Velocity variations complicate deepwater imaging
During marine seismic acquisition, obtain- ing complete subsurface coverage may require combining data from different acquisition dates. The time gaps between the overlapping coverage may vary from hours separating subsequent boat passes, to months when large surveys are acquired in sections. Time-lapse data are an extreme ex-ample of overlapping data sets acquired at widely varying acquisition dates.
Surface temperature variations offshore Nova Scotia (coastline in red); each color contour is 1° C. Up to 10° of temperature variation occurs.
Unfortunately, between the different times of acquisition, changes in physical ocean properties, such as temperature or salinity, can cause variations in water velocity. The result is a dynamic change in recorded travel times that makes accurate combination of the data difficult. In shallow water, the distortions are small and do not affect data quality. However, in deeper areas, the cumulative distortions can pose a serious impediment to accurate imaging.
The existence of water-velocity variations is well documented. The primary cause of the velocity variations is a change in water temperature. In the study area, a 3,600 sq km survey just south of Nova Scotia, surface temperature variations are visible on satellite images (see figure). In the approximately two-week period shown, surface temperatures varied as much as 10° C.
The temperature structures evident in the Nova Scotia survey are caused by eddies in the Gulf Stream and are indicative of deeper-water temperature variations. Significantly, each degree of change causes over 3 m/s of water-velocity variation. The effect of such changes on seismic data collected in deepwater areas is to introduce timing difference in the data (see figure).
Some form of correction is needed before the seismic data may be combined. The first step in resolving this issue requires obtaining some measure of the changing water velocities.
Determining water velocity
Because water velocity changes create timing differences in the data, we can infer relative changes in water velocity by quantifying the time shifts needed to place the overlapping data, acquired at different dates, onto a consistent time surface. This surface will be defined as the water-bottom model.
Creating the water-bottom model begins by forming a database of observed water-bottom picks. Because water velocities should vary slowly along the direction of acquisition, a sail line, we establish a perpendicular crossline grid for analysis every 2 km. Next, after selecting off the data along the crosslines, we pick the water-bottom reflector automatically. The pick times are projected to zero offset, using a method similar to conventional velocity analysis, to define the observed water-bottom times, Tobs. We now have a database of overlapping times to reconcile.
Next, we use an iterative approach to create a water-bottom model that represents a best-fit surface through the observed water-bottom times. The time shifts needed to move the seismic data from the observed times to the model times are defined as the vertical time corrections, Δt.
Once derived for the data volume, the values for Δt and Tobs may be used to define the observed water velocity, Vobs, relative to an arbitrary replacement velocity, Vw, given by:
Vobs = Vw (Δt / Tobs +1).
We have now defined the water-bottom model and the water velocities. These are the measures needed to correct for water-velocity variations.
To remove the effects of water-velocity variations, solutions exist such as layer replacement or depth migration. Unfortunately, layer replacement is difficult to implement with narrow-azimuth marine geometries. In terms of depth migration, the time-variant velocity field makes a straightforward implementation difficult. Both approaches mentioned above are also computationally intensive. A practical solution is needed that borrows from these methods. Because layer replacement is more oriented toward altering the velocity in the water column, we will examine it in more detail.
Layer replacement is usually applied in areas with severe water-bottom relief, and it is used to replace the water layer with a sediment velocity. However, water-velocity variations involve changes of only a few meters to tens of meters per second. Because we introduce only small changes in the velocity contrast between the seafloor sediments and the water column, the raypaths are almost unaffected. In other words, in the water-velocity variation case, layer replacement does not introduce significant changes in the lateral positioning of the data. Therefore, the methodology presented here focuses on correcting the timing of the data and does not address spatial positioning.
Dynamic time correction
Our new goal for layer replacement is to remove the timing effects of variable water velocity. We begin by deriving a vertical correction that maps the observed water-bottom times to the model case of constant velocity in the water layer:
Tw = 2Zw/Vw (model time),
Tobs = 2Zw/Vobs (observed time).
Tw is the vertical, two-way travel time to the water-bottom model, given the replacement velocity, Vw, and a water depth of Zw. The observed travel time, Tobs, corresponds to the observed water velocity, Vobs. The vertical time correction, Δt, is simply the difference between the two above values:
Δt = Tw - Tobs = 2Zw(1/Vw - 1/Vobs),
= Tobs(Vobs/Vw - 1).
As discussed previously, the second equation, when solved for Vobs, allows for the definition of the relative water velocity as shown in the first equation above.
The problem with vertical corrections is that rays usually arrive at the ocean's surface obliquely. Therefore, they have a larger time correction. Simple trigonometry shows that the relation between the vertical correction and the angle-dependent correction is:
Δt(Θ) = Δt/cos Θ.
where Δt is the vertical (Θ = 0) correction. Therefore, to define a more accurate correction, we need some measure of the surface arrival angle.
By combining basic relationships between the time-dip of seismic events recorded at the surface and the stacking velocities used in basic processing, it is possible to derive the needed surface-arrival angles. The result is the equation for dynamic correction:
The dynamic time correction is a function of the two-way travel time of a reflector, T(X), the initial stacking velocity, Vstack, and the distance between the seismic source and the receiver, offset X.
Nova Scotia data
The figure shows the same gather data above after applying the dynamic correction. The timing variations between the different acquisition dates are reduced substantially.
The original and corrected crossline stacks are shown. The stack expression of the velocity-variation problem includes false structure or amplitude deterioration. The amplitude and differential frequency loss caused by the time shifts can mimic the effects of gas or lithology, especially in the shallow section. The corrected data (right) show a simpler water-bottom structure and more consistent amplitude and phase behavior.
The worldwide push toward deepwater exploration makes water-velocity variations a primary concern in seismic imaging. Such concerns should not be limited to newly emerging exploration prov-inces. Even relatively mature areas, such as the Gulf of Mexico, contain well-documented velocity variations due to the quickly moving loop currents thrown off by the Gulf Stream.
In offshore areas influenced by rivers, the combination of dramatic salinity and temperature changes create extreme problems. Offshore West Africa and Brazil are areas where such conditions are commonly encountered. Indeed, some of the largest time shifts between datasets ever seen by the authors were encountered in the Santos Basin, offshore Brazil.
Unrecognized water-velocity variations may result in false structures and amplitude variations that may yield false indications of gas or other physical properties. Such distortions are a simple reality of seismic data collection in deepwater. More significantly, reservoir monitoring by means of time-lapse (4D) seismic measurements is proving to be a valuable tool for proper field development. The 4D measurements are usually separated by years, and encountering water-velocity changes is almost a certainty. Deliberate care to detect and minimize these effects will help ensure survey repeatability.
We wish to thank Alex Jackson, Vinod Agarwal, Terry Johnson, Paul Vascik, David Derharoutian Jr., Robert Vauthrin, and Dominic Fell for their contributions and WesternGeco for permission to publish the data examples shown in this paper.
For further information, contact Scott Mackay by email at firstname.lastname@example.org.