◽  
Amplitude Versus Offset ◽  
Bright Spots ◽  
Close Proximity ◽  
Pseudo Spectral ◽  
Amplitude Versus ◽  
Structure Class ◽  
Made In

Amplitude versus offset (AVO) measurements for deep hydrocarbon‐bearing sands can be compromised when made in close proximity to a shallow salt piercement structure. Anomalous responses are observed, particularly on low acoustic impedance bright spots. CMP data from key seismic profiles traversing the bright spots do not show the expected Class 3 offset responses. On these CMPs, significant decrease of far trace energy is observed. CMP data from other seismic profiles off‐structure do exhibit the Class 3 offset responses, implying that structural complications may be interfering with the offset response. A synthetic AVO gather was generated using well log data, which supports the off‐structure Class 3 responses, further reinforcing the concept of structurally‐biased AVO responses. Acoustic, pseudo‐spectral modeling of the structure substantiates the misleading AVO response. Pseudo‐spectral modeling results suggest that signal degradation observed on the far offsets is caused by wavefield refraction—a shadow zone, where the known hydrocarbon‐bearing sands are not completely illuminated. Such shadow zones obscure the correct AVO response, which may have bearing on exploration and development.

scholarly journals Crosswell Seismic Amplitude-Versus-Offset for Detailed Imaging of Facies and Fluid Distribution within Carbonate Oil Reservoirs

2008 ◽  
Author(s):  
Wayne Pennington ◽  
Mohamed Ibrahim ◽  
Roger Turpening ◽  
Sean Trisch ◽  
Josh Richardson ◽  
...  
Keyword(s):  
Oil Reservoirs ◽  
Fluid Distribution ◽  
Seismic Amplitude ◽  
Amplitude Versus Offset ◽  
Detailed Imaging ◽  
Amplitude Versus

scholarly journals QVOA Techniques for Estimation of Fracture Directions

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Vladimir Sabinin
Keyword(s):  
Quality Factor ◽  
Symmetry Axis ◽  
Factor Versus ◽  
Synthetic Data ◽  
Computational Techniques ◽  
High Quality ◽  
Amplitude Versus Offset ◽  
Target Layer ◽  
Analysis Quality ◽  
Amplitude Versus

Some new computational techniques are suggested for estimating symmetry axis azimuth of fractures in the viscoelastic anisotropic target layer in the framework of QVOA analysis (Quality factor Versus Offset and Azimuth). The different QVOA techniques are compared using synthetic viscoelastic surface reflected data with and without noise. I calculated errors for these techniques which depend on different sets of azimuths and intervals of offsets. Superiority of the high-order “enhanced general” and “cubic” techniques is shown. The high-quality QVOA techniques are compared with one of the high-quality AVOA techniques (Amplitude Versus Offset and Azimuth) in the synthetic data with noise and attenuation. Results are comparable.

High-resolution seismic velocity analysis by sign-based weighted semblance

Geophysics ◽  
2021 ◽  
pp. 1-35
Author(s):  
M. Javad Khoshnavaz
Keyword(s):  
Seismic Velocity ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Correlation Coefficients ◽  
Velocity Model ◽  
Seismic Attenuation ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Amplitude Versus Offset ◽  
Amplitude Versus

Building an accurate velocity model plays a vital role in routine seismic imaging workflows. Normal-moveout-based seismic velocity analysis is a popular method to make the velocity models. However, traditional velocity analysis methodologies are not generally capable of handling amplitude variations across moveout curves, specifically polarity reversals caused by amplitude-versus-offset anomalies. I present a normal-moveout-based velocity analysis approach that circumvents this shortcoming by modifying the conventional semblance function to include polarity and amplitude correction terms computed using correlation coefficients of seismic traces in the velocity analysis scanning window with a reference trace. Thus, the proposed workflow is suitable for any class of amplitude-versus-offset effects. The approach is demonstrated to four synthetic data examples of different conditions and a field data consisting a common-midpoint gather. Lateral resolution enhancement using the proposed workflow is evaluated by comparison between the results from the workflow and the results obtained by the application of conventional semblance and three semblance-based velocity analysis algorithms developed to circumvent the challenges associated with amplitude variations across moveout curves, caused by seismic attenuation and class II amplitude-versus-offset anomalies. According to the obtained results, the proposed workflow is superior to all the presented workflows in handling such anomalies.

Model Expansion in Model-Driven Architectures

2012 ◽  
pp. 28-50
Author(s):  
Tsung Lee ◽  
Jhih-Syan Hou
Keyword(s):  
Hierarchical Model ◽  
Expansion Method ◽  
Model Parameters ◽  
Model Composition ◽  
Tree Structures ◽  
Model Driven ◽  
Design Structure ◽  
Model Instance ◽  
Composition Graph ◽  
Model Expansion

In this chapter, the authors introduce a model expansion method that is used in a new methodology of model composition and evolution for broad design domains. In the methodology, hierarchical model compositional relationships are captured in a model composition graph (MCG) as a schema of designs. An MCG schema can be used as a blueprint for systematic and flexible evolution of designs with three hierarchical model refinement operations: expansion, synthesis, and configuration. In this methodology, due to the need of hierarchical sharing in software and hardware domains, the authors designed an algorithm to achieve conditional and recursive model expansion with hierarchical model instance sharing that is not achievable in other expansion methods. Hierarchical model instance sharing complicates the design structure from tree structures to graph structures. The model expansion algorithm was thus designed with enhanced features of maintenance of MCG instance consistency, path-based search of shared submodel instances, and dependency preserving expansion ordering. The expansion specification and the expansion process are integrated with the MCG-based methodology. Model parameters set by designers and other refinement operations can be used to guide each expansion step of design models iteratively.

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