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.

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.

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.

Time-lapse velocity analysis — Application to onshore continuous reservoir monitoring

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. B105-B117 ◽  
Author(s):  
Julien Cotton ◽  
Hervé Chauris ◽  
Eric Forgues ◽  
Paul Hardouin
Keyword(s):  
Heavy Oil ◽  
Reservoir Characterization ◽  
Real Data ◽  
Time Lapse ◽  
Velocity Model ◽  
Steam Injection ◽  
Calendar Time ◽  
Data Set ◽  
Time Migration ◽  
Velocity Changes

In 4D seismic, the velocity model used for imaging and reservoir characterization can change as production from the reservoir progresses. This is particularly true for heavy oil reservoirs stimulated by steam injection. In the context of sparse and low-fold seismic acquisitions, conventional migration velocity analyses can be inadequate because of a poorly and irregularly sampled offset dimension. We update the velocity model in the context of daily acquisitions with buried sources and receivers. The main objective is to demonstrate that subtle time-lapse effects can be detected over the calendar time on onshore sparse acquisitions. We develop a modified version of the conventional prestack time migration to detect velocity changes obtained after crosscorrelation of the base and monitor surveys. This technique is applied on a heavy oil real data set from the Netherlands and reveals how the steam diffuses over time within the reservoir.

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.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Variability in the Power Spectrum of Solar Five-Minute Oscillations

1983 ◽  
Vol 66 ◽  
pp. 411-425
Author(s):  
Frank Hill ◽  
Juri Toomre ◽  
Laurence J. November
Keyword(s):  
Large Scale ◽  
Solar Rotation ◽  
Temporal Frequency ◽  
Power Spectra ◽  
Giant Cells ◽  
Spectral Lines ◽  
Data Sets ◽  
Data Set ◽  
Temporal Sampling ◽  
Velocity Changes

AbstractTwo-dimensional power spectra of solar five-minute oscillations display prominent ridge structures in (k, ω) space, where k is the horizontal wavenumber and ω is the temporal frequency. The positions of these ridges in k and ω can be used to probe temperature and velocity structures in the subphotosphere. We have been carrying out a continuing program of observations of five-minute oscillations with the diode array instrument on the vacuum tower telescope at Sacramento Peak Observatory (SPO). We have sought to establish whether power spectra taken on separate days show shifts in ridge locations; these may arise from different velocity and temperature patterns having been brought into our sampling region by solar rotation. Power spectra have been obtained for six days of observations of Doppler velocities using the Mg I λ5173 and Fe I λ5434 spectral lines. Each data set covers 8 to 11 hr in time and samples a region 256″ × 1024″ in spatial extent, with a spatial resolution of 2″ and temporal sampling of 65 s. We have detected shifts in ridge locations between certain data sets which are statistically significant. The character of these displacements when analyzed in terms of eastward and westward propagating waves implies that changes have occurred in both temperature and horizontal velocity fields underlying our observing window. We estimate the magnitude of the velocity changes to be on the order of 100 m s -1; we may be detecting the effects of large-scale convection akin to giant cells.

Warping least-squares inversion for 4D velocity change: Gulf of Mexico case study

2019 ◽  
Vol 7 (2) ◽  
pp. SB23-SB31
Author(s):  
Chang Li ◽  
Mark Meadows ◽  
Todd Dygert
Keyword(s):  
Gulf Of Mexico ◽  
Least Squares ◽  
Synthetic Data ◽  
Inversion Method ◽  
Velocity Change ◽  
Data Set ◽  
Phase Constraints ◽  
Free Case ◽  
Velocity Changes

We have developed a new trace-based, warping least-squares inversion method to quantify 4D velocity changes. There are two steps to solve for these velocity changes: (1) dynamic warping with phase constraints to align the baseline and monitor traces and (2) least-squares inversion for 4D velocity changes incorporating the time shifts and 4D amplitude differences (computed after trace alignment by warping). We have demonstrated this new inversion workflow using simple synthetic layered models. For the noise-free case, phase-constrained warping is superior to standard, amplitude-based warping by improving trace alignment, resulting in more accurate inverted velocity changes (less than 1% error). For synthetic data with 6% rms noise, inverted velocity changes are reasonably accurate (less than 10% error). Additional inversion tests with migrated finite-difference data shot over a realistic anticline model result in less than 10% error. The inverted velocity changes on a 4D field data set from the Gulf of Mexico are more interpretable and consistent with the dynamic reservoir model than those estimated from the conventional time-strain method.

Pore-pressure detection sensitivities tested with time-lapse seismic data

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. O39-O50 ◽  
Author(s):  
Øyvind Kvam ◽  
Martin Landrø
Keyword(s):  
Pore Pressure ◽  
Seismic Data ◽  
Time Lapse ◽  
Pressure Increase ◽  
Burial Depth ◽  
Velocity Analysis ◽  
Seismic Velocities ◽  
Data Set ◽  
Pore Pressure Prediction ◽  
Velocity Changes

In an exploration context, pore-pressure prediction from seismic data relies on the fact that seismic velocities depend on pore pressure. Conventional velocity analysis is a tool that may form the basis for obtaining interval velocities for this purpose. However, velocity analysis is inaccurate, and in this paper we focus on the possibilities and limitations of using velocity analysis for pore-pressure prediction. A time-lapse seismic data set from a segment that has undergone a pore-pressure increase of 5 to 7 MPa between the two surveys is analyzed for velocity changes using detailed velocity analysis. A synthetic time-lapse survey is used to test the sensitivity of the velocity analysis with respect to noise. The analysis shows that the pore-pressure increase cannot be detected by conventional velocity analysis because the uncertainty is much greater than the expected velocity change for a reservoir of the given thickness and burial depth. Finally, by applying amplitude-variation-with-offset (AVO) analysis to the same data, we demonstrate that seismic amplitude analysis may yield more precise information about velocity changes than velocity analysis.

Adaptive subtraction using complex-valued curvelet transforms

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. V51-V60 ◽  
Author(s):  
Ramesh (Neelsh) Neelamani ◽  
Anatoly Baumstein ◽  
Warren S. Ross
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Seismic Reflection ◽  
Characteristic Frequency ◽  
Large Scale ◽  
Curvelet Transform ◽  
Real Data ◽  
Text Data ◽  
Data Set ◽  
Complex Valued

We propose a complex-valued curvelet transform-based (CCT-based) algorithm that adaptively subtracts from seismic data those noises for which an approximate template is available. The CCT decomposes a geophysical data set in terms of small reflection pieces, with each piece having a different characteristic frequency, location, and dip. One can precisely change the amplitude and shift the location of each seismic reflection piece in a template by controlling the amplitude and phase of the template's CCT coefficients. Based on these insights, our approach uses the phase and amplitude of the data's and template's CCT coefficients to correct misalignment and amplitude errors in the noise template, thereby matching the adapted template with the actual noise in the seismic data, reflection event-by-event. We also extend our approach to subtract noises that require several templates to be approximated. By itself, the method can only correct small misalignment errors ([Formula: see text] in [Formula: see text] data) in the template; it relies on conventional least-squares (LS) adaptation to correct large-scale misalignment errors, such as wavelet mismatches and bulk shifts. Synthetic and real-data results illustrate that the CCT-based approach improves upon the LS approach and a curvelet-based approach described by Herrmann and Verschuur.

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.

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