Evidence of Nonlinear Seismic Effects in the Earth from Downhole Distributed Acoustic Sensors

Seismic velocities and elastic moduli of rocks are known to vary significantly with applied stress, which indicates that these materials exhibit nonlinear elasticity. Monochromatic waves in nonlinear elastic media are known to generate higher harmonics and combinational frequencies. Such effects have the potential to be used for broadening the frequency band of seismic sources, characterization of the subsurface, and safety monitoring of civil engineering infrastructure. However, knowledge on nonlinear seismic effects is still scarce, which impedes the development of their practical applications. To explore the potential of nonlinear seismology, we performed three experiments: two in the field and one in the laboratory. The first field experiment used two vibroseis sources generating signals with two different monochromatic frequencies. The second field experiment used a surface orbital vibrator with two eccentric motors working at different frequencies. In both experiments, the generated wavefield was recorded in a borehole using a fiber-optic distributed acoustic sensing cable. Both experiments showed combinational frequencies, harmonics, and other intermodulation products of the fundamental frequencies both on the surface and at depth. Laboratory experiments replicated the setup of the field test with vibroseis sources and showed similar nonlinear combinations of fundamental frequencies. Amplitudes of the nonlinear signals observed in the laboratory showed variation with the saturating fluid. These results confirm that nonlinear components of the wavefield propagate as body waves, are likely to generate within rock formations, and can be potentially used for reservoir fluid characterization.

Monitoring Injected CO2 Using Earthquake Waves Measured by Downhole Fibre-Optic Sensors: CO2CRC Otway Stage 3 Case Study

Monitoring changes of formation properties along the well bore associated with the presence of carbon dioxide can be important for both tracking the plume inside of the primary containment and detecting leakage into the zone located above the reservoir. This can be achieved with time lapse wireline logging, but this approach requires well intervention and is not always possible. If the well is permanently instrumented with an optical fibre, it can be used as a distributed seismic receiver array to detect gas behind the casing by monitoring changes in amplitude of the seismic waves generated by active or passive seismic sources. Previous research showed the efficacy of this technique using continuous seismic sources. The Stage 3 Otway Project presented an opportunity to test this technique using passive seismic recording, as downhole fibre-optic arrays recorded numerous regional earthquakes over the period of nearly 2 years before, during, and after CO₂ injection. Analysis of P-wave amplitudes extracted from these downhole gathers shows a consistent amplitude anomaly at the injection level, visible in all events that occurred after the start of injection. This indicates that the anomaly is caused by changes in elastic properties in the reservoir caused by CO₂ saturation. However, extracted amplitudes show significant variability between earthquakes even without subsurface changes; thus, multiple events are required to distinguish the time-lapse anomaly from time-lapse noise. Ubiquity of these events even in a tectonically quiet region (such as Australia) makes this technique a viable and cost-effective option for downhole monitoring.

Optimal bounds for attenuation of elastic waves in porous fluid-saturated media

Explicit expressions for bounds on the effective bulk and shear moduli of mixture of an elastic solid and Newtonian fluid are derived. Since in frequency domain the shear modulus of the Newtonian fluid is complex valued, the effective mixture moduli are, in general, also complex valued and, hence, the bounds are curves in the complex plane. From the general expressions for bounds of effective moduli of viscoelastic mixtures, it is shown that effective bulk and shear moduli of such mixtures must lie between the real axis and a semicircle in the upper half-plane connecting formal lower and upper Hashin-Shtrikman bounds of the mixture of the solid and inviscid fluid of the same compressibility as the Newtonian fluid. Furthermore, it is shown that the bounds on the effective complex bulk and shear moduli of the mixture are optimal; that is, the moduli corresponding to any point on the bounding curves can be attained by the Hashin sphere assemblage penetrated by a random distribution of thin cracks. The results are applicable to a variety of solid/fluid mixtures such as fluid-saturated porous materials and particle suspensions.