Broadband acoustic impedance reconstruction from band-limited seismic reflection data: a feasibility study from first principles

Because seismic reflection data are band limited, acoustic impedance profiles derived from them are nonunique. The conventional inversion methods counter the nonuniqueness either by stabilizing the answer with respect to an initial model or by imposing mathematical constraints such as sparsity of the reflection coefficients. By making a nominal assumption of an earth model locally consisting of a stack of homogeneous and horizontal layers, we have formulated a set of linear equations in which the reflection coefficients are the unknowns and the recursively integrated seismic trace constitute the data. Drawing only on first principles, the Zoeppritz equation in this case, the approach makes a frontal assault on the problem of reconstructing reflection coefficients from band-limited data. The local layer-cake assumption and the strategy of seeking a singular value decomposition solution of the linear equations counter the nonuniqueness, provided that the objective is to reconstruct a smooth version of the impedance profile that includes only its crude structures. Tests on synthetic data generated from elementary models and from measured logs of acoustic impedance demonstrated the efficacy of the method, even when a significant amount of noise was added to the data. The emergence of consistent estimates of impedance, approximating the original impedance, from synthetic data generated for several frequency bands has inspired our confidence in the method. The other attractive outputs of the method are as follows: (1) an accurate estimate of the impedance mean, (2) an accurate reconstruction of the direct-current (DC) frequency of the reflectivity, and (3) an acceptable reconstruction of the broad outline of the original impedance profile. These outputs can serve as constraints for either more refined inversions or geologic interpretations. Beginning from the restriction of band-limited data, we have devised a method that neither requires a starting input model nor imposes mathematical constraints on the earth reflectivity and still yielded significant and relevant geologic information.

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Estimating broad trend of acoustic impedance profile from observed seismic reflection data using first principles only

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa006 ◽

2020 ◽

Vol 17 (3) ◽

pp. 475-483

Author(s):

Animesh Mandal ◽

Santi Kumar Ghosh

Keyword(s):

First Principles ◽

Acoustic Impedance ◽

Seismic Reflection ◽

Low Frequency ◽

Singular Value ◽

Earth Model ◽

Depth Range ◽

Seismic Reflection Data ◽

Reflection Data ◽

Impedance Profile

Abstract Estimation of broad features or the low-frequency part of acoustic impedance from conventional reflection data is an essential yet challenging step for quantitative interpretation of seismic data due to its band-limited nature. A missing low-frequency part leads to non-uniqueness in the solution as well as placing restrictions in recovering the absolute impedance values. The current industry practice fills this gap by assuming either an initial impedance model or statistical restrictions on such a model. Doing away with such assumptions but using only first principles (Zoeppritz's equations) and homogeneous layered earth model, we have formulated a set of linear equations that are then solved for an unknown reflection co-efficient using singular value decomposition (SVD) approach with time sampled seismic trace as the input data. The present work demonstrates the effectiveness of reconstructing a broad and smooth impedance profile from first principles and even from acquired seismic reflection data. It also illustrates the method's success with real data, while determining in one go the unknown scale factor linking the true and the relative seismic amplitudes, and the smallest singular value to be retained in the solution from only the knowledge of the average value of the acoustic impedance over the depth range in question. Thus, the salient feature of this work is the ability to reconstruct an approximate impedance profile from field data without the aid of an initial model or statistical assumption on the reflectivity series. This approximate impedance profile can serve as a reliable initial input for more refined inversion or geologic interpretation.

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Feasibility of broadband estimation of acoustic impedances from first principles and band-limited seismic reflection data

10.1190/segam2016-13859786.1 ◽

2016 ◽

Author(s):

Animesh Mandal ◽

Santi Ghosh

Keyword(s):

First Principles ◽

Seismic Reflection ◽

Seismic Reflection Data ◽

Reflection Data ◽

Band Limited

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Geostatistical seismic inversion for frontier exploration

Interpretation ◽

10.1190/int-2016-0171.1 ◽

2017 ◽

Vol 5 (4) ◽

pp. T477-T485 ◽

Cited By ~ 2

Author(s):

Ângela Pereira ◽

Rúben Nunes ◽

Leonardo Azevedo ◽

Luís Guerreiro ◽

Amílcar Soares

Keyword(s):

Acoustic Impedance ◽

Seismic Reflection ◽

Seismic Inversion ◽

Well Log ◽

Data Set ◽

Seismic Reflection Data ◽

Log Data ◽

The Real ◽

Reflection Data ◽

Impedance Models

Numerical 3D high-resolution models of subsurface petroelastic properties are key tools for exploration and production stages. Stochastic seismic inversion techniques are often used to infer the spatial distribution of the properties of interest by integrating simultaneously seismic reflection and well-log data also allowing accessing the spatial uncertainty of the retrieved models. In frontier exploration areas, the available data set is often composed exclusively of seismic reflection data due to the lack of drilled wells and are therefore of high uncertainty. In these cases, subsurface models are usually retrieved by deterministic seismic inversion methodologies based exclusively on the existing seismic reflection data and an a priori elastic model. The resulting models are smooth representations of the real complex geology and do not allow assessing the uncertainty. To overcome these limitations, we have developed a geostatistical framework that allows inverting seismic reflection data without the need of experimental data (i.e., well-log data) within the inversion area. This iterative geostatistical seismic inversion methodology simultaneously integrates the available seismic reflection data and information from geologic analogs (nearby wells and/or analog fields) allowing retrieving acoustic impedance models. The model parameter space is perturbed by a stochastic sequential simulation methodology that handles the nonstationary probability distribution function. Convergence from iteration to iteration is ensured by a genetic algorithm driven by the trace-by-trace mismatch between real and synthetic seismic reflection data. The method was successfully applied to a frontier basin offshore southwest Europe, where no well has been drilled yet. Geologic information about the expected impedance distribution was retrieved from nearby wells and integrated within the inversion procedure. The resulting acoustic impedance models are geologically consistent with the available information and data, and the match between the inverted and the real seismic data ranges from 85% to 90% in some regions.

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