Figure 3.21The effect of migration on the Fresnel zone for a 2D line (after Lindsey,1989).
Figure 3.19 Filter slopes and wavelet shape (after Koefoed,1981).
diameter). Key factors in lateral resolution for 3D seismic surveys are bandwidth, accuracy of the migra- tion velocity model, and adequate sampling of steep- dip information. Owing to the dense sampling of modern 3D data lateral resolution (in terms of the Fresnel zone) is not usually an issue.
3.8 Detectability
Although a gas sand may have a thickness below tuning thickness it will still potentially have ampli- tudes higher than background. Thus the sand is detectable without being fully resolved. The limit of detectability (i.e. the thickness at which the amp- litude merges with the background) depends essen- tially on the acoustic impedance contrast and the signal-to-noise ratio of the seismic. As a general rule of thumb, for low impedance hydrocarbon sands with reasonable data quality the limit of detectabil- ity can be aroundλ/20 to λ/30 (Sheriff and Geldart,
1995; Sheriff, 2006). Whenever net pay is deter- mined from seismic (Chapter 10) there is always the uncertainty that there may be pay in this‘below detectability’ zone. Whether this hydrocarbon is producible of course depends on the connectivity of the reservoir and is a question for the reservoir engineer.
Much of the power of 3D seismic is in detecting subtle features below seismic resolution. The notion of detectability is illustrated inFig. 3.22, which con- trasts the interpretability of subtle effects on ampli- tude maps and vertical sections. A 3D model is shown of a formation defined by two bounding surfaces with a hydrocarbon contact (Fig. 3.22a). The 3D synthetic models were generated to simulate the seismic before and after production and a differ- ence dataset was generated (Fig. 3.22b). It is evident that the change in the contact can be seen effectively as a composite of two interfering reflections (see also
Section 10.4 on time lapse seismic). For realism, noise was added and the corresponding section is shown in Fig. 3.22c. In the presence of noise the time lapse signature is not easily interpretable on the vertical section. Time slices were also generated at the level of the original contact (Figs. 3.22d,e) and it is clear that even in the noisy data the outline of the contact change is clearly visible. The effective dynamic range of amplitude maps (and other seis- mic attribute maps) is much greater than vertical sections. Depth Inline Crossline Contact 3D Model
a)
b)
c)
d)
e)
CDP TWT Signal only CDP TWT S:N=1.5 CDP Signal only Line Line CDP S:N=1.5Figure 3.22 Detectability in seismic sections and maps; (a) 3D model of top and base Oseberg reservoir and a hydrocarbon contact, (b) vertical difference section after pre-production and monitor models are subtracted, (c) vertical difference section with realistic levels of noise added, (d) time slice through model at level of contact, (e) time slice through model with added noise. Note how the time lapse signature is evident in the noise prone map (e) but quite indistinct on the noise
4
4.1 Introduction
There are several possible objectives in performing well ties:
zero phasing: checking whether data are zero phase, and helping to adjust the phase if required, horizon identification: relating stratigraphic
markers in the well to loops on the seismic section, wavelet extraction for seismic inversion or
modelling,
offset scaling: checking whether the seismic data have been‘true amplitude’ processed to have the correct AVO behaviour, and adjusting amplitudes if necessary.
Achieving these objectives requires integration of regional interpretation experience with well tie analy- sis, linking surface seismic to synthetic seismograms and vertical seismic profiles (VSPs), as shown in
Fig. 4.1. One way of looking at the well tie is that it is the interpreter’s chance to conduct an experiment to test the connection between the geology and the seis- mic data. In practice, there are numerous issues to consider and an analytical approach is useful. There are some situations where the tie and the phase of the seismic data are not in doubt; in other cases there is significant uncertainty. Estimates of well tie and wave- let accuracy frame the context for assessing the quality of calibration in an interpretation and amongst other benefits they provide insight into the feasibility of a good quality trace inversion (Chapter 9).
4.2 Log calibration – depth to time
An important element in any well tie technique is the conversion of depth to time. Typically this will involve the use of checkshot or VSP depth and time data. These data are derived from the direct arrivals of shots from seismic sources suspended over the side of the drilling rig. In the past it was not uncommon for interpreters to re-interpret these data from paper
copies. In today’s digital world the individual shot data are seldom included in well data packages, so the interpreter is usually reliant on the final contractor compilation of depth–time data presented in the final well report or well seismic report. Understanding the datum of the data is critical for land data. Marine data are invariably referenced to mean sea level.
Determining a continuous function of time and depth requires the integration of checkshot and log data. Given that velocity is dispersive (i.e. it is depend- ent on the frequency), thought should be applied to how these datasets are integrated. Effectively this means that log based velocities should be upscaled to the seismic scale prior to performing the well tie.
4.2.1 Velocities and scale
Different velocity averaging methods are appropriate for different wavelength and layer spacing situations (Marion et al.,1994). When the ratio of wavelength (λ)
to layer spacing (d) is≤1, as it tends to be at logging frequencies, then an appropriate averaging method is to sum the travel times through each layer. This is usually referred to as the time average and for regularly spaced data such as sonic logs this equates to a simple arithmetic average of the slowness over a sliding window. When the ratio of wavelength (λ) to layer spacing (d) is 1 (e.g. at seismic wavelengths and with typical rock layering) the situation becomes com- plicated by the fact that the layering gives rise to anisot- ropy. In this case the average or ‘effective medium’ velocity is dependent on the nature of the layering and the path that the acoustic energy takes through the rock (e.g. Backus,1962; Mavko et al.,1998).
The Backus average (Backus,1962) is an appropri- ate way to describe average P and S wave velocities through finely layered media. Essentially this method averages moduli rather than velocity. For the purposes of routine well ties, where vertical acoustic propagation and isotropy are usually assumed, an appropriate
38
average Vp and Vs can be determined from the har- monic averages of the P wave modulus (Μ) and the shear modulus (μ) as follows.
(1) Determine the M modulus and shear modulus from P wave velocity, S wave velocity and density (Vp, Vsandρ) using μ ¼ Vs2ρ and M ¼ Vp2ρ. (2) Over an averaging length to be defined below,
calculate the arithmetic average ofρ and the harmonic average ofΜ and μ, e.g. Mbavg1¼ n1 P
M1
(3) Use these averaged parameters to calculate the Backus averaged velocities using: Vp bavg ¼
ffiffiffiffiffiffiffiffi Mbavg ρavg q and Vs bavg ¼ ffiffiffiffiffiffiffi μbavg ρavg q .
Various suggestions have been made for the averaging length required in the Backus average. Liner and Fei (2007), who provide a useful general background to the theory of the method, propose a maximum value of Vs_min/3f, where Vs_minis the minimum shear vel- ocity after Backus averaging and f is the dominant frequency in the wavelet (Chapter 3). In general, Backus upscaling is important where there are strong contrasts in velocity, such as in a sequence of interbed- ded shales and limestones, but has a much less marked effect where the velocity contrasts are small, as is often the case for a sand/shale sequence (Fig. 4.2).
4.2.2 Drift analysis and correction
Log calibration seeks to analyse and resolve the dif- ferences in times derived from the sonic log and from checkshots. The general workflow is described below and with reference toFig. 4.3.
(1) Integrate velocity log from the uppermost or lowermost checkshot that ties the log.
(2) Calculate the drift (i.e. seismic time minus time from integrated log).
(3) Evaluate quality of checkshots using drift points and checkshot velocities.
(4) Repeat (2) if checkshots are de-selected (5) Fit a curve to the drift points such that the
differences between the final time–depth relation and the integrated calibrated velocity log are less than about 2 ms.
(6) Apply the drift correction to the time–depth curve from the integrated velocity log. The corrections may also be applied to the velocity log to generate the calibrated velocity log.
(7) Evaluate the effect of corrections on the velocity log (large differences are not expected).