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.

Restricted model domain time Radon transforms

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. A17-A21 ◽  
Author(s):  
Juan I. Sabbione ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Model Space ◽  
Radon Transforms ◽  
Iterative Solver ◽  
Hard Thresholding ◽  
Restricted Model ◽  
Marine Data

The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.

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.

Mapping lithofacies and pore‐fluid probabilities in a North Sea reservoir: Seismic inversions and statistical rock physics

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 988-1001 ◽  
Author(s):  
T. Mukerji ◽  
A. Jørstad ◽  
P. Avseth ◽  
G. Mavko ◽  
J. R. Granli
Keyword(s):  
North Sea ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Probability Distributions ◽  
Rock Physics ◽  
Normal Incidence ◽  
Seismic Inversion ◽  
Training Data ◽  
Well Log ◽  
Statistical Rock Physics

Reliably predicting lithologic and saturation heterogeneities is one of the key problems in reservoir characterization. In this study, we show how statistical rock physics techniques combined with seismic information can be used to classify reservoir lithologies and pore fluids. One of the innovations was to use a seismic impedance attribute (related to the [Formula: see text] ratio) that incorporates far‐offset data, but at the same time can be practically obtained using normal incidence inversion algorithms. The methods were applied to a North Sea turbidite system. We incorporated well log measurements with calibration from core data to estimate the near‐offset and far‐offset reflectivity and impedance attributes. Multivariate probability distributions were estimated from the data to identify the attribute clusters and their separability for different facies and fluid saturations. A training data was set up using Monte Carlo simulations based on the well log—derived probability distributions. Fluid substitution by Gassmann’s equation was used to extend the training data, thus accounting for pore fluid conditions not encountered in the well. Seismic inversion of near‐offset and far‐offset stacks gave us two 3‐D cubes of impedance attributes in the interwell region. The near‐offset stack approximates a zero‐offset section, giving an estimate of the normal incidence acoustic impedance. The far offset stack gives an estimate of a [Formula: see text]‐related elastic impedance attribute that is equivalent to the acoustic impedance for non‐normal incidence. These impedance attributes obtained from seismic inversion were then used with the training probability distribution functions to predict the probability of occurrence of the different lithofacies in the interwell region. Statistical classification techniques, as well as geostatistical indicator simulations were applied on the 3‐D seismic data cube. A Markov‐Bayes technique was used to update the probabilities obtained from the seismic data by taking into account the spatial correlation as estimated from the facies indicator variograms. The final results are spatial 3‐D maps of not only the most likely facies and pore fluids, but also their occurrence probabilities. A key ingredient in this study was the exploitation of physically based seismic‐to‐reservoir property transforms optimally combined with statistical techniques.

Depth-domain seismic reflectivity inversion with compressed sensing technique

2017 ◽  
Vol 5 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Rui Zhang ◽  
Kui Zhang ◽  
Jude E. Alekhue
Keyword(s):  
Compressed Sensing ◽  
Time Domain ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Depth Migration ◽  
Band Limited ◽  
The Time Domain

More and more seismic surveys produce 3D seismic images in the depth domain by using prestack depth migration methods, which can present a direct subsurface structure in the depth domain rather than in the time domain. This leads to the increasing need for applications of seismic inversion on the depth-imaged seismic data for reservoir characterization. To address this issue, we have developed a depth-domain seismic inversion method by using the compressed sensing technique with output of reflectivity and band-limited impedance without conversion to the time domain. The formulations of the seismic inversion in the depth domain are similar to time-domain methods, but they implement all the elements in depth domain, for example, a depth-domain seismic well tie. The developed method was first tested on synthetic data, showing great improvement of the resolution on inverted reflectivity. We later applied the method on a depth-migrated field data with well-log data validated, showing a great fit between them and also improved resolution on the inversion results, which demonstrates the feasibility and reliability of the proposed method on depth-domain seismic data.

Methods of correlation noise minimization and suppression for multisource acquisition in vibroseis survey

2019 ◽  
pp. 98-106
Author(s):  
A. N. Oshkin ◽  
A. I. Kon’kov ◽  
A. V. Tarasov ◽  
A. A. Shuvalov ◽  
V. I. Ignat’ev
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Seismic Source ◽  
Recording System ◽  
Signal Separation ◽  
Median Filtering ◽  
Data Recording ◽  
Single Source ◽  
Correlation Noise ◽  
Incoherent Noise

The use of several simultaneously operating sources in seismic operations allows one to obtain large amounts of data per unit of time than for classical works with a single source, and also to improve the seismic data recording system. Depending on the type of seismic source used (vibrating or pulsed), different methods of signal separation are used. When working with vibroseismic method, separation of signals becomes possible at the stage of correlative processing of vibrograms. In this paper, we demonstrate methods for constructing noncorrelating signals for use in vibroseis survey (with an example of using such signals on synthetic data) and hyperbolic median filtering to minimize correlation and incoherent noise.

Approximate computation of the acoustic impedance from seismic data

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1351-1358 ◽  
Author(s):  
K. A. Berteussen ◽  
B. Ursin
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Recursive Formula ◽  
Continuous Model ◽  
Low Noise ◽  
Nonlinear Transformation ◽  
Earth Model ◽  
Approximate Computation ◽  
Impedance Function ◽  
Band Limited

The approximate computation of the acoustic impedance from seismic data is usually based on the recursive formula [Formula: see text] where [Formula: see text] is the acoustic impedance in layer number k and [Formula: see text] is the pressure reflection coefficient for the interface between layer k and [Formula: see text]. The above formula is derived from a discrete layered earth model. When we consider a continuous earth model and discretize the results, we obtain the recursive formula [Formula: see text] The two expressions give very similar numerical results. For [Formula: see text], the relative difference is less than 5 percent and this cannot be visually recognized on an acoustic impedance section. The expression for the continuous model is more suitable for understanding the result of the approximate computation of the acoustic impedance function from band‐limited seismic data. The calculated impedance minus the impedance in the top layer is approximately equal to the reflectivity function convolved with the integrated seismic pulse multiplied with twice the impedance in the top layer. For impedance values less than 0.2 in absolute value this is also equal to the acoustic impedance function (minus the acoustic impedance in the top layer) convolved with the seismic pulse. The computation of the acoustic impedance from band‐limited seismic data corresponds to an exponential transformation of the integrated seismic trace. On a band‐limited acoustic impedance section with well‐separated reflectors and low noise level the direction of change in the acoustic impedance can be correctly identified. The effect of additive noise in the seismic data is governed by a nonlinear transformation. Our data examples show that the computation of acoustic impedance becomes unstable when noise is added. In order to avoid the nonlinear transformation of the seismic data, it has been suggested to integrate the seismic data. This results in an estimate of the logarithm of the acoustic impedance. For band‐limited seismic data with noise this gives a band‐limited estimate of the logarithm of the acoustic impedance plus the integrated noise. A disadvantage of this method is that the variance of the integrated noise increases linearly with time.

Acoustic impedance estimation from combined harmonic reconstruction and interval velocity

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R385-R400
Author(s):  
Luca Bianchin ◽  
Emanuele Forte ◽  
Michele Pipan
Keyword(s):  
Velocity Field ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Low Frequency ◽  
Reconstruction Method ◽  
Well Log ◽  
Data Set ◽  
Low Frequencies ◽  
Interval Velocity ◽  
Frequency Components

Low-frequency components of reflection seismic data are of paramount importance for acoustic impedance (AI) inversion, but they typically suffer from a poor signal-to-noise ratio. The estimation of the low frequencies of AI can benefit from the combination of a harmonic reconstruction method (based on autoregressive [AR] models) and a seismic-derived interval velocity field. We have developed the construction of a convex cost function that accounts for the velocity field, together with geologic a priori information on AI and its uncertainty, during the AR reconstruction of the low frequencies. The minimization of this function allows one to reconstruct sensible estimates of low-frequency components of the subsurface reflectivity, which lead to an estimation of AI model via a recursive formulation. In particular, the method is suited for an initial and computationally inexpensive assessment of the absolute value of AI even when no well-log data are available. We first tested the method on layered synthetic models, then we analyzed its applicability and limitations on a real marine seismic data set that included tomographic velocity information. Despite a strong trace-to-trace variability in the results, which could partially be mitigated by multitrace inversion, the method demonstrates its capability to highlight lateral variations of AI that cannot be detected when the low frequencies only come from well-log information.

Plane‐layer prestack inversion in the presence of surface reverberation

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1789-1800 ◽  
Author(s):  
Alastair D. McAulay
Keyword(s):  
Velocity Profile ◽  
Reference Data ◽  
Jacobian Matrix ◽  
High Surface ◽  
Synthetic Data ◽  
Surface Effects ◽  
Plane Layer ◽  
Linear Inversion ◽  
Band Limited ◽  
Shallow Strata

Experiments with synthetic data have indicated that generalized linear inversion may be used to estimate compressional velocities as a function of depth with high resolution directly from band‐limited, unstacked data. The ocean surface was not included in these experiments. In the presence of strong surface multiples, inversion is expected to take longer and be less accurate, because events from multiple surface reflections overlie primary events and normally have differing moveout. Existing velocity‐analysis techniques rely on the ability of an observer to make the difficult distinction between multiples and primaries. Equations are provided for adding the surface to the inversion procedure. This involves adding the surface effects to the Jacobian matrix as well as to the forward modeling procedure. To speed computation, the addition of the surface effects to the Jacobian matrix is delayed until after the matrix has been multiplied by a vector in the linear‐equation solution. Absorption is added to the inversion to represent the real world more closely and to improve computation speed by reducing sampling requirements. Realistic synthetic band‐limited data with high surface reverberation content were generated from a well‐log velocity profile. The inversion recovered the velocity profile to within 3 percent when a velocity increasing linearly with depth was used as a starting profile. The error in the model‐generated seismogram converges from 100 percent to within 2 percent of the reference data. The positions of interfaces are located more accurately at greater depths than at shallower depths because more sensors are observing deep strata than shallow strata. Convergence is to within 0.1 percent of that of the reference data at the maximum depth. The computation required 25 iterations and a total time of 66 hours on a DEC VAX 11/780. Reducing this time should be possible. In a preliminary study of the effects of noise, additive Gaussian noise was seen to limit the accuracy of the velocity estimate monotonically as the variance of the added noise was increased.

scholarly journals Application of maximum likelihood and model-based seismic inversion techniques: a case study from K-G basin, India

2021 ◽  
Author(s):  
Richa ◽  
S. P. Maurya ◽  
Kumar H. Singh ◽  
Raghav Singh ◽  
Rohtash Kumar ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Gamma Ray ◽  
Seismic Inversion ◽  
Reservoir Rock ◽  
Well Log ◽  
Log Data ◽  
Petrophysical Parameters ◽  
Model Based

AbstractSeismic inversion is a geophysical technique used to estimate subsurface rock properties from seismic reflection data. Seismic data has band-limited nature and contains generally 10–80 Hz frequency hence seismic inversion combines well log information along with seismic data to extract high-resolution subsurface acoustic impedance which contains low as well as high frequencies. This rock property is used to extract qualitative as well as quantitative information of subsurface that can be analyzed to enhance geological as well as geophysical interpretation. The interpretations of extracted properties are more meaningful and provide more detailed information of the subsurface as compared to the traditional seismic data interpretation. The present study focused on the analysis of well log data as well as seismic data of the KG basin to find the prospective zone. Petrophysical parameters such as effective porosity, water saturation, hydrocarbon saturation, and several other parameters were calculated using the available well log data. Low Gamma-ray value, high resistivity, and cross-over between neutron and density logs indicated the presence of gas-bearing zones in the KG basin. Three main hydrocarbon-bearing zones are identified with an average Gamma-ray value of 50 API units at the depth range of (1918–1960 m), 58 API units (2116–2136 m), and 66 API units (2221–2245 m). The average resistivity is found to be 17 Ohm-m, 10 Ohm-m, and 12 Ohm-m and average porosity is 15%, 15%, and 14% of zone 1, zone 2, and zone 3 respectively. The analysis of petrophysical parameters and different cross-plots showed that the reservoir rock is of sandstone with shale as a seal rock. On the other hand, two types of seismic inversion namely Maximum Likelihood and Model-based seismic inversion are used to estimate subsurface acoustic impedance. The inverted section is interpreted as two anomalous zones with very low impedance ranging from 1800 m/s*g/cc to 6000 m/s*g/cc which is quite low and indicates the presence of loose formation.

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.

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