Paul M. Krail

4-C/4-D at Teal South

In late 1996, Texaco and Input/Output embarked on a novel experiment to test a low‐cost 4-C/4-D permanent reservoir monitoring system (PRMS). Western Geophysical and Digicourse were brought into the project to provide data acquisition and positioning services. In July and August 1997, four‐component (4-C) data acquisition was performed over 9 km2 in Eugene Island Block 354 (Teal South), using a dense shot grid (25×25 m). In late 1997, Texaco turned control of the project over to the Energy Research Clearing House and invited industry participation. The consortium remains open to new members.

Vertical cable as a subsalt imaging tool

The vertical cable is a patented method for acquiring and processing prestack 3-D marine seismic data that is based on technology developed by the US Navy for antisubmarine warfare. The engineering requirements for a vertical cable are quite different than for a horizontal towed cable because the vertical cable and hydrophone array must retain electrical and mechanical integrity under high hydrostatic pressure at depth.

Reflection of spherical seismic waves in elastic layered media

The solution of the elastic wave equation for a plane wave incident on a plane interface has been known since the turn of the century. For reflections from reasonably shallow beds, however, it is necessary to treat the incident wave as spherical rather than plane. The formalism for expressing spherical wavefronts as contour integrals over plane waves goes back to Sommerfeld (1909) and Weyl (1919). Brekhovskikh (1960) performed a steepest descent evaluation of the integrals to attain analytic results in the acoustic case. We have extended his approach to elastic waves to obtain spherical‐wave Zoeppritz coefficients. We illustrate the impact of the curvature correction parametrically (as the velocity and density contrasts and Poisson’s ratios are varied). In particular, we examine conditions appropriate to “bright spot” analysis; expectedly, the situation becomes less simple than in the plane‐wave limit. The curvature‐corrected Zoeppritz coefficients vary more strongly (and in a more complicated manner) wit...

The shape of a marine streamer in a cross current

A serious problem in marine data collection (particularly 3‐D) is the necessity to assign to each hydrophone a precise location on the surface of the earth. The data available for this purpose can come from the vessel’s navigation system, a radio beacon (at the tail buoy), an acoustic transponder (at the head of the streamer and occasionally elsewhere), and magnetic compasses distributed over the length of the cable. The shape of the streamer is commonly reconstructed by fitting a curve’s tangents to the compass readings. The shape deduced in this fashion is highly sensitive to compass errors. As an alternative to the ad hoc numerical fit, we have derived the shape of the streamer in a cross current from physical principles. The mechanical equilibrium of tension and drag forces leads to differential equations which we integrate analytically to obtain a formal solution for the tension. A further analytic integration yields an equation (containing two integration constants) that relates arc length along the...

Deconvolution of a directional marine source

A single source firing below the surface of the ocean, because of the surface reflection, has directionality. Directionality is defined as variation of amplitude with angle. Conceptually the radiation field of such a source may be treated as due to a vertical dipole of finite length. A formulation for transforming data recorded with a dipole wavelet to that of a monopole or plane‐wave wavelet is derived in this study. We have found that the cylindrical τ-p transform allows the removal of the source waveform and amplitude variation in the data due to the dipole and observed on the offset‐time record. The spherical wave field of a vertical dipole can be expanded in a conical bundle of plane waves. Accordingly, the recorded seismic data are transformed into a conical bundle of plane waves by the cylindrical τ-p transform. In this form the directionality effects of the vertical dipole are removed from the data. The formulation derived here was implemented in discrete form. A model study was conducted using sy...

Analysis of multicomponent seismic data from offshore Gulf of Mexico

SUMMARY 3D 4C surveys are a natural extension of 3D streamer surveys for time lapse reservoir monitoring. Until the use of seafloorrecorded converted waves reaches a level of maturity comparable to that of P waves, extra care will need to be taken to assure that events interpreted as converted-wave arrivals add value to the interpretation process. Careful analysis of the velocities associated with interpreted converted waves can indicate whether the interpretation is plausible. Using horizontal-component seismic data collected at Teal South, we generated velocity profiles for P-wave and S-wave velocities that agree with earlier published work (Hamilton, 1979). Modeling based on velocity fields generated by focusing analysis (with extrapolations for the shallow S-wave velocities from Hamilton) yields a synthetic common-receiver gather that closely resembles the field data in terms of changes in arrival time and amplitude with offset. This agreement between modeled data and field data supports our interpretation of the high amplitude events as waves that convert from P to S at the reflector.

3-D Gas Cloud Imaging of the Donald Field With Converted Waves

We present results from a newly acquired four component 3-D survey over the Donald Field in the Gulf of Mexico. The converted wave image is dramatically better than the compressional wave image, which was largely obscured by the presence of a shallow gas cloud. Interpretation of this 4-C data revealed new drilling prospects. Consequently, the risk and costs associated with further development have been reduced. These results were achieved with data acquired using an orthogonal patch geometry from ocean bottom cables deployed without tension.

Measurements of cable shape in a cross current

In a previous paper, Krail and Brysk (1989), we gave a theory for the curve shape of a streamer in a constant cross current. The curve shape predicted by this theory was compared with the shape of a towed streamer cable determined from a small number of field measurements. The agreement was judged to be fair. At the conclusion of the paper we promised to do a more extensive comparison with field measurements.

Water-gun cavity collapse in a compressible liquid

The velocity of the cavity wall is all important in the calculation of the far‐field signature for a water gun firing in the ocean. I use a method of successive approximation to solve Herring’s energy equation for the collapse of a spherical cavity in a compressible liquid. The velocity of the collapse of the cavity wall depends upon the compressibility of the liquid, the amount of residual gas in the cavity, and the amount of acoustic radiation. The compressibility of the liquid has a significant effect on cavity velocity, but it has very little effect on the collapse period. The maximum value of the cavity velocity determines the peak magnitude of the far‐field pressure signature; the pressure signature depends strongly on the amount and rate of residual gas compression. The results from solving Herring’s equation agreed satisfactorily with a numerical solution of the fluid equations of motion. This solution to Herring’s equation includes the compressibility of the liquid, the residual gas compression, ...

Anisotropic 3D Prestack Depth Imaging of the Donald Field With Converted Waves

We apply prestack depth migration to a four-component (4C) 3D ocean-bottom-cable (OBC) data set obtained in 1999 over the Donald Field in the Gulf of Mexico. This is an area where a shallow gas cloud obscures a large portion of the field in conventional images. We produce both a Pwave and a converted-wave image. In order to make these two images consistent with each other, we need to include anisotropy (with TIV symmetry) in the migration technique. We obtain a 3D converted-wave image of excellent quality which clearly shows reflectors and faults that have never been imaged before.