Experience
Figure 4.1 The well tie process.
2000 2570 Vp (m/s) Vp Time Avg Backus Avg 2580 2590 Depth (m) 2600 2610 2620 4000 6000
Figure 4.2 Model showing effect of averagingVplogs; grey
curve¼ Vpmodel, blue curve¼ time average over 7 m window,
red¼ Backus average over 7 m window.
Drift, in general, is a real effect of the subsurface, principally related to velocity dispersion between log and seismic frequencies (e.g. Stewart et al.,1984). Each formation usually has its own drift characteristics. Usually, sonic log velocities are higher than seismic velocities, giving rise to positive drift (i.e. shorter inte- grated log times compared to the seismic) (Fig. 4.3). In cases where the sonic velocity is less than the seismic (i.e. negative drift), the log data should be checked for hole problems such as washouts. It has been common practice for positive drift corrections to be applied linearly to the data whereas negative drift corrections are preferentially applied to the lower velocities. This is based on the assumption that the negative drift is likely to be due to erroneously low sonic velocities in zones where hole conditions are poor. In deviated wells, drift may also be in part caused by velocity anisotropy (for example shale velocities in deviated wells are often
higher than in vertical wells). It should be noted that in deviated wells rig source checkshots are not particu- larly useful, as it can be difficult to accurately correct the slant ray times to vertical. Walk-above VSP shots are the best dataset for this purpose.
Commonly used drift functions are linear trends with knee points (e.g. Fig. 4.3), polynomial fits and spline fits. The knee points for linear trends should be located at major changes in lithology or at unconfor- mities where there are changes in velocity in order to avoid generating spurious reflections if the calibrated velocity log is used for synthetic generation. Spline fits are reasonable if there are a large number of points such as in a VSP, but care should be taken when applying a spline fit to sparse checkshots. Polynomial fits are useful in basin fill sequences where there is a simple compaction trend and linear fits with knee points are appropriate in basins with a number of prominent unconformities and variations in litho- logical style. If linear fits are made between each checkshot (i.e. simply using the checkshots as the time vs depth function) it is important to check the effect on the velocities.
When using the time–depth relations in a well tie the interpreter has a choice of whether to use the calibrated velocity log or the original log in the well tie match. Given that the differences should not be large the choice is not usually important. Many workers favour using the calibrated time–depth rela- tionship with the original (upscaled) velocity log, although benchmark tests appear to show slightly better ties when using the calibrated velocity log (Roy White, personal communication).
4.3 The role of VSPs
Vertical seismic profiles (VSPs) are useful in the well tie process because they provide a link between wells and seismic at the correct scale. The essence of the VSP method is to record a surface seismic source using down-hole geophones. The simplest geometry is for a vertical well (Fig. 4.4). A string of geophones is deployed in the well and, by shifting them up between shots, it is possible to record signals at a large number of levels. For example, records might be obtained at 50 ft spacing over an interval of 5000 ft in the well, to give 100 levels in all. At each level, the geophone will record down-going waves (such as the direct arrival, the leftmost raypath in Fig. 4.4) and up-going waves (such as the two reflections inFig. 4.4). Multiples are
Depth (ft) Vp(m/s) 6000 2000 6000 0 607 -10 0 10 7000 8000 TWT(ms) Drift (ms)
Figure 4.3 Log (depth–time) calibration: column 1, black – Vplog,
red– calibrated velocity log, blue – velocities from checkshots; column 2, blue– integrated depth–time curve from Vp, red–
calibrated depth-time curve (i.e. with drift applied); column 3, blue crosses– drift points, black – drift curve fitted to the data using linear segments with knee points.
also present but these arrive after the direct wave and single bounce up-going reflections. When the direct arrival can be clearly defined it is possible to accur- ately convert the direct arrival and the reflections that immediately follow it to zero phase.
A schematic travel-time display for VSP data is shown inFig. 4.5. Key steps in the processing of VSP data include the following.
(1) Measurement of the arrival time for the direct wave arrival (energy onset or max/min of first loop).
(2) Zero phasing operator design on the direct arrival. (3) Determination of the down-going wavefield by
horizontal alignment of the data at the direct arrival time followed by filtering to enhance laterally continuous events.
(4) Estimation of up-going wavefield by subtraction of downgoing wavefield from the data.
(5) Re-alignment of upgoing wavefield to position reflections at their two-way times from surface and enhancement by various processing methods (Fig. 4.6).
(6) Generation of the corridor stack from the processed upgoing wavefield. This involves
Figure 4.4 Schematic geometry of VSP raypaths from a surface source to borehole geophones. The separation of the source from the borehole would in practice be very small for the case of a zero offset VSP, but is here exaggerated for clarity.
Geophone depth Arrival time Direct arrival Reflected arrivals Seabed multiples
Figure 4.5 Schematic graph of VSP arrival time against geophone depth for VSP data.
Geophone depth Time 700 600 500 400 300
Figure 4.6 Example of VSP up-going wavefield after signal enhancement (after Chopraet al.,2004; reprinted with permission of the author and the CSEG Recorder).
stacking the data in a time window immediately following the first arrival. This should be free from multiples and is therefore the ideal reference trace to compare with both the well synthetic and the actual surface seismic.
Figure 4.7compares a multiple-free‘outside’ corridor stack with an‘inside’ corridor stack which is contam- inated by interbed multiples. At the horizontal red line there is a strong event on the inside corridor stack that is absent from the outside stack, and is thus inferred to be an intra-bed multiple. The event is absent from the surface seismic, implying that the processor has been successful in removing the multiple.
The VSP can be particularly useful in highly devi- ated wells. It is common for well synthetics to tie surface seismic poorly for such wells, perhaps because of anisotropic effects (see Section 8.4.5). In a walk- above acquisition, the surface source is positioned vertically above the geophone at a series of levels in the deviated borehole. This makes acquisition more time-consuming and costly, as the source has to be moved to an accurately determined location for each level. However, the benefit is that the raypaths are
constrained to be nearly vertical. An image is pro- duced of the subsurface directly below the borehole, which can be compared with the surface seismic along the well trajectory. An example is shown inFig. 4.8.
The benefits of the VSP are numerous (Campbell et al.,2005).
High-density sampling gives good control on the time–depth relationship.
Control on phase: trace by trace deconvolution of the upwave using the down-going wavefield results in a zero phase upwave corridor stack. The upwave corridor stack is largely multiple free;
comparison with seismic can highlight potential multiple problems.
In favourable situations the absorption parameter Q can be estimated from wavelet shape changes in the downgoing wavefield (e.g. Tonn,1991; Harris et al.,1997).
It may be possible to apply inverse Q filtering to optimise resolution as well as using the VSP to determine zero phasing operators for surface seismic.
However, there are several reasons why VSPs may not tie exactly to seismic.
Filtered upgoing wavefield Outside corridor Outside corridor Inside corridor Inside corridor Surface seismic Inside corridor Interbed multiple Event termination
Figure 4.7 Example of a VSP corridor stack (after Campbellet al.,2005). The up-going wavefield is shown on the left with shading to indicate the zones stacked to make the outside corridor stack (blue) and inside corridor stack (red).
The volume of rock sampled is different. Difference in frequency content (the VSP will
generally be higher frequency and will need to be filtered back to match the seismic bandwidth). Differences in wave propagation effects, e.g.
anisotropy and attenuation, due to differences in raypath.
Migration effects.
There are some practical issues that affect the way that the seismic interpreter makes use of VSPs.
In general the key step is to compare the corridor stack with the surface seismic.
If this comparison is documented in the VSP processing report, it is important to check that the seismic that was used is still the current version; if not, new displays need to be created.
If a VSP processing report compares the VSP with a well synthetic, the wavelet used to create the synthetic needs to be checked. It is likely to have been a simple idealised wavelet.
Routine digital manipulation of VSPs by the interpreter is less easy than creation of synthetics from log data, because more specialised software is needed.
Greater integration of VSPs into standard interpretation workflows would be beneficial, including VSP inversion to impedance.
4.4 Well tie approaches
using synthetics
When tying wells to seismic it is quite indefensible simply to use a time–depth relation from checkshots, post the well tops on the seismic and start picking. Whilst the timing of the seismic and the checkshots is likely to be close they are probably not the same and making assumptions about wavelet phase, as will be shown below, is prone to error. The well tie is a basic tool to analyse the connection of geology and seismic and two approaches will be discussed that can be imple- mented with most seismic interpretation software. The first, referred to as the ‘well matching technique’, requires good control on depth and time and seeks to extract a wavelet from the seismic without making any assumptions about phase and timing. In the absence of good time–depth control the second approach, referred to here as the‘adaptive technique’, involves more trial and error.
4.4.1 Well tie matching technique
In order to estimate the correct wavelet for the purposes of picking seismic or designing zero phasing or inver- sion operators, a pragmatic approach is to estimate the wavelet directly from the seismic data. The technique described here is that of White (1980) and White and Simm (2003). The wavelet is extracted from the data through a least squares technique (Fig. 4.9), treating the well tie as a noisy input–noisy output problem. It is essentially a stochastic approach which treats the well tie as a noisy input–noisy output problem (Walden and White, 1998). Vertical well ties are the most
1000m
2.0
2.0
Two way time (s)
NW
SE
Figure 4.8 A walk-above VSP image from a deviated well inserted into surface seismic data. VSP data is the greyed zone between the blue and white lines. Also shown in blue is a corridor stack for a vertical borehole drilled from the same surface location (after Kaderaliet al.,2007).
straightforward but most software now offers the possi- bility of extracting the wavelet along the borehole path. To achieve a reliable extraction the quality of the log data has to be good and the time–depth conversion has to be accurate. Matching involves extracting a wavelet operator (of length L) from a time window of seismic data (of length T). In signal processing terms L is the‘lag window length’. Confusingly, L is often referred to as the ‘wavelet length’ but it is approximately twice the length of a three-loop wavelet. The time segment length should be around 500 ms. If it is any longer the statio- narity assumption concerning phase may be invalid and phase rotation with depth could adversely affect the results. If the segment is shorter, the chances of a statis- tically valid tie are reduced. If possible it is best to choose a time segment for which the start and end have muted reflectivity; wavelet extractions are likely to be distorted if the time segment truncates close to a large reflection. In order for matching measures such as the cross- correlation to be statistically meaningful L and T
(Fig. 4.10) need to satisfy the following relations (White1980; Walden and White,1984; White,1997):
bT¼ (3.408 T) / L,
where b¼ analysis bandwidth and is related to L by: b¼ constant / L (for correlations tapered with a Papoulis window, constant¼ 3.408);
bT is referred to as the spectral smoothing factor. This parameter needs to be>6;
b/B should between 0.25 and 0.5 (where B¼ statistical bandwidth estimated from the data). Effectively these relationships mean that the time segment to (three-loop) wavelet length ratio should be around 3 for low-bandwidth data (B ~ 25 Hz) and around 6 for high-bandwidth data (B ~ 50 Hz).