General Dislocation Research Articles

Comparison of Single-Well Microseismic Focal Mechanism Inversions with Different Source Models

ABSTRACT Through downhole monitoring, the focal mechanisms of microearthquakes can be quantitatively determined, thus providing valuable information for characterizing the fracturing process and the in situ stress status. The double-couple (DC) and moment tensor (MT) source models are commonly used to study microearthquakes. However, the DC model fails to include non-DC mechanisms, and MT inversion from single-well data is still challenging. One possible way to address this is using the shear–tensile general dislocation (GD) source model. We provide a detailed comparison of the DC, GD, and MT models, and introduce the differences in their modeling and inversion theories. These three models are described by four, five, and six parameters, and correspond to a single point, a straight line, and the entire space in the Hudson source-type plots, respectively. Both the DC and GD models yield nonlinear inversions, whereas the MT inversion is linear. Synthetic tests set up from a field single-well monitoring case are performed to study the resolvability of the DC, GD, and MT models in single-well focal mechanism inversions. The results indicate that the inversion error increases from DC→GD→MT for a single-well acquisition system, and the GD and DC inversions are both stable, whereas the MT inversion deviates from the inputs in cases with a perfectly vertical receiver array, 5% model velocity perturbations, 10 m horizontal source location errors, or 40% noise levels. We also find that the focal mechanism inversion mainly depends on the horizontal source–receiver azimuth coverage, and that the nonvertical well direction is helpful for constraining single-well inversions. According to our study, focal mechanism inversions based on the GD model can obtain reliable solutions from near-vertical single-well data, which will help improve non-DC earthquake studies.

The general dislocation source model and its application to microseismic focal mechanism inversion

Research on the non-double-couple (NDC) components in an earthquake is important for characterizing true source processes. The moment-tensor (MT) source model is commonly used to study NDC earthquakes. However, MT inversions are still challenging when earthquakes have small magnitudes, especially microearthquakes. The general-dislocation (GD) model specifies the focal mechanism as a shear-tensile slip on a fault plane; thus, GD inversion is better constrained than MT inversion. We focus on GD model-based waveform forward modeling and its application to microseismic source inversions. We expand the generalized reflection-transmission matrix method to synthesize waveforms based on the GD model and fully describe a GD source with five parameters: the scalar seismic moment (which defines the magnitude) and the strike, dip, rake, and slope angles (which define the fault geometry). We compare the GD, MT, and double-couple models and introduce the differences in their characterization and wave synthesis theories. We have developed a GD model-based microseismic focal mechanism inversion method that requires calculating only four angles under hybrid constraints. Two sets of solutions correspond to the same seismograms in a GD model-based inversion. These two solutions have the same scalar seismic moment and slope angle but different strike, dip, and rake angles, and we have derived formulas for mapping from one solution to the other. Synthetic and field surface microseismic data sets are used to test our GD model-based modeling and inversion methods. According to our study, the GD model is effective in microseismic focal mechanism inversion. By developing specific wave synthesis and inversion methods for the GD model, we offer a novel perspective to study this model and the NDC mechanisms for hydraulic fracturing-induced microearthquakes.

Books Reveiwed

Australian and New Zealand Journal of SurgeryVolume 19, Issue 4 p. 351-352 Books Reveiwed First published: May 1950 https://doi.org/10.1111/j.1445-2197.1950.tb06579.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract PHOTO-RADIOGRAPHY IN SEARCH OF TUBERCULOSIS. FRACTURES AND DISLOCATIONS IN GENERAL PRACTICE. A TEXTBOOK OF SURGICAL PATHOLOGY. A MANUAL OF THE PENICILLIA. Volume19, Issue4May 1950Pages 351-352 RelatedInformation

FRACTURES AND DISLOCATIONS IN GENERAL PRACTICE. By John P. Hosford, M.S., F.R.C.S., Surgeon to St Bartholomew's Hospital. Second edition, revised by W. D. Coltart, M.B., F.R.C.S., Assistant Orthopaedic Surgeon to St Bartholomew's Hospital. 8x6 in. Pp. x+290, with 87 figures. Index and Appendix. 1949. London: H. K. Lewis & Co. Ltd. Price 21/-

FRACTURES AND DISLOCATIONS IN GENERAL PRACTICE. By John P. Hosford, M.S., F.R.C.S., Surgeon to St Bartholomew's Hospital. Second edition, revised by W. D. Coltart, M.B., F.R.C.S., Assistant Orthopaedic Surgeon to St Bartholomew's Hospital. 8x6 in. Pp. x+290, with 87 figures. Index and Appendix. 1949. London: H. K. Lewis & Co. Ltd. Price 21/-