Graham A. Winbow

RTM angle gathers using Poynting vectors

Angle-domain common image gathers have been shown to provide several advantages for the analysis of migrated images. In this abstract we describe an efficient new method for creating angle gathers for reverse time migration (RTM). The method relies on the computation of the direction of energy flux (known in electromagnetics as the Poynting vector) in the space-time domain. Given the Poynting vectors for source and receiver wavefields, we may readily derive reflection angle and azimuth, and reflector dip and azimuth if desired. Unlike some previously considered angle-gather algorithms, the method depends only on local information at the reflection point, thereby avoiding the loss of resolution inherent in mixing quantities from different horizontal locations. In addition, we derive the weight function needed to produce correct relative amplitudes for these angle gathers.

A theoretical study of acoustic S-wave and P-wave velocity logging with conventional and dipole sources in soft formations

This paper is focused on the special features of the wavetrains recorded by conventional and dipole sonic logging tools in soft formations defined to be those whose shar velocity is less than the sound velocity of drilling mud. Such formations are commonn in the Gulf Coast, the Canadian Arctic, the Bass Strait of Australia, and many other region. A conventional logging tool operating at normal frequencies (f∼15kHz) records P waves, water waves, and Stoneley waves in soft formations. A dipole tool records modal waves and water waves at frequencies of order 15 kHz, but produces almost pure S-wave first arrivals at low frequencies (f∼1kHz), since at 1 kHz, a mode which we refer to as a “dipole Stoneley wave” is efficiently excited. For very soft materials such as clays, where the formation P-wave velocity can be less than the fluid velocity, the formation P velocity can be logged by operating a conventional sonic tool at low frequencies (f∼1kHz) so as to excite a leaky mode traveling at very close to the for...

Multipole P-wave logging in formations altered by drilling

Wave trains produced by conventional and multipole sonic logging tools may be expected to depend upon whether the formation has been altered by the drilling process. Such alteration may include invasion by drilling fluids and/or drilling damage. We show, by theoretical modeling, that a dipole or quadrupole tool operating at conventional logging frequencies (in the range 10–20 kHz) detects P waves from the virgin formation with a much higher signal‐to‐noise ratio than does a monopole tool. This permits the multipole tool to measure formation P‐wave velocities two to three times farther away from the borehole than a conventional monopole tool. This larger radius of investigation typically extends beyond the altered zone for most situations, even for sources and receivers spaced several meters apart. Our conclusion is valid only if the velocity of the altered zone is less than the velocity of the virgin formation. If the velocity of the altered zone is larger than that of the virgin formation, no appreciable...

Compressional and shear arrivals in a multipole sonic log

A sound source in a liquid‐filled borehole generates, among other excitations, compressional and shear waves in the rock which are detected in the fluid as refractions. It is practical to be able to separate the latter components. I show that this can always be achieved in principle by appropriately choosing the properties of the source. Solutions of the acoustic wave equation in the “far field” of the source are analyzed in detail. Suppose the source radiation depends upon the azimuthal angle η through some function F(η). The refracted waves are analyzed conveniently in terms of Fourier components Fn, where n and η are Fourier conjugates. For a source symmetrical about the axis of the borehole, as conventional sources are, Fn vanishes except for n = 0. Our principal results concern the z dependence of the pressure radiation field in the drilling mud p (r, η, z) (using cylindrical polar coordinates). For a fixed n, as z → ∞, the refracted P‐wave is proportional to z-n-1 for n = 0, 1, … . The refracted S‐w...

Spatial resolution of diffraction tomography

Diffraction tomography is an imaging technique applicable to crosshole seismic data and aimed at achieving optimal spatial resolution away from the borehole. In principle the method can form acoustic images equivalent to extending acoustic well logs away from the wellbore and into the formation with a spatial resolution less than one wavelength of the radiation employed to gather the crosshole data. This paper reports on the capability of diffraction tomography to produce high-resolution reconstructions of simple targets from limited-view-angle data. The goal is to quantify the resolution and velocity-reconstruction capability of diffraction tomography with realistic source–receiver geometries. Simple targets (disks and low-contrast sequences of layers) are used for this study. The scattering from these targets can be calculated without approximation, making them ideal test cases for the algorithm. The resolution capability of diffraction tomography is determined to be on the order of one wavelength for s...

Narrow band magnetostrictive acoustic source

A downhole seismic source for producing seismic waves in the 0.2-5 KHz frequency with a bandwidth of between 5 and 50 Hz is formed from a magnetostrictive bar with undamped end weights.

Weights For 3-D Controlled Amplitude Prestack Time Migration

This paper presents a new explicit formula for the weight factor needed for controlled amplitude common offset migration in v(z) media (“time migration”). The weight is explicitly evaluated for the case of constant velocity (where it agrees with a previous result), and for the case of velocity varying linearly with depth. For flat reflectors or for zero offset, a simplified form of the weight factor (equation 8) suffices. For dipping reflectors, failure to use controlled amplitude weights can result in errors of 40% or more in an exceptional case. Errors for AVO analysis can become substantial if the target is dipping and an incorrect weight is used.

Borehole stresses created by downhole seismic sources

This paper analyzes the stresses created by downhole acoustic sources used for crosshole or reverse VSP data acquisition. The pressures created by downhole sources may be as large as p1∼70 bars which cannot affect intact steel casing. However, such pressures might in principle either (A) crack the cement radially through excessive hoop stress pH, or (B) loosen the cement from the casing through an excessive value of shear stress prz.

CRAM and Kirchhoff images of a west Africa salt structure

The main objective of this project was to optimize the seismic image underneath the salt overhangs for better interpretation of the reservoir beds as they approach the salt body. Target depths from 680 to 5970 m were imaged, with input and output bins of 12.5 × 12.5 m and a depth step of 5 m. The velocity model was set up using Kirchhoff migration with some minor modification after WEM imaging. Total area imaged was 23 km2. Input was from a square about 160 km2. CRAM (common reflection-angle migration) imaging resulted in better imaging of the steep salt flanks, steeply dipping beds, and improved lateral spatial resolution. In addition, the CRAM image indicates that the salt model would benefit from further adjustment, although this would probably not materially affect the shallower section.

Multipath imaging into common-reflection-angle volumes at a GOM site

This article summarizes a case history of imaging under a GOM salt mass. Our common-reflection-angle migration (CRAM) algorithm is a multipath ray-based imaging method that generates either common-offset or common-reflection-angle volumes. Results from common-reflection-angle volumes imaged with CRAM are compared with full-stack results for Kirchhoff (single path ray-based imaging) and wave-equation migration (WEM). The main conclusion is that, for shallow dip reflectors under steeply dipping salt, signal/noise is significantly improved by splitting the output data into common-reflection-angle volumes. This is efficiently accomplished using CRAM.