Feasibility of approximate broadband estimation of acoustic impedance profile from first principles and band-limited reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R57-R74 ◽  
Author(s):  
Santi Kumar Ghosh ◽  
Animesh Mandal
Keyword(s):  
First Principles ◽  
Acoustic Impedance ◽  
Linear Equations ◽  
Synthetic Data ◽  
Reflection Coefficients ◽  
Limited Data ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Profile ◽  
Band Limited

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.

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

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.

Wavelet-based detection of singularities in acoustic impedances from surface seismic reflection data

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. V1-V9 ◽  
Author(s):  
Chun-Feng Li ◽  
Christopher Liner
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Synthetic Data ◽  
Singularity Analysis ◽  
Real Surface ◽  
Multiple Reflections ◽  
Data Set ◽  
Seismic Reflection Data ◽  
Seismic Processing ◽  
Reflection Data

Although the passage of singularity information from acoustic impedance to seismic traces is now well understood, it remains unanswered how routine seismic processing, mode conversions, and multiple reflections can affect the singularity analysis of surface seismic data. We make theoretical investigations on the transition of singularity behaviors from acoustic impedances to surface seismic data. We also perform numerical, wavelet-based singularity analysis on an elastic synthetic data set that is processed through routine seismic processing steps (such as stacking and migration) and that contains mode conversions, multiple reflections, and other wave-equation effects. Theoretically, seismic traces can be approximated as proportional to a smoothed version of the [Formula: see text] derivative of acoustic impedance,where [Formula: see text] is the vanishing moment of the seismic wavelet. This theoretical approach forms the basis of linking singularity exponents (Hölder exponents) in acoustic impedance with those computable from seismic data. By using wavelet-based multiscale analysis with complex Morlet wavelets, we can estimate singularity strengths and localities in subsurface impedance directly from surface seismic data. Our results indicate that rich singularity information in acoustic impedance variations can be preserved by surface seismic data despite data-acquisition and processing activities. We also show that high-resolution detection of singularities from real surface seismic data can be achieved with a proper choice of the scale of the mother wavelet in the wavelet transform. Singularity detection from surface seismic data thus can play a key role in stratigraphic analysis and acoustic impedance inversion.

Colored and linear inversions to relative acoustic impedance

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N15-N27 ◽  
Author(s):  
Carlos A. M. Assis ◽  
Henrique B. Santos ◽  
Jörg Schleicher
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Computational Cost ◽  
Synthetic Data ◽  
Seismic Source ◽  
Alternative Methods ◽  
Well Log ◽  
Linear Inversion ◽  
Amplitude Inversion ◽  
Band Limited

Acoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization.

Using instantaneous frequency and colored inversion attributes to distinguish and determine the sandstones facies of the Late Ordovician Mamuniyat reservoir, R-field in Murzuq Basin, Libya

2016 ◽  
Vol 4 (4) ◽  
pp. T507-T519 ◽  
Author(s):  
Yousf Abushalah ◽  
Laura Serpa
Keyword(s):  
Instantaneous Frequency ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Rock Physics ◽  
Side Lobe ◽  
Petroleum Reservoir ◽  
Seismic Reflection Data ◽  
Frequency Bands ◽  
Reflection Data ◽  
Sandstone Facies

The Mamuniyat petroleum reservoir in southwestern Libya is comprised of clean sandstones and intercalated shale and sand facies that are characterized by spatial porosity variations. Seismic reflection data from the field exhibit relatively low vertical seismic resolution, side lobes of reflection wavelets, reflection interference, and low acoustic impedance contrast between the reservoir and the units underneath the reservoir, which make mapping those facies a difficult task. In the absence of broadband seismic data, optimizing frequency bands of bandlimited data can be used to suppress pseudoreflectors resulting from side-lobe effects and help to separate the clean sandstone facies of the reservoir. We have optimized the data based on our investigation of seismic frequency bands and used instantaneous frequency analysis to reveal the reflection discontinuity that is mainly associated with the reservoir boundary of the sandstone facies of the clean Mamuniyat reservoir. We also preformed rock-physics diagnostic modeling and inverted the seismic data using spectral-based colored inversion into relative acoustic impedance. The inverted impedance matches the up-scaled impedance from the well data and the inversion of relative acoustic impedance confirms the conclusion that was drawn from the instantaneous frequency results. The interpretation of facies distributions based on the instantaneous frequency was supported by the inversion results and the rock-physics models.

scholarly journals The Use of Seismic Reflection Data Inversion Technique to Evaluate the Petro- Physical Properties of Nahr Umr Formation at Kumait and Dujaila Oil Fields – Southern Iraq

2021 ◽  
pp. 565-577
Author(s):  
Nowfal A. Nassir ◽  
Ahmed S. AL- Banna ◽  
Ghazi H. Al-Sharaa
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Water Saturation ◽  
Water Reservoir ◽  
Effective Porosity ◽  
Oil Fields ◽  
Seismic Reflection Data ◽  
Data Inversion ◽  
Reflection Data ◽  
Southern Iraq

The estimation of rock petrophysical parameters is an essential matter to characterize any reservoir. This research deals with the evaluation of  effective porosity (Pe), shale volume (Vsh) and water saturation (Sw) of reservoirs at Kumait and Dujalia fields, which were analyzed from well log and seismic data. The absolute acoustic impedance (AI) and relative acoustic impedance (RAI) were derived from a model which is based on the inversion of seismic 3-D post-stack data. NahrUmr formation’s sand reservoirs are identified by the RAI section of the study area. Nahr Umr sand-2 unit in Kumait field is the main reservoir; its delineation depends on the available well logs and AI sections information. The results of well logging interpretation showed a decrease of Sw and Vsh and an increase of effective porosity in the oil reservoir area, which coincides with the decrease of AI values. The existence of the water reservoir in Du-2 well revealed a convergence of the results of AI and effective porosity with those of Kumait wells , along with and some differential results of Sw and Vsh values that may be related to changes in lithology and fluid density.

EXPLORATION HORIZONS FROM NEW SEISMIC CONCEPTS OF CDP AND DIGITAL PROCESSING

Geophysics ◽  
1967 ◽  
Vol 32 (2) ◽  
pp. 207-224 ◽  
Author(s):  
John D. Marr ◽  
Edward F. Zagst
Keyword(s):  
Data Processing ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Synthetic Data ◽  
Digital Processing ◽  
Seismic Data Processing ◽  
Multiple Reflections ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Recent Developments

The more recent developments in common‐depth‐point techniques to attenuate multiple reflections have resulted in an exploration capability comparable to the development of the seismic reflection method. The combination of new concepts in digital seismic data processing with CDP techniques is creating unforeseen exploration horizons with vastly improved seismic data. Major improvements in multiple reflection and reverberation attenuation are now attainable with appropriate CDP geometry and special CDP stacking procedures. Further major improvements are clearly evident in the very near future with the use of multichannel digital filtering‐stacking techniques and the application of deconvolution as the first step in seismic data processing. CDP techniques are briefly reviewed and evaluated with real and experimental data. Synthetic data are used to illustrate that all seismic reflection data should be deconvolved as the first processing step.

Band-limited scattered wavefield reconstruction beneath complex overburdens using the Marchenko method

2021 ◽  
Author(s):  
David Vargas ◽  
Ivan Vasconcelos ◽  
Matteo Ravasi
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Accurate Estimation ◽  
Target Area ◽  
Complex Media ◽  
Depth Level ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Band Limited ◽  
Internal Multiples

<p>Structural imaging beneath complex overburdens, such as sub-salt or sub-basalt, typically characterized by high-impedance contrasts represents a major challenge for state-of-the-art seismic methods. Reconstructing complex geological structures in the vicinity of and below salt bodies is challenging not only due to uneven, single-sided illumination of the target area but also because of the imperfect removal of surface and internal multiples from the recorded data, as required by traditional migration algorithms. In such tectonic setups, most of the downgoing seismic wavefield is reflected toward the surface when interacting with the overburden's top layer. Similarly, the sub-salt upcoming energy is backscattered at the salt's base. Consequently, the actual energy illuminating the sub-salt reflectors, recorded at the surface, is around the noise level. In diapiric trap systems, conventional seismic extrapolation techniques do not guarantee sufficient quality to reduce exploration and production risks; likewise, seismic-based reservoir characterization and monitoring are also compromised. In this regard, accurate wavefield extrapolation techniques based on the Marchenko method may open up new ways to exploit seismic data.</p><p>The Marchenko redatuming technique retrieves reliable full-wavefield information in the presence of geologic intrusions, which can be subsequently used to produce artefact-free images by naturally including all orders of multiples present in seismic reflection data. To achieve such a goal, the method relies on the estimation of focusing operators allowing the synthesis of virtual surveys at a given depth level. Still, current Marchenko implementations do not fully incorporate available subsurface models with sharp contrasts, due to the requirements regarding the initialization of the focusing functions. Most importantly, in complex media, even a fairly accurate estimation of a direct wave as a proxy for the required initial focusing functions may not be enough to guarantee sufficiently accurate wavefield reconstruction.</p><p>In this talk, we will discuss a scattering-based Marchenko redatuming framework which improves the redatuming of seismic surface data in highly complex media when compared to other Marchenko-based schemes. This extended version is designed to accommodate for band-limited, multi-component, and possibly unevenly sampled seismic data, which contain both free-surface and internal multiples, whilst requiring minimum pre-processing steps. The performance of our scattering Marchenko method will be evaluated using a comprehensive set of numerical tests on a complex 2D subsalt model.</p>

The relationship between Born inversion and migration for common‐midpoint stacked data

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2117-2131 ◽  
Author(s):  
Guan Cheng ◽  
Shimon Coen
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Reflectivity Function ◽  
Inverse Source Problems ◽  
Band Limited ◽  
And Migration ◽  
Definition Of ◽  
The Relationship

The relationship between Born inversion and wave‐equation migration of common‐midpoint (CMP) stacked seismic reflection data is analytically determined. The three‐dimensional (3-D) velocity distribution obtained by Born inversion is shown to be directly related to the 3-D reflectivity function obtained by wave‐equation migration for full bandwidth or band‐limited data. The relationship is obtained by the reformulations of migration and Born inversion methods as inverse source problems for the 3-D wave equation. The reformulation leads to a definition of the reflectivity function as the source function for the wave equation. It also leads to determination of the Born inversion results by applying the algorithm for wave‐equation migration to modified surface data. The modified data are simply related to the CMP stacked data. Alternatively, Born inversion results may be obtained directly from the migrated section. Results from synthetic and recorded data are presented and found to be consistent with the theoretical developments.

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