Solving for Source Parameters Using Nested Array Data: A Case Study from the Canterbury, New Zealand Earthquake Sequence

Low stress drops observed for aftershocks of the 2011 Mw 5.7 Prague, Oklahoma, earthquake

“…Individual spectra are first corrected for site effects by considering the H / V ratio of the station to minimize the effects of local resonances and other site effects. We then apply a Gauss‐Newton global downhill optimization method to the Brune source model and determine the best fit moment and corner frequency for each event, as well as a residual kappa for each station following the method of Neighbors et al []. We apply tests for convergence with varying initial parameters and estimate uncertainties through bootstrap, which suggest the corner frequencies and moments are well resolved.…”

“…We divide each of the horizontal event‐station amplitude spectra by the median H / V spectral ratio recorded at the corresponding station to aid in the removal of near‐surface site effects. Having corrected the horizontal spectra, we then apply the Gauss‐Newton nonlinear least squares spectral fitting method [ Neighbors et al , ] to obtain the stress drops of the induced events, as described below.…”

“…We require three or more stations to have recorded the event to solve for each of the parameters ( M 0 , f 0 , and κ ). We also impose the criterion that an event has a single M 0 and f 0 for each iteration, but allow κ to vary across station‐event pairs to reflect variations in source, path, and site effects [e.g., Neighbors et al , , ]. Due to the nonlinear appearance of κ in the Anderson and Hough [] adaptation of the Brune model, we linearize the form of equation with respect to κ by taking the natural logarithm:…”

“…Then, we use the nonlinear least squares Gauss‐Newton method, a deterministic downhill optimization technique, to solve for best fitting parameters. We calculate the squared residual between the data and the initial inputs for the first iteration of the forward model, as described by Neighbors et al [] and, by applying the Jacobian matrix of partial first derivatives, iteratively produce new values of M 0 , f 0 , and κ into the forward model [e.g., Deuflhard , ]. This iterative procedure allows for convergence through minimization of the residuals, with the assumption that the initial parameter values are relatively close to the true parameter value.…”

Development of a Seismic Detection Technology for High-Speed Trains Using Signal Analysis Techniques

“…To address this challenge, various studies have been conducted on seismometer networks overseas. QuakeCatcherNetwork (QCN: ) constructed a global seismic observation network using micro-electromechanical system (MEMS) accelerometers attached to desktops, laptops, and USB devices that are fixed to the floor [ 4 , 5 , 6 , 7 ]. QCN is now operating the network in the Southern California Earthquake Center (SCEC) and the Incorporated Research Institutions for Seismology (IRIS).…”