Bayesian time-lapse inversion

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R43-R48 ◽  
Author(s):  
Arild Buland ◽  
Youness El Ouair
Keyword(s):  
Water Injection ◽  
Rock Physics ◽  
Real Data ◽  
Time Lapse ◽  
Baseline Survey ◽  
Inversion Method ◽  
Data Set ◽  
Uncertainty Calculation ◽  
The Difference ◽  
Fast Inversion

A new, fast inversion approach for time-lapse seismic data is developed where the uncertainty of the inversion results is an integral part of the solution. The inversion method estimates changes in the elastic material properties of a reservoir because of production of hydrocarbons, including uncertainty bounds on these estimates. The changes in elastic properties then can be related to changes in hydrocarbon saturation and reservoir pressure by using rock-physics relations. The inversion operates directly on the difference between a repeat survey and a baseline survey. This is advantageous with respect to the uncertainty calculation, because an estimate of the seismic uncertainty can be obtained directly from the difference data in zones not affected by production. The method is formulated in a Bayesian setting, and the solution is represented by explicit expressions for the posterior expectation and the covariance of the elastic parameter changes. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Results of the applied approach to a real data set from the Norne field are consistent with the expected effects of water flushing because of water injection.

Time-lapse tomographic inversion using a Gaussian parameterization of the velocity changes

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. U29-U38 ◽  
Author(s):  
Andreas Kjelsrud Evensen ◽  
Martin Landrø
Keyword(s):  
Large Scale ◽  
Weighted Least Squares ◽  
Real Data ◽  
Time Lapse ◽  
Two Dimensions ◽  
Inversion Method ◽  
Data Set ◽  
Tomographic Inversion ◽  
Gaussian Functions ◽  
Velocity Changes

Most seismic studies of changes in traveltimes are of a qualitative nature and a major challenge in four dimensions is to use the information contained in time shifts to quantify the nature of velocity changes in the subsurface layers. We propose a 4D tomographic inversion method that uses time shifts from prestack seismic data to estimate parameters describing the 2D velocity field after changes have occurred. Prestack data allow for the usage of many offsets, thus increasing the information input for the inversion. The velocity changes are parameterized by a chosen number of Gaussian functions in two dimensions and weighted least-squares inversion is used to estimate the parameters describing these functions. We have found that the parameters describing the position and shape of the Gaussian velocity anomalies can be estimated with this method for simple synthetic cases. For more complex cases with overlapping Gaussian functions, resolution of the parameters can be difficult and in these cases our recommendation is to find the best fit for a simple smooth anomaly to a more complex real world. The method is tested on a real data set from a [Formula: see text] injection project above the Sleipner field in the North Sea, where quantification of changes is important for monitoring purposes. We have found that the noise levels in prestack traveltime data are on the high side for large-scale analysis; however, we estimate reasonable [Formula: see text] layer thickness and velocity compared to previous work in a nearby area.

Bayesian lithology and fluid prediction from seismic prestack data

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. C13-C21 ◽  
Author(s):  
Arild Buland ◽  
Odd Kolbjørnsen ◽  
Ragnar Hauge ◽  
Øyvind Skjæveland ◽  
Kenneth Duffaut
Keyword(s):  
Seismic Data ◽  
Rock Physics ◽  
Real Data ◽  
Feasibility Analysis ◽  
Bayesian Inversion ◽  
Inversion Method ◽  
Elastic Parameters ◽  
Data Set ◽  
Prior Probabilities ◽  
Simultaneous Inversion

A fast Bayesian inversion method for 3D lithology and fluid prediction from prestack seismic data, and a corresponding feasibility analysis were developed and tested on a real data set. The objective of the inversion is to find the probabilities for different lithology-fluid classes from seismic data and geologic knowledge. The method combines stochastic rock physics relations between the elastic parameters and the different lithology-fluid classes with the results from a fast Bayesian seismic simultaneous inversion from seismic data to elastic parameters. A method for feasibility analysis predicts the expected modification of the prior probabilities to posterior probabilities for the different lithology-fluid classes. The feasibility analysis can be carried out before the seismic data are analyzed. Both the feasibility method and the seismic lithology-fluid probability inversion were applied to a prospect offshore Norway. The analysis improves the probability for gas sand from 0.1 to about 0.2–0.4 with seismic data.

scholarly journals Determination of a stress-dependent rock-physics model using anisotropic time-lapse tomographic inversion

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. C141-C152
Author(s):  
Nicolas Mastio ◽  
Pierre Thore ◽  
Marianne Conin ◽  
Guillaume Caumon
Keyword(s):  
Rock Physics ◽  
Real Data ◽  
Time Lapse ◽  
P Wave ◽  
Velocity Change ◽  
Data Set ◽  
Tomographic Inversion ◽  
P Wave Velocity ◽  
Cap Rock ◽  
Velocity Changes

In the petroleum industry, time-lapse (4D) studies are commonly used for reservoir monitoring, but they are also useful to perform risk assessment for potential overburden deformations (e.g., well shearing, cap-rock integrity). Although complex anisotropic velocity changes are predicted in the overburden by geomechanical studies, conventional time-lapse inversion workflows only deal with vertical velocity changes. To retrieve the geomechanically induced anisotropy, we have adopted a reflection traveltime tomography method coupled with a time-shift estimation algorithm of prestack data of the baseline and monitor simultaneously. For the 2D approach, we parameterize the anisotropy using five coefficients, enough to cover any type of anisotropy. Before applying the workflow to a real data set, we first study a synthetic data set based on the real data set and include velocity variations between baseline and monitor found in the literature (vertical P-wave velocity decrease in the cap rock and isotropic P-wave velocity change in the reservoir). On the synthetics, we measure the angular ray coverage necessary to retrieve the target anisotropy and observe that the retrieved anisotropies depend on the offset range. Based on a synthetic experiment, we believe that the acquisition of the real case study is suitable for performing tomographic inversion. The anisotropic velocity changes obtained on three inlines separated by 375 m are consistent and show a strong positive anomaly in the cap rock along the 45° direction (the [Formula: see text] parameter in Thomsen notation), whereas the vertical velocity change is surprisingly almost negligible. We adopt a rock-physics explanation compatible with these observations and geologic considerations: a reactivation of water-filled subvertical cracks.

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.

Common-focus point-based target-oriented imaging approach for continuous seismic reservoir monitoring

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. M41-M48 ◽  
Author(s):  
Hongwei Liu ◽  
Mustafa Naser Al-Ali
Keyword(s):  
Seismic Data ◽  
Rock Physics ◽  
Time Lapse ◽  
Velocity Estimation ◽  
Estimation Methods ◽  
Data Sets ◽  
Data Set ◽  
Velocity Models ◽  
Reservoir Monitoring ◽  
Focus Point

The ideal approach for continuous reservoir monitoring allows generation of fast and accurate images to cope with the massive data sets acquired for such a task. Conventionally, rigorous depth-oriented velocity-estimation methods are performed to produce sufficiently accurate velocity models. Unlike the traditional way, the target-oriented imaging technology based on the common-focus point (CFP) theory can be an alternative for continuous reservoir monitoring. The solution is based on a robust data-driven iterative operator updating strategy without deriving a detailed velocity model. The same focusing operator is applied on successive 3D seismic data sets for the first time to generate efficient and accurate 4D target-oriented seismic stacked images from time-lapse field seismic data sets acquired in a [Formula: see text] injection project in Saudi Arabia. Using the focusing operator, target-oriented prestack angle domain common-image gathers (ADCIGs) could be derived to perform amplitude-versus-angle analysis. To preserve the amplitude information in the ADCIGs, an amplitude-balancing factor is applied by embedding a synthetic data set using the real acquisition geometry to remove the geometry imprint artifact. Applying the CFP-based target-oriented imaging to time-lapse data sets revealed changes at the reservoir level in the poststack and prestack time-lapse signals, which is consistent with the [Formula: see text] injection history and rock physics.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

Seismic characterization of heavy oil reservoir during thermal production: A case study

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. B13-B27 ◽  
Author(s):  
Hemin Yuan ◽  
De-Hua Han ◽  
Weimin Zhang
Keyword(s):  
Heavy Oil ◽  
Rock Physics ◽  
Time Lapse ◽  
Steam Injection ◽  
Oil Reservoirs ◽  
Inversion Method ◽  
Oil Reservoir ◽  
Steam Chamber ◽  
Heavy Oil Reservoirs ◽  
Heavy Oil Reservoir

Heavy oil reservoirs are important alternative energy resources to conventional oil and gas reservoirs. However, due to the high viscosity, most production methods of heavy oil reservoirs involve thermal production. Heavy oil reservoirs’ properties change dramatically during thermal production because the viscosity drops drastically with increasing temperature. Moreover, the velocity and density also decrease after steam injection, leading to a longer traveltime of seismic velocities and low impedance of the steam chamber zone. These changes of properties can act as indicators of the steam chamber and can be detected through the time-lapse inversion method. We first establish the rock-physics relationship between oil sands’ impedance and temperature on the basis of our previous laboratory work. Then, we perform the forward modeling of the heavy oil reservoir with the steam chamber to demonstrate the influence of steam injection on seismic profiles. Then, we develop a modified-Cauchy prior-distribution-based time-lapse inversion method and perform a 2D model test. The inversion method is then applied on the real field data, and the results are analyzed. By combining the inverted impedance and rock-physics relation between impedance and temperature, the temperature distribution map is obtained, which can work as an indicator of steam chamber. Finally, an empirical relation between impedance and velocity is established, and velocity is derived from the impedance.

Time-lapse acoustic impedance variations during CO2 injection in Weyburn oilfield, Canada

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. M1-M13 ◽  
Author(s):  
Yichuan Wang ◽  
Igor B. Morozov
Keyword(s):  
Oil Recovery ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Time Lapse ◽  
Time Shift ◽  
Co2 Injection ◽  
Inversion Method ◽  
Data Sets ◽  
Storage Site ◽  
Data Set

For seismic monitoring injected fluids during enhanced oil recovery or geologic [Formula: see text] sequestration, it is useful to measure time-lapse (TL) variations of acoustic impedance (AI). AI gives direct connections to the mechanical and fluid-related properties of the reservoir or [Formula: see text] storage site; however, evaluation of its subtle TL variations is complicated by the low-frequency and scaling uncertainties of this attribute. We have developed three enhancements of TL AI analysis to resolve these issues. First, following waveform calibration (cross-equalization) of the monitor seismic data sets to the baseline one, the reflectivity difference was evaluated from the attributes measured during the calibration. Second, a robust approach to AI inversion was applied to the baseline data set, based on calibration of the records by using the well-log data and spatially variant stacking and interval velocities derived during seismic data processing. This inversion method is straightforward and does not require subjective selections of parameterization and regularization schemes. Unlike joint or statistical inverse approaches, this method does not require prior models and produces accurate fitting of the observed reflectivity. Third, the TL AI difference is obtained directly from the baseline AI and reflectivity difference but without the uncertainty-prone subtraction of AI volumes from different seismic vintages. The above approaches are applied to TL data sets from the Weyburn [Formula: see text] sequestration project in southern Saskatchewan, Canada. High-quality baseline and TL AI-difference volumes are obtained. TL variations within the reservoir zone are observed in the calibration time-shift, reflectivity-difference, and AI-difference images, which are interpreted as being related to the [Formula: see text] injection.

Repeatability issues of 3-D VSP data

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1673-1679 ◽  
Author(s):  
Martin Landrø
Keyword(s):  
Vertical Component ◽  
Time Lapse ◽  
Management Tool ◽  
Data Set ◽  
Hydrocarbon Reservoir ◽  
Vertical Seismic Profiling ◽  
Positioning Errors ◽  
Vsp Data ◽  
The Difference ◽  
Pressure Changes

Increased repeatability is recognized as one major issue for improving the time‐lapse seismic technology as a reservoir management tool. A 3-D vertical seismic profiling (VSP) data set, acquired over a period of two days, is used to analyze how repeatable a permanent installed geophone array can be and how repeatability changes with inaccuracies in source positioning. It is found that for a frequency range between 3.5 and 50 Hz, the difference root‐mean‐square (rms) level between two recorded traces belonging to two different shots is about 8%. This fact shows that there is a potential for acquiring very accurate time‐lapse seismic data by using a permanently installed downhole geophone array. Repeatability variation with increasing shot separation distances is analyzed, showing a rapid decrease in repeatability as the accuracy of the positioning of the repeat survey decreases. Horizontal geophone components show approximately the same degree of repeatability compared to the vertical component, but horizontal geophone data is slightly more sensitive to positioning errors. The results show that repeated 3-D VSP surveys (preferably using permanently installed geophone arrays) might be an efficient tool for detailed and precise monitoring of fluid and pressure changes within a hydrocarbon reservoir.

scholarly journals Application of time-lapse ERT imaging to watershed characterization

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. G7-G17 ◽  
Author(s):  
Carlyle R. Miller ◽  
Partha S. Routh ◽  
Troy R. Brosten ◽  
James P. McNamara
Keyword(s):  
Reference Model ◽  
Time Lapse ◽  
Data Sets ◽  
Data Set ◽  
Resistivity Tomography ◽  
Practical Applications ◽  
Data Inversion ◽  
Time Periods ◽  
The Difference ◽  
Base Data

Time-lapse electrical resistivity tomography (ERT) has many practical applications to the study of subsurface properties and processes. When inverting time-lapse ERT data, it is useful to proceed beyond straightforward inversion of data differences and take advantage of the time-lapse nature of the data. We assess various approaches for inverting and interpreting time-lapse ERT data and determine that two approaches work well. The first approach is model subtraction after separate inversion of the data from two time periods, and the second approach is to use the inverted model from a base data set as the reference model or prior information for subsequent time periods. We prefer this second approach. Data inversion methodology should be consideredwhen designing data acquisition; i.e., to utilize the second approach, it is important to collect one or more data sets for which the bulk of the subsurface is in a background or relatively unperturbed state. A third and commonly used approach to time-lapse inversion, inverting the difference between two data sets, localizes the regions of the model in which change has occurred; however, varying noise levels between the two data sets can be problematic. To further assess the various time-lapse inversion approaches, we acquired field data from a catchment within the Dry Creek Experimental Watershed near Boise, Idaho, U.S.A. We combined the complimentary information from individual static ERT inversions, time-lapse ERT images, and available hydrologic data in a robust interpretation scheme to aid in quantifying seasonal variations in subsurface moisture content.

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