4D Time Shifts Research Articles

Angle-dependent 4D seismic time-strain inversion for estimating subsurface thickness and velocity changes

In time-lapse (also called 4D) seismic analysis, the time shift of a certain seismic reflection event is caused by changes in the seismic velocity and the depth of the event. An interpretation of 4D time shifts is normally simplified by neglecting displacement changes (strains) or assuming linear relations between thickness and velocity strains. Here, we go beyond these assumptions and propose a least-squares optimization method to simultaneously estimate the thickness and velocity strains in vertical transverse isotropic media from angle-dependent 4D seismic time strains. Through examples from synthetic and field data, we show that 4D thickness strains, velocity strains, and anisotropic parameter changes can be estimated simultaneously without prior knowledge about the geomechanics of the survey area. Our time-strain inversion method can be applied to any other 4D seismic data set in which angle-stack images are available. We see that our method has high potential in many other applications, because thickness and velocity strains are the fundamental components of most physical properties used in 4D seismic and geomechanics applications.

Analysis of 4D seismic timeshifts overburden and its relation with the geomechanical model of reservoirs in a Campos Basin field

This paper seeks to interpret the 4D seismic timeshifts in the overburden of a conventional turbidite sandstone reservoir in the Campos Basin and to calculate an empirical factor of sensitivity between these 4D data and the geomechanical deformations. Gaining information on how the production of the reservoir affects the surrounding rocks is of great interest for the management of oil fields, with impacts ranging from optimization of production to the safety of operations and workers. The study of timeshift anomalies are common in chalk fields and unconventional fields of high temperature or pressure. We used two techniques for timeshift calculations, cross-correlation and DTW, as well as structural attributes that are calculated to assist in interpretations. Then, we estimate the sensitivity factor, which allows the construction of synthetic 4D timeshifts from the deformations simulated by the geomechanical model. In most of the field regions there was agreement between simulated deformations and 4D anomalies, showing that it is possible to extract useful information for reservoir management. The estimate of the sensitivity factor indicates that the overburden studied is sensitive to deformations in the rocks, allowing that small deformations can be detected by the given 4D seismic.

Overburden 4D time shifts — Indicating undrained areas and fault transmissibility in the reservoir

Production-induced geomechanical stress changes cause velocity changes in the overburden that might be detected as 4D seismic time shifts. The strength of the velocity changes depends on the degree of pressure changes and the elastic properties of the reservoir and overburden layers. Even small velocity changes (less than 1%) might accumulate into detectable seismic time shifts at the top reservoir, since the overburden thickness typically ranges from one to several kilometers. Reservoir pressure changes inducing seismic time shifts are observed in the overburden of the Snorre, Heidrun, and Statfjord fields, all located on the Norwegian Continental Shelf. The strong correlation between overburden time shifts, geomechanics, and reservoir pressure changes is used to indicate undrained areas and transmissibility across faults, which is useful information for increased oil recovery, well planning, and reservoir model updating. 4D geomechanical models are built with input from simulated reservoir pressures. Geomechanical strain and velocity changes are linked through a “dilation” factor, R. The Snorre, Heidrun, and Statfjord fields indicate an average R value of about 15 for the overburden, when combining modeled vertical strain with observed seismic time shifts. However, this study also shows strong vertical variation in R, implying that R might be layer dependent. For the Statfjord Field, seabed subsidence measurements from gravity and GPS monitoring are used to calibrate the geomechanical model. The Snorre Field results show that both reservoir pressure depletion and pressure buildup can be identified by the use of overburden time shifts. The properties of the reservoir formations and surrounding layers of the investigated fields are typical for many fields on the Norwegian Continental Shelf. This implies that pressure-induced time shifts might be expected for many producing fields, not only chalk or high-pressure, high-temperature reservoirs but also sandstone reservoirs close to hydrostatic pressure.

Rock-physics modeling of stress sensitivity and 4D time shifts in patchy cemented sandstones — Application to the Visund Field, North Sea

The patchy cement model predicts stress sensitivity in poorly to moderately consolidated sandstones using a multiply nested Hashin-Shtrikman approach combined with contact theory. This model can be used to quantify stress sensitivity in reservoir sandstones where core samples are lacking or unreliable. We demonstrate a strategy based on this model that can be used to quantify 4D seismic time shifts and time-shift derivatives associated with stress changes. The time shifts will be a function of the rock stiffness (i.e., volume of patchy cement); therefore, it is important to determine the local changes in rock properties before we can predict stress and fluid changes from time-shift attributes. We apply this approach to four exploration wells in the Visund Field area where we have good control on the rock properties. We first compare modeled time shifts with observed 4D time shifts in the Visund S1 segment where pressure data are available, and we obtain a very good match at two selected well locations. Next, we use the observed seismic time shifts as constraints to estimate the pore-pressure changes in the Pan and Pandora segments just south of the depleting S1 segment. Pressure changes are significantly lower than in the S1 segment but still indicate potential pressure communication between these segments and the main Visund, in spite of fault barriers and deeper fluid contacts.

Time-lapse full-waveform inversion as a reservoir-monitoring tool — A North Sea case study

Full-waveform inversion (FWI) has become an enabling tool for 3D velocity-model building, especially in the shallow part of the seismic image that is well probed by diving waves. Given that FWI provides direct access to P-wave velocities, its application to time-lapse (4D) studies is of obvious interest. Can 4D FWI give fast access to small reservoir production-related velocity changes and compete with traditional 4D time-shift results based on fully processed and imaged reflection data? Also, what algorithmic developments may be needed to achieve robust 4D FWI results? Time-lapse data sets acquired with highly repeatable permanent-reservoir-monitoring (PRM) acquisition systems, such as the one deployed over the Grane Field in the Norwegian North Sea, are well suited to help address these questions. We demonstrate the success of the 4D FWI technique using a synthetic study involving 3D elastic modeling through a highly realistic earth model akin to the actual Grane PRM data. This study indicates there is minimal sensitivity of the method to various residual uncertainties in the data and in the modeling for this acquisition configuration. The 4D FWI results using real time-lapse Grane PRM data acquired in the field with a six-month acquisition interval between vintages show changes at the reservoir level that correlate with both injecting and producing wells. We also find good agreement when comparing the velocity differences from 4D FWI to 4D time shifts and time strains from the fully processed and imaged seismic reflection data. Given that the FWI updates are driven mainly by diving waves, whereas the time-strain analysis uses reflection data, this gives increased confidence in both sets of results. Overall, this case study demonstrates the potential of FWI as a reservoir-monitoring tool.

Evaluation of time-shift extraction methods on a synthetic model with 4D geomechanical changes

Imaging and characterizing time-lapse changes in reservoir properties rely on accurate estimation of the corresponding time shifts and amplitude changes. We evaluated the accuracy of competing time-shift extraction algorithms — cross correlation, nonlinear inversion, dynamic warping, the correlated-leakage method, and the optical-flow-warping method — for estimating 4D time shifts, particularly from subsalt reservoirs. A synthetic model of a Gulf of Mexico field was used for testing these methods. The model contains both subsalt and extra-salt reservoirs. We imposed 4D velocity changes within both reservoirs and in the overburden of the subsalt reservoir. Each of the time-shift extraction methods was evaluated, and each was found to have various strengths and weaknesses. The correlated-leakage and optical-flow-warping methods reproduced the model time shifts most accurately and with the best resolution.

Wave-equation-based image warping

In seismic processing and reservoir characterization, we often need to measure relative displacements between different realizations of data. Over the years, many methods have been developed using different measures of similarity. Such alignment or warping methods are often effective signal or image processing tools. However, none of the available methods are directly driven by the physics of seismic imaging. We have found that a seismic image can be considered as a field governed by the wave equation. We visualized different image realizations as snapshots of the wavefield at different times, and these conveyed the required displacements or time shifts. By formulating the problem in a physical context, we obtained displacements that honored the directionality of the wave propagation. For example, 4D time shifts on migrated stacks were obtained in a direction normal to the reflectors. We have computed these shifts in an inverted finite-difference scheme. To overcome limitations of the two-way wave equation in this application, we factorized it to its one-way counterparts. The method was demonstrated on synthetic and real data sets.

Overburden 4D time shifts induced by reservoir compaction at Snorre field

Interpreting and understanding overburden seismic changes are important to avoid health, safety, and environmental (HSE) accidents and well-drilling problems. Furthermore, overburden time shifts might indicate areas with reservoir compaction and depletion. In the Snorre sandstone field, 4D seismic time shifts of as much as 3 ms are observed in the overburden. The cumulative overburden time shifts captured at top reservoir correlate well with pressure-depletion areas in the reservoir, indicating that the time shifts might be related to changes in stress and strain because of reservoir compaction. For further investigation, a 2D geomechanical model is built in the area with the most prominent overburden time shifts. Based on the stiffness of the reservoir and surrounding rocks and simulated reservoir pore-pressure changes, the geomechanical model predicts a maximum downward displacement at the top reservoir of 0.4 m and maximum seabed subsidence of 0.25 m. By defining an appropriate strain-sensitivity parameter, the results from the geomechanical model are forward-modeled into velocity changes. For comparison, velocity changes are estimated from the time shifts. A good qualitative match is obtained between the geomechanical model and the observed time shifts, indicating that the time shifts are caused by geomechanical effects related to production. Other explanations of the observed overburden time shifts, such as fluid leakage, out-of-zone-injection, or seismic acquisition or processing problems, are found to be less realistic causes of the observed time shifts.

Volumetric bounds on subsurface fluid substitution using 4D seismic time shifts with an application at Sleipner, North Sea

A method is presented for the volumetric estimation of subsurface fluid substitution based on the analysis of 4D seismic time shifts. Since time shifts cannot resolve for fluid saturation and layer thickness simultaneously without additional constraints, mass estimates are derived from the complete set of possible fluid saturations and layer thicknesses. The method considers velocity-saturation relationships that range from uniform fluid mixing to patchy fluid mixing. Based on a generalized velocity-saturation relationship that is parameterized by the degree of patchiness, explicit upper and lower fluid mass bounds are provided. We show that the inherent ambiguity between fluid saturation, fluid mixing, and layer thickness has a severe impact on the convergence of these mass bounds. That is, fluid substitution scenarios with patchy fluid mixing and roughly linear velocity-saturation relationships allow for more accurate fluid quantification than scenarios associated with uniform mixing. Application of the method to two 4D seismic monitor data sets from Sleipner results in [Formula: see text] mass bounds that are consistent with the true injected masses of [Formula: see text]. Moreover, a linear relationship between progressively developing 4D time shifts and known injected [Formula: see text] mass is observed, suggesting that the evolving patterns of fluid saturation and fluid mixing in the [Formula: see text] plume have remained roughly constant with time.

Dynamic time warping — An improved method for 4D and tomography time shift estimation?

Time shift estimation is a key issue in many areas of seismic exploration such as time-lapse studies and traveltime tomography. Automated estimation is useful because it enables applications such as time strain analysis and automated velocity model building. A commonly used automated estimation algorithm is the windowed crosscorrelation. Unfortunately, this method can be inaccurate in areas where time shifts vary significantly over short intervals. Algorithms based on mismatch minimization have been proposed to remedy this problem. All the mentioned methods suffer from cycle skipping in the face of large time shifts. I, therefore, used the dynamic time warping (DTW) algorithm as an alternative method to estimate time shifts. I claimed the time shift estimates produced by DTW are of higher quality than those produced by the previous methods, especially with regard to the cycle-skipping problem. I found that DTW always is able to perfectly restore time shifts applied to traces when the changes are purely temporal. I investigated its accuracy when amplitude changes are present, and found that the algorithm is well suited for time-lapse analysis. Finally, we determined that DTW is resilient against cycle-skipping errors, in the presence of large time shifts and with significant changes in the data, and thus a candidate for use in automated velocity model-building methods, such as waveform tomography or full-waveform inversion.

Using a pseudo-steady-state flow equation and 4D seismic traveltime shifts for estimation of pressure and saturation changes

Pressure and saturation changes cause a change in seismic P-wave velocity resulting in a shift in 4D traveltime. A discrimination between both effects is important to enhance reservoir management decisions. We explored the possibility of linking the fields of reservoir engineering and 4D seismic. A simple inversion scheme based on a reservoir engineering flow equation for pore pressure predictions combined with the Hertz-Mindlin and Gassmann rock-physics models to discriminate pressure and saturation effects from 4D time shifts was presented. To account for no-flow reservoir boundaries, the pseudo-steady-state flow equation giving the pressure distribution was extended with a superpositioning method. During the inversion, three parameters were determined by a nonlinear, least-squares fitting method: the thickness of the hydrocarbon column, the pressure at the well position, and its decay rate away from the well. We successfully tested our approach on a synthetic and a field data case, where the [Formula: see text] injection well at the Snøhvit field, Norway, served as a good example to demonstrate our method. We observed a good correlation between simulation and inversion in our synthetic study. Our theory was limited to homogeneous reservoir conditions and produces spatially low frequent outputs. To apply the model in complex fields, such as at Snøhvit, we introduced a spatially varying Mindlin-exponent over the field and used the theory as an heuristic model assuming that a variation of the Mindlin-exponent takes a change in pressure sensitivity into account. This assumption provided the possibility to indirectly include heterogeneities in grain sorting and porosity variation and improved the model significantly. We see the advantage of our method in its fast and direct implementation to study first-order effects of pressure and saturation behavior on time-lapse seismic data using a simple inversion algorithm instead of computationally intensive simulations.

Time-lapse wave-equation migration velocity analysis

Time-lapse (4D) analysis of seismic data acquired at different stages of hydrocarbon production or gas/fluid injection has been very successful at imaging detailed reservoir changes. Conventional time-domain analysis of 4D data sets usually assumes a linear perturbation about a reference baseline earth model. However, this assumption is violated when production/injection significantly alters the subsurface generating large 4D velocity changes, time shifts, and complicated 4D wavefield coda, necessitating a more robust 4D analysis involving prestack wave-equation depth migration and velocity analysis. We address these situations by extending conventional 3D wave-equation migration velocity analysis (WEMVA) based on one-way wave-equations and single-scattering theory to 4D velocity estimation using a “parallel” inversion approach involving parallel solution of two separate inversion problems. Recognizing that the 4D WEMVA strategy requires precomputed baseline/monitor image-difference volumes, we develop an approximate 4D WEMVA technique that replaces these differences with a single weight function derived from the smooth background time-lapse image difference. We demonstrate the usefulness of the parallel and an approximate 4D WEMVA approach using a synthetic time-lapse [Formula: see text] geosequestration experiment that requires inverting for a thin-layer velocity change derived from [Formula: see text] injection in an analogue North Sea reservoir. The parallel 4D WEMVA solutions generate an excellent high-resolution velocity estimates, whereas the approximate methods recover lower-resolution estimates with magnitudes that must be rescaled through a post-inversion gradient line-search.

Time-lapse wave-equation migration velocity analysis

Time-lapse (4D) analysis of seismic data acquired at different stages of hydrocarbon production or gas/fluid injection has been very successful at imaging detailed reservoir changes. Conventional time-domain analysis of 4D data sets usually assumes a linear perturbation about a reference baseline earth model. However, this assumption is violated when production/injection significantly alters the subsurface generating large 4D velocity changes, time shifts, and complicated 4D wavefield coda, necessitating a more robust 4D analysis involving prestack wave-equation depth migration and velocity analysis. We address these situations by extending conventional 3D waveequation migration velocity analysis (WEMVA) based on one-way wave-equations and single-scattering theory to 4D velocity estimation using a “parallel”inversion approach involving parallel solution of two separate inversion problems. Recognizing that the 4D WEMVA strategy requires precomputed baseline/monitor image-difference volumes, we develop an approximate 4D WEMVA technique that replaces these differences with a single weight function derived from the smooth background time-lapse image difference. We demonstrate the usefulness of the parallel and an approximate 4D WEMVA approach using a synthetic time-lapse CO2 geosequestration experiment that requires inverting for a thin-layer velocity change derived from CO2 injection in an analogue North Sea reservoir. The parallel 4D WEMVA solutions generate an excellent highresolution velocity estimates, whereas the approximate methods recover lower-resolution estimates with magnitudes that must be rescaled through a post-inversion gradient line-search.

Monitoring a shallow subsurface gas flow by time-lapse refraction analysis

Studying time-lapse time shifts for refracted events is a complementary method to conventional 4D analysis. Especially for detecting changes in relatively shallow subsurface layers, we find that this method has potential. By studying data associated with an old underground blowout, we find consistent time shifts of up to 4 ms when comparing a base survey that was acquired before the underground blowout with a monitor survey acquired 20 months after the blowout. These time shifts are interpreted as caused by shallow gas migration. The 4D refraction time shifts are estimated by a standard windowed crosscorrelation technique. Observed time shifts are compared with a simple synthetic modeling to find the possible property and location of the anomaly. The synthetic result was qualitatively matched with real data. We believe that more quantitative matches can obtained when the method is combined with full waveform inversions. Time-lapse refraction analysis has some clear limitations, for instance, the presence of refracted events, which requires a positive velocity contrast for the interface to be studied. Another limitation is that for deeper events, the signal from shallower refractions and noise associated with the water layer will distort the 4D time shifts. However, we found that these results demonstrate the potential of refraction time shifts as a complementary 4D analysis technique. We believe that the method has a significant potential for quantitative 4D interpretation.

Estimation of thickness and velocity changes of injected carbon dioxide layers from prestack time-lapse seismic data

In this study, we bring together the two main categories of time-lapse seismic analysis — amplitude analysis and time-shift analysis — to estimate simultaneously the changes in thickness and velocity of a 4D seismic anomaly. The methodology is applied to time-lapse seismic monitoring of carbon dioxide [Formula: see text] storage at Sleipner field, Norway, that shows significant 4D effects. The 4D anomalies resulting from [Formula: see text] injection appear as a multilayer reflection pattern within the relatively shallow Utsira Sand. This multireflective appearance within the sand layer is interpreted as [Formula: see text] layers trapped below thin shale layers. Because most of the [Formula: see text] layers are believed to be thin [Formula: see text], the interference between top and base of these layers needs to be taken into account in 4D seismic analysis. By studying the reflected event from a horizon below the Utsira Sand, we estimate 4D traveltime shifts caused by the presence of the [Formula: see text] layer above thishorizon. We then combine these traveltime shifts with measured amplitude changes for the top and base of the [Formula: see text] layer to estimate velocity and thickness changes for the thin [Formula: see text] layer. In 1999, after three years of injection, the most likely velocity change was around [Formula: see text] and the thickness of the [Formula: see text] layer was around [Formula: see text]. In 2001, the corresponding velocity change and thickness estimates were [Formula: see text] and [Formula: see text], respectively. Finally, in 2002, the most likely velocity change was [Formula: see text] and the thickness of the [Formula: see text] layer was [Formula: see text]. It is not straightforward to apply this method to a stack of [Formula: see text] layers because 4D time shifts below the Utsira Sand only provide information about the average time shift for all layers. The amplitude information for each individual [Formula: see text] layer cannot be resolved without knowing the velocity change within each layer. However, our result from a single [Formula: see text] layer may be used to constrain the velocity changes for the multilayer [Formula: see text] case.

4D reservoir geomechanics: a case study from the HP/HT reservoirs of the Elgin and Franklin fields

The quest for better predictability of reservoir behaviour has led to the need to construct more realistic and complex models, where the geoscience and reservoir engineering disciplines interact more effectively. In this paper we present an integrated workflow that combines results from 4D seismic inversion, geomechanics modelling, and reservoir simulations in a shared earth model. It has been applied to the Elgin and Franklin high-pressure/high-temperature fields located in the UK Central Graben of the North Sea. These structurally complex fields are a challenge for a shared earth model approach. The 4D seismic datasets have been inverted into interval time-shifts using an in-house warping method. In parallel, a coupled faulted reservoir and geomechanical model has been used to determine both the stress redistribution within and around the reservoir including associated reactivated fault slips, and to derive synthetic 4D time-shifts with the help of a rock physics model. Good matches have been achieved between observed and synthetic 4D time-shifts. This integrated study proved to be a useful tool for understanding the reservoir and production behaviour of the Elgin and Franklin fields, with the ultimate goal being identification of new drilling targets and mitigation of casing integrity risks.

Inverting for reservoir pressure change using time-lapse time strain: Application to Genesis Field, Gulf of Mexico

There are increasing numbers of published examples from around the world in which significant 4D time shifts have been observed in the overburden above producing reservoirs.

Feasibility of monitoring compaction and compartmentalization using 4D time shifts and seafloor subsidence

Seismic monitoring of compacting reservoirs is known to be a difficult task and depends critically on the amount of compaction of the reservoir and velocity changes of the rocks as the effective stress changes (Tura et al., 2005; Hatchell and Bourne, 2005). The main question addressed in this study is whether a combination of surveillance methods can be used to help identify and manage the risks that are posed by an unknown degree of compartmentalization in a compacting offshore gas reservoir.

Quantitative estimation of compaction and velocity changes using 4D impedance and traveltime changes

In some hydrocarbon reservoirs, severe compaction of the reservoir rocks is observed. This compaction is caused by production, and it is often associated with changes in the overburden. Time‐lapse (or 4D) seismic data are used to monitor this compaction process. Since the compaction causes changes in both layer thickness and seismic velocities, it is crucial to distinguish between the two effects. Two new seismic methods for monitoring compacting reservoirs are introduced, one based on measured seismic prestack traveltime changes, and the other based on poststack traveltime and amplitude changes. In contrast to earlier methods, these methods do not require additional empirical relationships, such as, for instance, a velocity‐porosity relationship. The uncertainties in estimates for compaction and velocity change are expressed in terms of errors in the traveltime and amplitude measurements. These errors are directly related to the quality and repeatability of time‐lapse seismic data. For a reservoir at 3000‐m depth with 9 m of compaction, and assuming a 4D timeshift error of 0.5 ms at near offset and 2 ms at far offset, we find relative uncertainty in the compaction estimate of approximately 50–60% using traveltime information only.