Elastic waveform inversion for double-couple microseismic source estimation in vertically fractured transversely isotropic media

Abstract

Accurate characterization of microseismic events during fluid injection in sedimentary formations is essential to mitigate environmental risks. The source mechanism for microseismic events related to a slip on a fault plane is given by a double-couple. Waveform inversion has emerged as a promising technique for estimating the moment tensor and the position vector of double-couple sources. In most applications of waveform inversion for the moment tensor of double-couple sources, the formation is typically assumed to be isotropic or, less frequently, transversely isotropic. Modification of the moment-tensor representation to account for anisotropy created by aligned vertical fractures in transversely isotropic formations has not been included while inverting microseismic waveform data. In this study on synthetic microseismic data, we present a waveform inversion algorithm that includes this modification, considering the formation in the focal region to be vertically fractured transversely isotropic (VFTI) and possessing orthorhombic symmetry. Since VFTI media lack rotational symmetry, no assumptions have been made about the orientation of the fault plane where the slip occurred. The moment tensor of double-couple sources is formulated in terms of the elastic parameters of the VFTI medium and geometrical parameters which are slip magnitude, slip angle, fault dip, and azimuth angle of the fault-normal. Source inversion is treated as a local optimization problem, and we invert for the source location and the geometrical parameters. These geometrical parameters are more directly constrained by seismic data than the moment tensor components and offer geologically meaningful insights. This approach enhances microseismic monitoring in fractured formations and can be extended to more complex anisotropic media, such as monoclinic systems.

Figures (18)

• Figure 1: Vertically fractured transversely isotropic (VFTI) media with fracture planes parallel to yz-plane. Here, blue lines represent the horizontal layers and red lines represent the vertical fractures in the rock.
• Figure 2: Geometrical elements associated with the fault in a double-couple microseismic event. Here, ${\bf b}$ is the slip on the fault, ${\bf n}$ is the normal to the fault, $\alpha$ is the dip angle and $\varphi$ is the slip angle. Note that the strike of the fault plane can be in any direction and not necessarily parallel to y-axis.
• Figure 3: The source-time function used to generate the synthetic particle displacement data.
• Figure 4: The layered model is a typical representation of the overburden-reservoir-underburden system, and is used to test the source inversion scheme. The elastic parameters, fracture weaknesses and densities values in different layers are given in Table 1.
• Figure 5: Snapshot of the elastic displacement field due to the double-couple source at the center of the layered model when the azimuth angle $\theta$ of the fault-normal is (a) $\pi/6$ rad, and (b) $2\pi/3$ rad.