## Publication: PhD thesis: Integration of seismic data with well-log data

### by Frédéric Verhelst, 2000, Ph.D. thesis, Delft University of Technology, ISBN 90-9014386-6

#### Summary:

Two main topics are addressed in this thesis. Firstly, the effect of fine layering on seismic wave propagation is studied. A second topic is the use of the matching pursuit method to extract attributes for seismic interpretation. In the following, the two topics will be discussed seperately.

In seismic exploration, the information contained in well-log measurements is used to verify and calibrate at several stages during processing and interpretation. In order to be able to use the information contained in the well-log, the information in the well-log needs to be aligned with the seismic data. This process is called well-tieing, and includes the conversion of the well-log measurements from depth to the time domain. It is often observed that a discrepancy occurs between the travel-times from the seismic measurement and the traveltimes computed from the P-wave velocity measurements in the well. Commonly this difference is in the order of a few percents, but can occasionally reach five up to ten percent. One of the most important reasons for this difference is the different frequency range at which the well-log and the seismic measurements are performed; well-log measurements are performed using acoustic signals with a much broader frequency spectrum, especially towards the higher frequencies. Small scale layering will have a different effect at these different frequency ranges. From a review of literature, it was found that the ration between the scale of the measurement and the scale of the small scale layering is an important factor. In Chapter 2 a first order correction is used to compensate for the effect of scale differences between measurements of P-wave propagation perpendicular to the layering. The method was first described by Sams and Williamson (1994) and Rio et al. (1996), and consists of a moving averaging procedure with a window of approximately one fifth of the dominant wavelength of the seismic wave. The result is a velocity at a specified scale. This procedure was successfully verified with numerical modelling experiments. When the earth properties in depth are stationary, and the layer thicknesses are smaller than one fifth of the seismic wavelength, the result of this procedure is equal to an equivalent medium averaging velocity.

Using techniques similar to the wavelet transform, the effect of a change of the scale on the velocity was studied in detail, resulting in the observation that the scale-dependency of the velocity is important. Because the scale-dependent velocity establishes also the link between the well-log measurements made in depth and the seismic data recorded in time, a catch 22 problem occurs. Because of this observation, an iterative procedure was developed to derive a mutual dependent scale in depth and velocity at that scale that together match the scale in time of the seismic data.

In Chapter 3 the procedure is extended to P-wave propagation under oblique angles. A method is proposed to calculate the Thomsen anisotropy parameters (Thomsen, 1986) when the earth properties are non-stationary in depth. In these situation the Thomsen parameters become scale-dependent. A variation of the Thomsen parameters across the scales in the order of 100% was found. Due to this fact, the iterative procedure as established in Chapter 2 was extended to include propagation under oblique angles. The result of this iterative procedure is a regularized anisotropic velocity at a defined scale for plane waves travelling under oblique angles. This regularized velocity is a first order correction for the effect of non-stationary fine layering on the propagation of P-waves. The results obtained from this procedure were compared with numerical modelling results, and the comparison was favourable. The scale dependent velocities as described in Chapters 2 and 3 can be used for different pruposes. The velocities can be used for the time-to-depth or depth-to-time conversion for well-tie, modelling or inversion purposes. Using the velocities derived with this method, will diminish the traveltime mismatch between seismic and well-log data. The anisotropic velocity results may be used as a background model in pre-stack inversion. Due to the non-linear effect the background velocity has on the inversion result, a large different is found between the inversion results based on a conventional equivalent average velocity and the regularized velocity as found using the method described in this chapter.

The second topic deals with seismic interpretation and is described in Chapter 4 of this thesis. The need for more detailed interpretations in the reservoir management stage of the reservoir is increasing. A few of the driving forces for this increasing need are the increasing sedimentological complexity of the petroleum reservoirs under production, the increasing use of advanced production methods (e.g. horizontal wells, gas and/or water injection) and the fact that a large number of the important fields in for instance the North Sea are at the end of the plateau stage and are about to decline in production. All these factors lead to an increased need for detailed interpretations at the scale of individual sandbodies or stacks of sandbodies. A method to derive robust attributes and relate those attibutes in some favourable cases to the type of sandbody is discussed in this thesis (Chapter 4). By use of a matching pursuit approach and by making an assumption on the range of wavelet shapes and wavelengths, a robust extraction of seismic attributes from noisy seismic signals is made. Compared to the conventional response phase computed from the analytic trace, the phase extracted using the matching pursuit method allows 6 to 9 dB extra noise for the same accuracy.

In cases with a low net-to-gross ratio (i.e. low percentage of reservoir sands in a non-reservoir matrix), with relative thick sands (between 0.5 and 1.25 times the dominant wavelength of the seismic wave) and with a lateral invariant matrix (e.g. a marine shale) it is possible to relate the phase attribute to the type of sand sequence (coarsing or fining upward sequence). This information is directly useful for reservoir engineers to update their reservoir model and to optimise well-planning. The amplitude as extracted from the wavelet is also very sensitive for the pore fluids.

The matching pursuit method was applied on a 3-D data set from the Gulf of Mexico, and proved to be able to pick consistent geological features in a delta front environment. The phase attribute also allowed an interpretation of the type of sequence. In a more complicated example from Northern Europe, the results could only be used qualitatively.

#### References:

Sams M.S. and Williamson P.R. 1994. Backus averaging, scattering and drift. Geophysical Prospecting (42), 541–564, DOI: 10.1111/j.1365-2478.1994.tb00230.x.

Rio P., Mukerji T., Mavko G. and Marion D. 1996. Velocity dispersion and upscaling in a laboratory-simulated VSP. Geophysics (61), 584–593, DOI: 10.1190/1.1443984.

Thomson L. 1986. Weak elastic anisotropy. Geophysics (51), 1954–1966, DOI: 10.1190/1.1442051.

© 2000 by Frédéric Verhelst

A scanned PDF-version is made available by the Library at Delft University of Technology.

A copy of the book may be obtained from the author.

Cited by 12 (source: Google Scholar, retrieved 30-09-2012).