L1–2 minimization for P- and S-impedance inversion

2020 ◽  
Vol 8 (2) ◽  
pp. T379-T390
Author(s):  
Wenliang Nie ◽  
Xiaotao Wen ◽  
Jixin Yang ◽  
Jian He ◽  
Kai Lin ◽  
...  
Keyword(s):  
Objective Function ◽  
Reservoir Characterization ◽  
A Priori ◽  
Low Frequency ◽  
Superior Performance ◽  
Minimization Method ◽  
Block Boundary ◽  
Avo Inversion ◽  
Impedance Inversion ◽  
The Difference

Amplitude variation with offset (AVO) inversion has been widely used in reservoir characterization to predict lithology and fluids. However, some existing AVO inversion methods that use [Formula: see text] norm regularization may not obtain the block boundary of subsurface layers because the AVO inversion is a severely ill-posed problem. To obtain sparse and accurate solutions, we have introduced the [Formula: see text] minimization method as an alternative to [Formula: see text] norm regularization. We used [Formula: see text] minimization for simultaneous P- and S-impedance inversion from prestack seismic data. We first derived the forward problem with multiangles and set up the inversion objective function with constraints of a priori low-frequency information obtained from well-log data. Then, we introduced minimization of the difference of [Formula: see text] and [Formula: see text] norms, denoted as [Formula: see text] minimization, to solve this objective function. The nonconvex penalty function of the [Formula: see text] minimization method is decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem is solved by the alternating direction method of multipliers. Compared to [Formula: see text] norm regularization, the results indicate that [Formula: see text] minimization has superior performance over [Formula: see text] norm regularization in promoting blocky/sparse solutions. Tests on synthetic and field data indicate that our method can provide sparser and more accurate P- and S-impedance inversion results. The overall results confirm that our method has great potential in the detection and identification of fluids.

Anisotropic correction of sonic logs in wells with large relative dip

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. E1-E5 ◽  
Author(s):  
Lev Vernik
Keyword(s):  
Reservoir Characterization ◽  
Low Frequency ◽  
P Wave ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Avo Inversion ◽  
Pore Pressure Prediction ◽  
Siliciclastic Rocks ◽  
Dip Angle ◽  
Sonic Logs

Seismic reservoir characterization and pore-pressure prediction projects rely heavily on the accuracy and consistency of sonic logs. Sonic data acquisition in wells with large relative dip is known to suffer from anisotropic effects related to microanisotropy of shales and thin-bed laminations of sand, silt, and shale. Nonetheless, if anisotropy parameters can be related to shale content [Formula: see text] in siliciclastic rocks, then I show that it is straightforward to compute the anisotropy correction to both compressional and shear logs using [Formula: see text] and the formation relative dip angle. The resulting rotated P-wave sonic logs can be used to enhance time-depth ties, velocity to effective stress transforms, and low-frequency models necessary for prestack seismic amplitude variation with offset (AVO) inversion.

Full-waveform inversion with borehole constraints for elastic VTI media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R553-R563
Author(s):  
Sagar Singh ◽  
Ilya Tsvankin ◽  
Ehsan Zabihi Naeini
Keyword(s):  
Objective Function ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Rock Physics ◽  
Anisotropic Media ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Trade Offs ◽  
Vti Media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.

Structurally constrained impedance inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T577-T589 ◽  
Author(s):  
Haitham Hamid ◽  
Adam Pidlisecky
Keyword(s):  
Objective Function ◽  
Seismic Data ◽  
Field Data ◽  
A Priori ◽  
Structural Constraints ◽  
Inversion Algorithm ◽  
Data Set ◽  
Impedance Inversion ◽  
Single Trace ◽  
Complex Geology

In complex geology, the presence of highly dipping structures can complicate impedance inversion. We have developed a structurally constrained inversion in which a computationally well-behaved objective function is minimized subject to structural constraints. This approach allows the objective function to incorporate structural orientation in the form of dips into our inversion algorithm. Our method involves a multitrace impedance inversion and a rotation of an orthogonal system of derivative operators. Local dips used to constrain the derivative operators were estimated from migrated seismic data. In addition to imposing structural constraints on the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We investigated this algorithm on a complex synthetic 2D model as well as a seismic field data set. We compared the result obtained with this approach with the results from single trace-based inversion and laterally constrained inversion. The inversion carried out using dip information produces a model that has higher resolution that is more geologically realistic compared with other methods.

Impedance inversion by using the low-frequency full-waveform inversion result as an a priori model

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R149-R164 ◽  
Author(s):  
Sanyi Yuan ◽  
Shangxu Wang ◽  
Yaneng Luo ◽  
Wanwan Wei ◽  
Guanchao Wang
Keyword(s):  
A Priori ◽  
Complex Structure ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Real Data ◽  
Well Logs ◽  
Low Frequencies ◽  
Impedance Model ◽  
Full Waveform ◽  
Impedance Inversion

Prestack acoustic full-waveform inversion (FWI) can provide long-wavelength components of the P-wave velocity by using low frequencies and long-offset direct/diving/refracted waves, which could be simulated via a large space grid, and it is weakly sensitive to density. Poststack impedance inversion can usually quickly yield high-resolution impedance, and it is sensitive to density. Therefore, we have combined these two methods to develop an FWI-driven impedance inversion. Our method first uses FWI to obtain the long-wavelength velocity with a guaranteed overlap between the high frequencies of the velocity and the low frequencies of the poststack data. Then, the fitting rock-physics relationship between the density and the velocity is adopted to translate the FWI velocity into the low-frequency impedance. Finally, the resulting low-frequency impedance is used to construct an a priori constraint for poststack impedance inversion. The method has the ability to solve the overlap between the FWI-based converted prior impedance model and poststack data, and it can thereby yield a broadband absolute impedance result. We adopt a Marmousi II model example and a real data case to test the performances of the FWI-driven impedance inversion and indicate its advantages compared with the conventional well-driven impedance inversion that uses well logs and interpreted horizons to build the prior impedance model. The synthetic data example demonstrates that well-driven impedance inversion produces a result with a relatively large deviation to the true impedance model at complex structure zones. However, FWI-driven impedance inversion favorably recovers all interesting sediment layers at complex structure zones. The real data example illustrates that well-driven impedance inversion yields a result with a distinct footprint of the prior model created from well logs and horizons. On the other hand, we find that FWI-driven impedance inversion yields a geologically reasonable solution, which not only conforms to the time-space variation trend of the well logs, but it also reveals a basin structural-depositional evolution.

Seismic reservoir characterization of Utica-Point Pleasant shale with efforts at fracability evaluation — Part 2: A case study

2018 ◽  
Vol 6 (2) ◽  
pp. T325-T336 ◽  
Author(s):  
Ritesh Kumar Sharma ◽  
Satinder Chopra ◽  
James Keay ◽  
Hossein Nemati ◽  
Larry Lines
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Rock Physics ◽  
Well Log ◽  
X Ray Diffraction ◽  
Impedance Inversion ◽  
Seismic Reservoir ◽  
Petrophysical Modeling

The Utica Formation in eastern Ohio possesses all the prerequisites for being a successful unconventional play. Attempts at seismic reservoir characterization of the Utica Formation have been discussed in part 1, in which, after providing the geologic background of the area of study, the preconditioning of prestack seismic data, well-log correlation, and building of robust low-frequency models for prestack simultaneous impedance inversion were explained. All these efforts were aimed at identification of sweet spots in the Utica Formation in terms of organic richness as well as brittleness. We elaborate on some aspects of that exercise, such as the challenges we faced in the determination of the total organic carbon (TOC) volume and computation of brittleness indices based on mineralogical and geomechanical considerations. The prediction of TOC in the Utica play using a methodology, in which limited seismic as well as well-log data are available, is demonstrated first. Thereafter, knowing the nonexistence of the universally accepted indicator of brittleness, mechanical along with mineralogical attempts to extract the brittleness information for the Utica play are discussed. Although an attempt is made to determine brittleness from mechanical rock-physics parameters (Young’s modulus and Poisson’s ratio) derived from seismic data, the available X-ray diffraction data and regional petrophysical modeling make it possible to determine the brittleness index based on mineralogical data and thereafter be derived from seismic data.

Relative P-impedance estimation using a dipole-based matching pursuit decomposition strategy

2015 ◽  
Vol 3 (4) ◽  
pp. T197-T206 ◽  
Author(s):  
Xiaotao Wen ◽  
Bo Zhang ◽  
Wayne Pennington ◽  
Zhenhua He
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Reservoir Characterization ◽  
Matching Pursuit ◽  
Low Frequency ◽  
Data Set ◽  
Adaptive Smoothing ◽  
Impedance Inversion ◽  
Matching Pursuit Decomposition

The P-impedance is one of the most important elastic parameters of rocks, and it is commonly used for reservoir characterization. Conventional P-impedance inversion merges a low-frequency log-based model with a high-frequency seismic-derived model. We have proposed a method to estimate the P-impedance by employing dipole-based matching pursuit (DMP) decomposition. The matching pursuit decomposes the seismic traces into a superposition of scaled wavelets, and the associated scalar information represents the reflectivity series, which can be integrated for P-impedance estimation. Unfortunately, DMP analysis is usually performed trace by trace, resulting in a poor lateral continuity. Applying conventional lateral smoothing through mean or median filtering improves the lateral continuity but typically decreases the vertical resolution. We have evaluated an adaptive smoothing strategy that required the filtering to follow bed boundaries in an automated manner, sharpening the boundaries while maintaining the high quality of inversion. We have determined the effectiveness of our algorithm by first applying it to a synthetic wedge model and then to a real seismic data set.

scholarly journals Prestack Seismic Inversion via Nonconvex L1-2 Regularization

2021 ◽  
Vol 11 (24) ◽  
pp. 12015
Author(s):  
Wenliang Nie ◽  
Fei Xiang ◽  
Bo Li ◽  
Xiaotao Wen ◽  
Xiangfei Nie
Keyword(s):  
Objective Function ◽  
Regularization Method ◽  
Oil And Gas ◽  
A Priori ◽  
Low Frequency ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Data Logging ◽  
Elastic Parameters ◽  
Geological Interpretation

Using seismic data, logging information, geological interpretation data, and petrophysical data, it is possible to estimate the stratigraphic texture and elastic parameters of a study area via a seismic inversion. As such, a seismic inversion is an indispensable tool in the field of oil and gas exploration and development. However, due to unknown natural factors, seismic inversions are often ill-conditioned problems. One way to work around this unknowable information is to determine the solution to the seismic inversion using regularization methods after adding further a priori constraints. In this study, the nonconvex L1−2 regularization method is innovatively applied to the three-parameter prestack amplitude variation angle (AVA) inversion. A forward model is first derived based on the Fatti approximate formula and then low-frequency models for P impedance, S impedance, and density are established using logging and horizon data. In the Bayesian inversion framework, we derive the objective function of the prestack AVA inversion. To further improve the accuracy and stability of the inversion results, we remove the correlations between the elastic parameters that act as initial constraints in the inversion. Then, the objective function is solved by the nonconvex L1−2 regularization method. Finally, we validate our inversion method by applying it to synthetic and observational data sets. The results show that our nonconvex L1−2 regularization seismic inversion method yields results that are highly accurate, laterally continuous, and can be used to identify and locate reservoir formation boundaries. Overall, our method will be a useful tool in future work focused on predicting the location of reservoirs.

Comparative Evaluation of Balancing Properties of Stratified Randomization Procedures

2009 ◽  
Vol 48 (02) ◽  
pp. 129-134 ◽  
Author(s):  
G. Kundt
Keyword(s):  
Clinical Trial ◽  
Prognostic Factors ◽  
Block Size ◽  
Multicenter Trial ◽  
Superior Performance ◽  
Good Tool ◽  
Minimization Method ◽  
Block Randomization ◽  
The Difference ◽  
The Impact

Summary Objectives: If in a clinical trial prognostic factors are known in advance to be associated with the outcome of a patient it is often recommended that the randomization for a clinical trial should be stratified on these factors, particularly in a multicenter trial. Unfortunately, stratified or covariate-adaptive randomization does not always promote greater balance between the numbers of treatment assignments to A and B within each stratum and thus overall. Because such designs have numerous parameters that must be specified, simulation is a good tool to investigate the impact of these parameters on balance. Methods: We investigate and discuss in more detail the difference in balancing performance of three stratified randomization procedures. The permuted-block randomization within strata, the “minimization” method and “self-adjusting” design are assessed overall, within levels of prognostic factors, and within strata. Results: We show the superior performance of “self-adjusting” design and the extent of balancing losses occurring with permuted-block randomization within levels of factors and with “minimization” within strata. A summary of principal conclusions regarding the balancing properties of stratified randomization procedures is presented and general recommendations are offered. Conclusions: The relative merits of each procedure should be weighted carefully in relation to the characteristics of the trial. Considering the likelihood of imbalances, the sample size and values of parameters of stratified randomization procedures (number of prognostic factors, number of factor levels, block size) are important when choosing a randomization procedure.

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

scholarly journals Low-Frequency Expansion Approach for Seismic Data Based on Compressed Sensing in Low SNR

2021 ◽  
Vol 11 (11) ◽  
pp. 5028
Author(s):  
Miaomiao Sun ◽  
Zhenchun Li ◽  
Yanli Liu ◽  
Jiao Wang ◽  
Yufei Su
Keyword(s):  
Reflection Coefficient ◽  
Compressed Sensing ◽  
Objective Function ◽  
Low Frequency ◽  
Original Data ◽  
Seismic Exploration ◽  
High Signal ◽  
Inversion Process ◽  
Frequency Information ◽  
Low Snr

Low-frequency information can reflect the basic trend of a formation, enhance the accuracy of velocity analysis and improve the imaging accuracy of deep structures in seismic exploration. However, the low-frequency information obtained by the conventional seismic acquisition method is seriously polluted by noise, which will be further lost in processing. Compressed sensing (CS) theory is used to exploit the sparsity of the reflection coefficient in the frequency domain to expand the low-frequency components reasonably, thus improving the data quality. However, the conventional CS method is greatly affected by noise, and the effective expansion of low-frequency information can only be realized in the case of a high signal-to-noise ratio (SNR). In this paper, well information is introduced into the objective function to constrain the inversion process of the estimated reflection coefficient, and then, the low-frequency component of the original data is expanded by extracting the low-frequency information of the reflection coefficient. It has been proved by model tests and actual data processing results that the objective function of estimating the reflection coefficient constrained by well logging data based on CS theory can improve the anti-noise interference ability of the inversion process and expand the low-frequency information well in the case of a low SNR.

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