The uncertainty in layered models from wide-angle seismic data

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. WB31-WB36 ◽  
Author(s):  
M. Majdański
Keyword(s):  
Quantitative Estimation ◽  
A Priori ◽  
Forward Modeling ◽  
Small Error ◽  
Head Wave ◽  
Wide Angle ◽  
Simultaneous Inversion ◽  
Analytical Estimation ◽  
Modeling Strategy ◽  
Layered Models

The analytical method of estimating the uncertainty in layered models is addressed to models obtained using a layer-stripping modeling strategy or forward modeling. It is based on a simple principle of small error propagation. There are two variants of the method: a simplified one that includes refraction and vertical reflections and one that also includes wide-angle reflections. Both give a quantitative estimation for the existing models. To allow for a simple analytical estimation, refracted waves are described using a head-wave approximation in constant velocity layers; wide angle reflection paths are also simplified. In the case of trial and error forward modeling, this method can help determine how well the used parameterization is reflected in the data and avoid over-fitting the structures. This is especially important because the forward modeling is very subjective and there is no method to assess the parameterization without generating alternative models. For inversion problems using the layer-stripping method, the analysis allows for a correct propagation of errors and will help to evaluate the effect of including a priori information with known uncertainty. As a result, the layer-stripping modeling strategy is worse than simultaneous inversion for layered models because it gives larger uncertainties.

scholarly journals Estimation of rock physics properties from seismic attributes — Part 1: Strategy and sensitivity analysis

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. M35-M53 ◽  
Author(s):  
Bastien Dupuy ◽  
Stéphane Garambois ◽  
Jean Virieux
Keyword(s):  
Input Data ◽  
Reservoir Characterization ◽  
Quantitative Estimation ◽  
A Priori ◽  
Rock Physics ◽  
Fluid Phase ◽  
Quality Factors ◽  
Simultaneous Inversion ◽  
Fluid Saturation ◽  
Wide Range

The quantitative estimation of rock physics properties is of great importance in any reservoir characterization. We have studied the sensitivity of such poroelastic rock physics properties to various seismic viscoelastic attributes (velocities, quality factors, and density). Because we considered a generalized dynamic poroelastic model, our analysis was applicable to most kinds of rocks over a wide range of frequencies. The viscoelastic attributes computed by poroelastic forward modeling were used as input to a semiglobal optimization inversion code to estimate poroelastic properties (porosity, solid frame moduli, fluid phase properties, and saturation). The sensitivity studies that we used showed that it was best to consider an inversion system with enough input data to obtain accurate estimates. However, simultaneous inversion for the whole set of poroelastic parameters was problematic due to the large number of parameters and their trade-off. Consequently, we restricted the sensitivity tests to the estimation of specific poroelastic parameters by making appropriate assumptions on the fluid content and/or solid phases. Realistic a priori assumptions were made by using well data or regional geology knowledge. We found that (1) the estimation of frame properties was accurate as long as sufficient input data were available, (2) the estimation of permeability or fluid saturation depended strongly on the use of attenuation data, and (3) the fluid bulk modulus can be accurately inverted, whereas other fluid properties have a low sensitivity. Introducing errors in a priori rock physics properties linearly shifted the estimations, but not dramatically. Finally, an uncertainty analysis on seismic input data determined that, even if the inversion was reliable, the addition of more input data may be required to obtain accurate estimations if input data were erroneous.

scholarly journals THE ERROR TERM IN THE HISTORY OF TIME SERIES ECONOMETRICS

2001 ◽  
Vol 17 (2) ◽  
pp. 424-450 ◽  
Author(s):  
Duo Qin ◽  
Christopher L. Gilbert
Keyword(s):  
Time Series ◽  
Rational Expectations ◽  
Time Series Data ◽  
A Priori ◽  
Theoretical Models ◽  
Series Data ◽  
London School ◽  
Time Series Econometrics ◽  
Cowles Commission ◽  
Modeling Strategy

We argue that many methodological confusions in time-series econometrics may be seen as arising out of ambivalence or confusion about the error terms. Relationships between macroeconomic time series are inexact, and, inevitably, the early econometricians found that any estimated relationship would only fit with errors. Slutsky interpreted these errors as shocks that constitute the motive force behind business cycles. Frisch tried to dissect the errors further into two parts: stimuli, which are analogous to shocks, and nuisance aberrations. However, he failed to provide a statistical framework to make this distinction operational. Haavelmo, and subsequent researchers at the Cowles Commission, saw errors in equations as providing the statistical foundations for econometric models and required that they conform to a priori distributional assumptions specified in structural models of the general equilibrium type, later known as simultaneous-equations models. Because theoretical models were at that time mostly static, the structural modeling strategy relegated the dynamics in time-series data frequently to nuisance, atheoretical complications. Revival of the shock interpretation in theoretical models came about through the rational expectations movement and development of the vector autoregression modeling approach. The so-called London School of Economics dynamic specification approach decomposes the dynamics of the modeled variable into three parts: short-run shocks, disequilibrium shocks, and innovative residuals, with only the first two of these sustaining an economic interpretation.

Compressional head waves in attenuative formations: Forward modeling and inversion

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1908-1920 ◽  
Author(s):  
Qing‐Huo Liu ◽  
Chung Chang
Keyword(s):  
Radiation Condition ◽  
Forward Modeling ◽  
Head Wave ◽  
Transmission Measurement ◽  
Processing Scheme ◽  
Straightforward Application ◽  
Head Waves ◽  
Simple Processing ◽  
The Individual ◽  
Branch Cut

We develop a method of forward modeling and inverting formation attenuation data from sonic compressional head waves in a fluid‐filled borehole using a branch‐cut integration (BCI) technique to calculate individual acoustic arrivals. We validate this approach with a real‐ axis integration (RAI) method that does not separate the individual arrivals. We show that the straightforward application of the original BCI method for lossless media gives erroneous results for attenuative formations. With a choice of the Riemann sheets satisfying the radiation condition, the new BCI method gives correct results for most lossy and lossless formations. However, modeling very slow formations needs to include the contribution of a leaky pole near the vertical branch cut. With a constant‐Q assumption, we develop a simple processing scheme to extract the formation compressional Q factor from the P head‐wave arrivals. We used experimental data from laboratory‐scale borehole measurements to invert for the compressional Q value of a Lucite block. The inverted results agree within 4.5% of an independent ultrasonic transmission measurement of Q.

Uniqueness and stability of the recovery of an absorbing obstacle from a knowledge of its scattering resonances

2000 ◽  
Vol 130 (1) ◽  
pp. 63-80
Author(s):  
C. Labreuche
Keyword(s):  
A Priori ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Large Error ◽  
Small Error ◽  
Compact Set ◽  
Far Field ◽  
Scattering Problems ◽  
Resonant Frequencies ◽  
Ill Posed

In a previous paper, I investigated the use (for the inverse scattering problem) of the resonant frequencies and the associated eigen far-fields. I showed that the shape of a sound soft obstacle is uniquely determined by a knowledge of one resonant frequency and one associated eigen far-field. Inverse obstacle scattering problems are ill-posed in the sense that a small error in the measurement may imply a large error in the reconstruction. This is contrary to the idea of continuity. I proved that, by adding some a priori information, the reconstruction becomes continuous. More precisely, continuity holds if we assume that the obstacle lies a fixed and known compact set.The goal of this paper is to extend these results to the case of absorbing obstacles.

NONAUTONOMOUS SADDLE-NODE BIFURCATION IN A CANONICAL ELECTROSTATIC MEMS

2013 ◽  
Vol 23 (05) ◽  
pp. 1350088 ◽  
Author(s):  
ALEXANDER GUTIÉRREZ ◽  
PEDRO J. TORRES
Keyword(s):  
Quantitative Estimation ◽  
A Priori ◽  
Micro Electro Mechanical System ◽  
Saddle Node Bifurcation ◽  
Electrostatically Actuated ◽  
Saddle Node ◽  
Electrostatic Mems ◽  
Mass Spring Model ◽  
Existence And Stability ◽  
Mass Spring

We study the existence and stability of periodic solutions of a canonical mass-spring model of electrostatically actuated Micro-Electro-Mechanical System (MEMS) by means of classical topological techniques like a priori bounds, Leray–Schauder degree and topological index. A saddle-node bifurcation is revealed, in analogy with the autonomous case. A quantitative estimation of the bifurcation value in terms of realistic values of the involved parameters can be made.

Simultaneous inversion of petrophysical parameters based on geostatistical a priori information

2014 ◽  
Vol 11 (3) ◽  
pp. 311-320 ◽  
Author(s):  
Xing-Yao Yin ◽  
Rui-Ying Sun ◽  
Bao-Li Wang ◽  
Guang-Zhi Zhang
Keyword(s):  
A Priori ◽  
A Priori Information ◽  
Petrophysical Parameters ◽  
Simultaneous Inversion ◽  
Priori Information

scholarly journals A Viscous Fluid Flow through a Thin Channel with Mixed Rigid-Elastic Boundary: Variational and Asymptotic Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-47 ◽  
Author(s):  
R. Fares ◽  
G. P. Panasenko ◽  
R. Stavre
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Solution ◽  
A Priori ◽  
Small Error ◽  
Thin Tube ◽  
Elastic Boundary ◽  
Thin Channel ◽  
Flow Through ◽  
Regularity Results ◽  
Tube Structure

We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and somea prioriestimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of thea prioriestimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.

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