Root‐mean‐square velocities and recovery of the acoustic impedance

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1653-1663 ◽  
Author(s):  
D. W. Oldenburg ◽  
S. Levy ◽  
K. Stinson
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Velocity Structure ◽  
Low Frequency ◽  
Full Band ◽  
Impedance Profile ◽  
Band Limited ◽  
Point Velocity ◽  
Velocity Constraints ◽  
Additional Point

The loss of low‐frequency information in reflection seismograms causes serious difficulties when attempting to generate a full‐band impedance profile. Information about the low‐frequency velocity structure is available from rms (stacking velocities). We show how rms velocities can be inverted with additional point velocity constraints (if they are available) to construct either smooth or blocky velocity structures. Backus‐Gilbert averages of the constructed velocity are then autoregressive solutions for recovering a full band reflectivity from band‐limited seismograms. Our final result is therefore a full‐band acoustic impedance which is consistent with the seismic data section, stacking velocities, and available point constraints.

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.

Iterative P-wave velocity inversion using Markov chain Monte Carlo method

2020 ◽  
Author(s):  
Hyunggu Jun ◽  
Hyeong-Tae Jou ◽  
Han-Joon Kim ◽  
Sang Hoon Lee
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
Velocity Structure ◽  
Low Frequency ◽  
P Wave ◽  
Velocity Analysis ◽  
Seismic Section ◽  
Traveltime Tomography ◽  
P Wave Velocity ◽  
Frequency Components

<p>Imaging the subsurface structure through seismic data needs various information and one of the most important information is the subsurface P-wave velocity. The P-wave velocity structure mainly influences on the location of the reflectors during the subsurface imaging, thus many algorithms has been developed to invert the accurate P-wave velocity such as conventional velocity analysis, traveltime tomography, migration velocity analysis (MVA) and full waveform inversion (FWI). Among those methods, conventional velocity analysis and MVA can be widely applied to the seismic data but generate the velocity with low resolution. On the other hands, the traveltime tomography and FWI can invert relatively accurate velocity structure, but they essentially need long offset seismic data containing sufficiently low frequency components. Recently, the stochastic method such as Markov chain Monte Carlo (McMC) inversion was applied to invert the accurate P-wave velocity with the seismic data without long offset or low frequency components. This method uses global optimization instead of local optimization and poststack seismic data instead of prestack seismic data. Therefore, it can avoid the problem of the local minima and limitation of the offset. However, the accuracy of the poststack seismic section directly affects the McMC inversion result. In this study, we tried to overcome the dependency of the McMC inversion on the poststack seismic section and iterative workflow was applied to the McMC inversion to invert the accurate P-wave velocity from the simple background velocity and inaccurate poststack seismic section. The numerical test showed that the suggested method could successfully invert the subsurface P-wave velocity.</p>

Accurate poststack acoustic-impedance inversion by well-log calibration

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. R59-R67 ◽  
Author(s):  
Igor B. Morozov ◽  
Jinfeng Ma
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Joint Inversion ◽  
Low Frequency ◽  
Real Data ◽  
Data Sets ◽  
Frequency Model ◽  
Physical Constraints ◽  
Impedance Inversion ◽  
Reliable Solution

The seismic-impedance inversion problem is underconstrained inherently and does not allow the use of rigorous joint inversion. In the absence of a true inverse, a reliable solution free from subjective parameters can be obtained by defining a set of physical constraints that should be satisfied by the resulting images. A method for constructing synthetic logs is proposed that explicitly and accurately satisfies (1) the convolutional equation, (2) time-depth constraints of the seismic data, (3) a background low-frequency model from logs or seismic/geologic interpretation, and (4) spectral amplitudes and geostatistical information from spatially interpolated well logs. The resulting synthetic log sections or volumes are interpretable in standard ways. Unlike broadly used joint-inversion algorithms, the method contains no subjectively selected user parameters, utilizes the log data more completely, and assesses intermediate results. The procedure is simple and tolerant to noise, and it leads to higher-resolution images. Separating the seismic and subseismic frequency bands also simplifies data processing for acoustic-impedance (AI) inversion. For example, zero-phase deconvolution and true-amplitude processing of seismic data are not required and are included automatically in this method. The approach is applicable to 2D and 3D data sets and to multiple pre- and poststack seismic attributes. It has been tested on inversions for AI and true-amplitude reflectivity using 2D synthetic and real-data examples.

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.

Interpretation of full-azimuth broadband land data from Saudi Arabia and implications for improved inversion, reservoir characterization, and exploration

2013 ◽  
Vol 1 (2) ◽  
pp. T167-T176 ◽  
Author(s):  
Brian P. Wallick ◽  
Luis Giroldi
Keyword(s):  
Saudi Arabia ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Reservoir Characterization ◽  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Gas Field ◽  
Frequency Model ◽  
Low Frequencies ◽  
Limited Bandwidth

Interpretation of conventional land seismic data over a Permian-age gas field in Eastern Saudi Arabia has proven difficult over time due to low signal-to-noise ratio and limited bandwidth in the seismic volume. In an effort to improve the signal and broaden the bandwidth, newly acquired seismic data over this field have employed point receiver technology, dense wavefield sampling, a full azimuth geometry, and a specially designed sweep with useful frequencies as low as three hertz. The resulting data display enhanced reflection continuity and improved resolution. With the extension of low frequencies and improved interpretability, acoustic impedance inversion results are more robust and allow greater flexibility in reservoir characterization and prediction. In addition, because inversion to acoustic impedance is no longer completely tied to a wells-only low-frequency model, there are positive implications for exploration.

Seismic inversion of a carbonate buildup: A case study

2017 ◽  
Vol 5 (4) ◽  
pp. T641-T652 ◽  
Author(s):  
Mark Sams ◽  
Paul Begg ◽  
Timur Manapov
Keyword(s):  
Seismic Data ◽  
Probability Distributions ◽  
Low Frequency ◽  
Rock Physics ◽  
Seismic Inversion ◽  
Accurate Estimation ◽  
Amplitude Analysis ◽  
Simultaneous Inversion ◽  
Band Limited ◽  
Using Data

The information within seismic data is band limited and angle limited. Together with the particular physics and geology of carbonate rocks, this imposes limitations on how accurately we can predict the presence of hydrocarbons in carbonates, map the top carbonate, and characterize the porosity distribution through seismic amplitude analysis. Using data for a carbonate reef from the Nam Con Son Basin, Vietnam, the expectations based on rock-physics analysis are that the presence of gas can be predicted only when the porosity at the top of the carbonate is extremely high ([Formula: see text]), but that a fluid contact is unlikely to be observed in the background of significant porosity variations. Mapping the top of the carbonate (except when the top carbonate porosities are low) or a fluid contact requires accurate estimates of changes in [Formula: see text]. The seismic data do not independently support such an accurate estimation of sharp changes in [Formula: see text]. The standard approach of introducing low-frequency models and applying rock-physics constraints during a simultaneous inversion does not resolve the problems: The results are heavily biased by the well control and the initial interpretation of the top carbonate and fluid contact. A facies-based inversion in which the elastic properties are restricted to values consistent with the facies predicted to be present removes the well bias, but it does not completely obviate the need for a reasonably accurate initial interpretation in terms of prior facies probability distributions. Prestack inversion improves the quality of the facies predictions compared with a poststack inversion.

High-resolution acoustic impedance inversion to characterize turbidites at Marlim Field, Campos Basin, Brazil

2014 ◽  
Vol 2 (3) ◽  
pp. T143-T153 ◽  
Author(s):  
Tatiane M. Nascimento ◽  
Paulo T. L. Menezes ◽  
Igor L. Braga
Keyword(s):  
High Resolution ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Structural Information ◽  
Low Frequency ◽  
Seismic Inversion ◽  
Background Model ◽  
Rock Properties ◽  
High Porosity ◽  
Campos Basin

Seismic inversion is routinely used to determine rock properties, such as acoustic impedance and porosity, from seismic data. Nonuniqueness of the solutions is a major issue. A good strategy to reduce this inherent ambiguity of the inversion procedure is to introduce stratigraphic and structural information a priori to better construct the low-frequency background model. This is particularly relevant when studying heterogeneous deepwater turbidite reservoirs that form prolific, but complex, hydrocarbon plays in the Brazilian offshore basins. We evaluated a high-resolution inversion workflow applied to 3D seismic data at Marlim Field, Campos Basin, to recover acoustic impedance and porosity of the turbidites reservoirs. The Marlim sandstones consist of an Oligocene/Miocene deepwater turbidite system forming a series of amalgamated bodies. The main advantage of our workflow is to incorporate the interpreter’s knowledge about the local stratigraphy to construct an enhanced background model, and then extract a higher resolution image from the seismic data. High-porosity zones were associated to the reservoirs facies; meanwhile, the nonreservoir facies were identified as low-porosity zones.

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.

Limitations on impedance inversion of band‐limited reflection data

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 951-957 ◽  
Author(s):  
Santi Kumar Ghosh
Keyword(s):  
Seismic Data ◽  
Dominant Frequency ◽  
Seismic Exploration ◽  
Reflection Data ◽  
Homogeneous Half Space ◽  
Impedance Inversion ◽  
White Band ◽  
Full Band ◽  
Band Limited ◽  
Analytical Expressions

A seismic approximate impedance log is often the ultimate output in the sequence of seismic data‐processing steps. In principle, the true acoustic impedance is obtainable from the inversion of full‐band impulse response. Because the seismic data necessarily is band limited, its inversion obviously would produce an approximate impedance log. A question addressed is how the true and reconstructed logs are related and a mathematical relationship between the two is derived without the assumptions required in an existing derivation of the same result. The deductions also include the contribution of an individual seismic frequency in the reconstruction of the impedance and, in particular, a simple formula for the contribution of direct‐current (dc) frequency, which never is recorded but is required to supplement the inversion. Analytical expressions are derived for the reconstructed impedance corresponding to any given frequency band for two cases: a simple discontinuity and a bed sandwiched between two similar half‐spaces. While analyzing the results, some conclusions pertinent to seismic exploration are drawn. A criterion is formulated to decide what should be termed a thin bed within a homogeneous half‐space in the context of a white band of frequencies, in contrast to a single dominant frequency, which is the basis of the Widess criterion.

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.

Sign in / Sign up

Export Citation Format

Share Document