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.

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.

High resolution fixed-point seismic inversion

2021 ◽  
pp. 1-54
Author(s):  
Song Pei ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Kun Li
Keyword(s):  
Fixed Point ◽  
Objective Function ◽  
Seismic Data ◽  
Target Function ◽  
Recursive Formula ◽  
Frequency Component ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Good Convergence ◽  
Band Limited

Resolution improvement always presents the crucial task in geological inversion. Band-limited characteristics of seismic data and noise make seismic inversion complicated. Specifically, geological inversion suffers from the deficiency of both low- and high-frequency components. We propose the fixed-point seismic inversion method to alleviate these issues. The problem of solving objective function is transformed into the problem of finding the fixed-point of objective function. Concretely, a recursive formula between seismic signal and reflection coefficient is established, which is characterized by good convergence and verified by model examples. The error between the model value and the inverted value is reduced to around zero after few iterations. The model examples show that in either case, that is, the seismic traces are noise-free or with a little noise, the model value can almost be duplicated. Even if the seismic trace is accompanied by the moderate noise, the optimal inverted results can still be obtained with the proposed method. The initial model constraint is further introduced into the objective function to increase the low-frequency component of the inverted results by adding prior information into the target function. The singular value decomposition (SVD) method is applied to the inversion framework, thus making a high improvement of anti-noise ability. At last, the synthetic models and seismic data are investigated following the proposed method. The inverted results obtained from the fixed-point seismic inversion are compared with those obtained from the conventional seismic inversion, and it is found that the former has a higher resolution than the latter.

Joint inversion of seismic data for acoustic impedance

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 994-1004 ◽  
Author(s):  
Li‐Yun Fu
Keyword(s):  
Neural Network ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Joint Inversion ◽  
Signal Reconstruction ◽  
Optimal Estimation ◽  
Data Sets ◽  
Seismic Wavelet ◽  
Model Based ◽  
Band Limited

I propose a joint inversion scheme to integrate seismic data, well data, and geological knowledge for acoustic impedance estimation. I examine the problem of recovering acoustic impedance from band‐limited seismic data. Optimal estimation of impedance can be achieved by combined applications of model‐based and deconvolution‐based methods. I incorporate the Robinson seismic convolutional model (RSCM) into the Caianiello neural network for network mapping. The Caianiello neural network provides an efficient approach to decompose the seismic wavelet and its inverse. The joint inversion consists of four steps: (1) multistage seismic inverse wavelets (MSIW) extraction at the wells, (2) the deconvolution with MSIW for initial impedance estimation, (3) multistage seismic wavelets (MSW) extraction at the wells, and (4) the model‐based reconstruction of impedance with MSW for improving the initial impedance model. The Caianiello neural network offers two algorithms for the four‐step process: neural wavelet estimation and input signal reconstruction. The frequency‐domain implementation of the algorithms enables control of the inversion on different frequency scales and facilitates an understanding of reservoir behavior on different resolution scales. The test results show that, with well control, the joint inversion can significantly improve the spatial description of reservoirs in data sets involving complex continental deposits.

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.

scholarly journals Deblending by direct inversion

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. A9-A12 ◽  
Author(s):  
Kees Wapenaar ◽  
Joost van der Neut ◽  
Jan Thorbecke
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Iterative Procedure ◽  
Inversion Process ◽  
Direct Inversion ◽  
Source Data ◽  
Band Limited ◽  
Blended Data ◽  
Simultaneous Source ◽  
Additional Constraints

Deblending of simultaneous-source data is usually considered to be an underdetermined inverse problem, which can be solved by an iterative procedure, assuming additional constraints like sparsity and coherency. By exploiting the fact that seismic data are spatially band-limited, deblending of densely sampled sources can be carried out as a direct inversion process without imposing these constraints. We applied the method with numerically modeled data and it suppressed the crosstalk well, when the blended data consisted of responses to adjacent, densely sampled sources.

scholarly journals Time-Lapse Seismic Monitoring of Onshore Reservoirs in Niger Delta, Field ‘K’ as a Case Study

2017 ◽  
Vol 1 (1) ◽  
pp. 23-27 ◽  
Author(s):  
A. Ogbamikhumi ◽  
T. Tralagba ◽  
E. E. Osagiede
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Niger Delta ◽  
Rock Physics ◽  
Time Lapse ◽  
Seismic Survey ◽  
Impedance Change ◽  
Data Set ◽  
Reservoir Fluid ◽  
4D Seismic

Field ‘K’ is a mature field in the coastal swamp onshore Niger delta, which has been producing since 1960. As a huge producing field with some potential for further sustainable production, field monitoring is therefore important in the identification of areas of unproduced hydrocarbon. This can be achieved by comparing production data with the corresponding changes in acoustic impedance observed in the maps generated from base survey (initial 3D seismic) and monitor seismic survey (4D seismic) across the field. This will enable the 4D seismic data set to be used for mapping reservoir details such as advancing water front and un-swept zones. The availability of good quality onshore time-lapse seismic data for Field ‘K’ acquired in 1987 and 2002 provided the opportunity to evaluate the effect of changes in reservoir fluid saturations on time-lapse amplitudes. Rock physics modelling and fluid substitution studies on well logs were carried out, and acoustic impedance change in the reservoir was estimated to be in the range of 0.25% to about 8%. Changes in reservoir fluid saturations were confirmed with time-lapse amplitudes within the crest area of the reservoir structure where reservoir porosity is 0.25%. In this paper, we demonstrated the use of repeat Seismic to delineate swept zones and areas hit with water override in a producing onshore reservoir.

scholarly journals Development of a new seismic-data acquisition station based on system-on-a-programmable-chip technology

2013 ◽  
Vol 56 (3) ◽  
Author(s):  
Zhang Qi-sheng ◽  
Deng Ming ◽  
Guo Jian ◽  
Luo Wei-bing ◽  
Wang Qi ◽  
...  
Keyword(s):  
Power Consumption ◽  
Data Acquisition ◽  
Digital Filter ◽  
Data Transmission ◽  
Seismic Data ◽  
Low Noise ◽  
High Definition ◽  
Control Data ◽  
Seismic Data Acquisition ◽  
Transmission Speed

<p>There has been considerable development of seismic detectors over the last 80 years. However, there is still a need to further develop new earthquake exploration and data acquisition systems with high precision. In particular, for China to keep up with the latest technology of these systems, it is important to be involved in the research and development, instead of importing systems that soon fall behind the latest technology. In this study, the features of system-on-a-programmable-chip (SoPC) technology are analyzed and used to design a new digital seismic-data acquisition station. The hardware circuit of the station was developed, and the analog board and the main control data-transmission board were designed according to the needs of digital seismic-data acquisition stations. High-definition analog-to-digital converter sequential digital filter technology of the station (cascade integrator comb filter, finite impulse response digital filter) were incorporated to provide advantages to the acquisition station, such as high definition, large dynamic scope, and low noise. A specific data-transmission protocol was designed for the station, which ensured a transmission speed of 16 Mbps along a 55-m wire with low power consumption. Synchronic acquisition was researched and developed, so as to achieve accuracy better than 200 ns. The key technologies were integrated into the SoPC of the main control data-transmission board, so as to ensure high-resolution acquisition of the station, while improving the accuracy of the synchronic acquisition and data-transmission speed, lowering the power consumption, and preparing for the follow-up efforts to tape out.</p>

Pore Pressure Prediction in Sandstone Using a Lateral Transfer Approach

2021 ◽  
Author(s):  
Jose Francisco Consuegra
Keyword(s):  
Pore Pressure ◽  
Seismic Data ◽  
Strong Relationship ◽  
Lateral Transfer ◽  
Earth Model ◽  
Driving Mechanism ◽  
Shale Formations ◽  
Sand Body ◽  
Pore Pressure Prediction ◽  
Normal Trend

Abstract Accurate pore pressure prediction is required to determine reliable static mud weights and circulating pressures, necessary to mitigate the risk of influx, blowouts and borehole instability. To accurately estimate the pore pressure, the over-pressure mechanism has to be identified with respect to the geological environment. One of the most widely used methods for pore pressure prediction is based on Normal Compaction Trend Analysis, where the difference between a ‘normal trend' and log value of a porosity indicator log such as sonic or resistivity is used to estimate the pore pressure. This method is biased towards shales, which typically exhibit a strong relationship between porosity and depth. Overpressure in non-shale formations has to be estimated using a different method to avoid errors while predicting the pore pressure. In this study, a different method for pore pressure prediction has been performed by using the lateral transfer approach. Many offset wells were used to predict the pore pressure. Lateral transfer in the sand body was identified as the mechanism for overpressure. This form of overpressure cannot be identified by well logs, which makes the pore pressure prediction more complex. Building a 2D geomechanical model, using seismic data as an input and following an analysis methodology that considered three type of formation fluids - gas, oil and water in the sand body, all pore pressure gradients related to lateral transfer for the respective fluids were evaluated. This methodology was applied to a conventional reservoir in a field in Colombia and was helpful to select the appropriate mud weight and circulating pressure to mitigate drilling risks associated to this mechanism of overpressure. Seismic data was critical to identifying this type of overpressure mechanism and was one of the main inputs for building the geomechanical earth model. This methodology enables drilling engineers and geoscientists to confidently predict, assess and mitigate the risks posed by overpressure in non-shale formations where lateral transfer is the driving mechanism of overpressure. This will ensure a robust well plan and minimize drilling/well control hazards associated with this mode of overpressure.

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