Frequency-dependent wave velocities in sediments and sedimentary rocks: Laboratory measurements and evidences

Abstract

The pioneering work of Mike Batzle and his colleagues has provided a fundamental understanding of mechanisms behind dispersion and attenuation of elastic waves in fluid-saturated rocks. It also has made way for a realization that these phenomena need to be accounted for in a better way when interpreting seismic and sonic data from the field. Laboratory experiments have formed the basis for new insight in the past and will continue to do so. Here, examples of experimental observations that give direct or indirect evidence for dispersion in sand, sandstone, and shale are presented. Ultrasonic data from compaction tests show that Biot flow is the most likely dispersion mechanism in pure unconsolidated sand. Strong shale dispersion has been identified through low-frequency and low-strain quasistatic measurements and through a novel technique based on static loading and unloading measurements. In shale and sandstone containing clay, there is evidence for water weakening. A comparative study shows an example where the stress dependences of P-and S-wave velocities at seismic frequencies exceed those measured by traditional ultrasonic methods.

Relations between static and dynamic moduli of sedimentary rocks

“…Bauer et al . () demonstrated that the method yields result in good agreement with low‐frequency measurements of dynamic Young's modulus.…”

“…It is well established that dynamic stiffness may depend on frequency, in particular in shales (Spencer ; Duranti, Ewy and Hofmann ; Batzle, Han and Hofmann ; Bauer et al . ). This phenomenon is called dispersion.…”

“…; Müller, Gurevich and Lebedev ; Bauer et al . ). The flow may occur on different length scales, from pore scale (Mavko and Nur ; O'Connell and Budiansky ), between patches of different saturation (White ) or global scale (Biot ).…”

Effective Fluid Bulk Modulus in the Partially Saturated Rock and the Amplitude Dispersion Effects

“…To conclude this section, we point out that the classical Gassmann's theory suggests that the shear modulus of porous rock does not depend on the fluid saturation, while published laboratory data suggest that this conclusion is not always correct at low frequencies and for isotropic rock (e.g., Adam et al, ; Adam et al, ; Adam & Otheim, ; Bauer et al, ; Fabricius et al, ; Khazanehdari & Sothcott, ; Mikhaltsevitch et al, ). Consideration of the fluid effect on the shear modulus is outside of the scope of this paper.…”

Mobility Effect on Poroelastic Seismic Signatures in Partially Saturated Rocks With Applications in Time‐Lapse Monitoring of a Heavy Oil Reservoir

“…From a more general perspective, in spite of the very low permeability characteristics, shales are heterogeneous porous rocks, more or less containing elastic heterogeneities. Frequency‐dependent elastic behaviors of shales based on the laboratory measurements have been reported by Jones and Wang (), Duranti et al (), Hofmann (), Batzle et al (), and Bauer et al (). Therefore, shales should also be considered as naturally dispersive geomaterials, even their characteristic frequency might occur at very low frequency range since it takes extremely long time to achieve pore pressure equilibration (Batzle et al, ).…”