Carcione, Jose M.

abstract - The description of wave propagation by a viscoelastic rheology allows for the introduction of two important phenomena: wave dissipation, i.e., the conversion of motion into heat, and velocity dispersion, the phenomenon in which two different Fourier components travel with different velocities. In this work, we consider a mechanical representation of viscoleastic media, which in virtue of its simplicity constitues a useful tool to model the variety of dissipation mechanisms present in real media. Examples of simulated wavefields in these type of media can be found, for instance, in the works of Carcione et al. (1988a,b), where the equations are based on the standard linear solid model. Here we analyze in detail the physical properties and capabilities of different mechanical models, and give some hints to obtain realistic models of attenuation and velocity dispersion; for example, the constant Q phenomenon and the set of relaxation peaks over a given frequency band.

Hydraulic fracturing in shales generates a cloud of seismic—tensile and shear—events that can be used to evaluate the extent of the fracturing (event clouds) and obtain the hydraulic properties of the medium, such as the degree of anisotropy and the permeability. Firstly, we investigate the suitability of novel semi-analytical reference solutions for pore-pressure evolution around a well after fluid injection in anisotropic media. To do so, we use cylindrical coordinates in the presence of a formation (a layer) and spherical coordinates for a homogeneous and unbounded medium. The involved differential equations are transformed to an isotropic diffusion equation by means of pseudo-spatial coordinates obtained from the spatial variables re-scaled by the permeability components. We consider pressure-dependent permeability components, which are independent of the spatial direction. The analytical solutions are compared to numerical solutions to verify their applicability. The comparison shows that the solutions are suitable for a limited permeability range and moderate to minor pressure dependences of the permeability. Once the pressure evolution around the well has been established, we can model the microseismic events. Induced seismicity by failure due to fluid injection in a porous rock depends on the properties of the hydraulic and elastic medium and in situ stress conditions. Here, we define a tensile threshold pressure above which there is tensile emission, while the shear threshold is obtained by using the octahedral stress criterion and the in situ rock properties and conditions. Subsequently, we generate event clouds for both cases and study the spatio-temporal features. The model considers anisotropic permeability and the results are spatially re-scaled to obtain an effective isotropic medium representation. For a 3D diffusion in spherical coordinates and exponential pressure dependence of the permeability, the results differ from those of the classical diffusion equation. Use of the classical front to fit cloud events spatially, provides good results but with a re-scaled value of these components. Modeling is required to evaluate the scaling constant in real cases.

CO2 injection in saline aquifers is one solution to avoid the emission of this greenhouse gas to the atmosphere. This process induces a pore-pressure build-up around the borehole that generates tensile and shear micro-earthquakes which emit P and S waves if given pressure thresholds are exceeded. Here, we develop a simple model to simulate micro-seismicity in a layer saturated with brine, based on an analytical solution of pressure diffusion and an emission criterion for P and S waves. The model is based on poroelasticity and allows us to obtain estimations of the hydraulic diffusivity on the basis of the location of the micro-earthquakes (defining the CO2 plume) and the triggering time. Wave propagation of P and S waves is simulated with a full-wave solver, where each emission point is a source proportional to the difference of the pore pressure and the tensile and shear pressure thresholds. Finally a reverse-time migration algorithm is outlined to locate the asynchronous sources induced by the fluid flow, determinated by the maximum amplitude at each cell versus the back propagation time.

The simulation of a stacked radargram requires the calculation of a set of common-source experiments and application of the standard processing sequence. To reduce computing time, a zero-offset stacked section can be obtained with a single simulation, by using the exploding-reflector concept and the so-called non-reflecting wave equation. This non-physical modification of the wave equation implies a constant impedance model to avoid multiple reflections, which are, in principle, absent from stacked sections and constitute unwanted artifacts in migration processes. Magnetic permeability is used as a free parameter to obtain a constant impedance model and avoid multiple reflections. The reflection strength is then implicit in the source strength. Moreover, the method generates normal-incidence reflections, i.e. those having identical downgoing and upgoing wave paths.Exploding reflector experiments provide correct travel times of diffraction and reflection events, in contrast to the plane-wave method.

eological storage is one of the solutions to avoid the emission of carbon dioxide to the atmosphere. This process requires a careful monitoring of the CO2 bubble, which can be performed by means of seismic and electromagnetic (EM) methods, on the basis of seismic velocity, attenuation and electrical conductivity contrasts before and after the injection. A successful monitoring depends on many factors, for instance the depth and properties of the reservoir. To test the feasibility of detecting the gas, we have performed cross-well seismic and EM tomographic inversions on a synthetic data set generated from a realistic aquifer partially saturated with CO2. We use two different algorithms based on traveltime picks. The method is novel regarding the EM inversion. Besides seismic velocity and conductivity, we have also obtained the seismic quality factor by performing attenuation tomography based on the frequency-shift approach. The RMS differences between the inverted and true initial models show that the methodology (and the adopted acquisition geometry) allows us to obtain reliable results which agree well with the true petrophysical model. Moreover, we have used a forward optimisation method to recover saturation, porosity and clay content from the tomographic seismic velocities, Q values and electric conductivity, with errors less than 15%