The measurable traveltimes of seismic events propagating in heterogeneous media depend on the geologic scale, the seismic wavelength, and the propagation distance. In general, the velocity inferred from arrival times is slower when the wavelength is longer than the scale of heterogeneity and faster when the wavelength is shorter. For normal incidence propagation in stratified media, this is the difference between averaging seismic slownesses in the short wavelength limit, and averaging elastic compliances in the long wavelength limit. In two and three dimensions there is also the path effect. Shorter wavelengths tend to find faster paths, thus biasing the traveltimes to lower values. In the short wavelength limit, the slowness inferred from the average traveltime is smaller than the mean slowness of the medium. When the propagation distance is much larger than the scale of the heterogeneity, the path effect causes the velocity increase from long to short wavelengths to be much larger in two dimensions than in one dimension, and even larger in three dimensions. The amount of velocity dispersion can be understood theoretically, but there is some discrepancy between theory and experiment as to what ratio of wavelength to heterogeneity scale separates the long and short wavelength limits. The scale‐dependent traveltime implies that a measured velocity depends not just on rock properties, but also on the scale of the measurement relative to the scale of the geology. When comparing measurements made at different scales, for example logs and surface seismic, it is not always correct to simply apply the Backus average; the correct procedure will vary from case to case with the scale of the geology. Scale effects must be included with other viscoelastic mechanisms of dispersion when comparing measurements made at different frequencies. The amount of observed scale‐dependent dispersion also depends on the spatial resolution of the receiver array. For example, the first‐break time of the average trace from a stack, a large group array, or a large laboratory transducer may be earlier than the average of first‐break times measured with individual small‐scale receivers.
We compare the attenuation obtained by the resonant bar technique in the sonic frequency range (3–10 kHz) with that obtained by the pulse transmission technique in the ultrasonic frequency range (500 kHz) on a set of 30 rocks, including sandstones and limestones. The sonic and ultrasonic measurements were performed under high effective pressure on adjacent water‐saturated samples from each rock block. Compressional ultrasonic attenuation was typically larger than extensional sonic attenuation, particularly in limestones. This is attributed to the presence of density heterogeneities, that can be seen on X‐ray scanner imagery. Heterogeneities at the scale of the ultrasonic wavelength produce diffraction of the waves, and as a consequence, high attenuation values. At ultrasonic frequencies, large apparent shear attenuation values, compared to compressional attenuation values, are explained by shear wave splitting.
This paper presents in detail the resonant bar technique used to measure acoustic properties of materials in the sonic frequency range (≃5–20 kHz). Measurements are corrected for the effects of added mass and jacketing; extrinsic effects such as the sample diameter or the dispersion at higher frequencies can mask intrinsic properties of material and are analyzed here. When this technique is used on porous saturated media such as rocks, it is important to avoid the “Biot–Gardner–White” effect; this intrinsic effect can lead to erroneous high attenuations in unjacketed saturated samples. Experimental evidence of its occurrence on water-saturated rods is presented. Experimental results of velocity and attenuation obtained on various rock types such as limestones and sandstones show the drastic sensitivity of these measurements to effective pressure. Hertz’s theory can be applied to describe the behavior of under-consolidated sandstones. Under high confining pressure, sonic attenuation in water-saturated limestone samples is found to be very low (Q⩾100); attenuation in sandstones is always low (Q⩾50), except for some shaly sandstones.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractIn reservoir characterization, the value of each piece of data does not lie in its isolated use, but rather in the value it adds to the analysis when integrated with other data. Earth scientists from different disciplines have made many efforts to better predict the spatial distribution of petrophysical properties. However, the interpretation of isolated piece of knowledge, without a real integration of disciplines, cannot lead to a quantitative answer in terms of reservoir characterization. In this paper we present a joint inversion scheme for estimating petrophysical properties by integrating both production and 4D seismic related data in geological modeling. Simultaneous history matching of production and 4D seismic related data leads to a better prediction of petrophysical reservoir properties and of production forecast.
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