ALBERT

Description: SUMMARY We present a method for imaging quasi-vertically dipping faults with surface records of reflected P waves from small earthquakes. Faults are boundaries between geological structures, such as tectonic plates, and are located in earthquake active regions such as Parkfield, California. The high degree of seismic activity enables the use of multiple seismic recordings in our fault identification algorithm. Major challenges occur because of the quasi-vertical orientation of the fault and the fact that the wave reflected by the fault and recorded by the surface receivers is not well modelled by the direct arrival of the propagating wave generated by the earthquake source. Our method uses the 2-D acoustic wave equation as the model for P -wave propagation. We assume that an approximate wave speed map on the reflection side of the fault is available and the source locations are known, for example, from traveltime tomography. We also assume that the source time function is known. The new features of our method arise because earthquake sources are located very close to the fault. This has two implications: (1) the direct arrival and the reflected wave arrive almost simultaneously, so that it is impossible to separate them on a seismogram using standard techniques, and (2) most of the reflections occur above the critical angle which introduces a distortion in the reflected wave. To overcome these difficulties we use a modelled incident wave to (1) remove the direct arrival from the data, and (2) remove the post-critical distortion from the reflected wave. We justify the distortion removal using the leading-order term of an asymptotic expansion, and an optimization procedure. To complete our algorithm we utilize some features of reverse time migration: (1) the use of full acoustic wave equation for modelling and backpropagation, and (2) zero-lag correlation of the backpropagated time reversed reflected and incident fields. We present numerical examples of fault reconstructions with synthetic data.

Description: SUMMARY We present a method for imaging quasi-vertically dipping faults with surface records of reflected P waves from small earthquakes. Faults are boundaries between geological structures, such as tectonic plates, and are located in earthquake active regions such as Parkfield, California. The high degree of seismic activity enables the use of multiple seismic recordings in our fault identification algorithm. Major challenges occur because of the quasi-vertical orientation of the fault and the fact that the wave reflected by the fault and recorded by the surface receivers is not well modelled by the direct arrival of the propagating wave generated by the earthquake source. Our method uses the 2-D acoustic wave equation as the model for P -wave propagation. We assume that an approximate wave speed map on the reflection side of the fault is available and the source locations are known, for example, from traveltime tomography. We also assume that the source time function is known. The new features of our method arise because earthquake sources are located very close to the fault. This has two implications: (1) the direct arrival and the reflected wave arrive almost simultaneously, so that it is impossible to separate them on a seismogram using standard techniques, and (2) most of the reflections occur above the critical angle which introduces a distortion in the reflected wave. To overcome these difficulties we use a modelled incident wave to (1) remove the direct arrival from the data, and (2) remove the post-critical distortion from the reflected wave. We justify the distortion removal using the leading-order term of an asymptotic expansion, and an optimization procedure. To complete our algorithm we utilize some features of reverse time migration: (1) the use of full acoustic wave equation for modelling and backpropagation, and (2) zero-lag correlation of the backpropagated time reversed reflected and incident fields. We present numerical examples of fault reconstructions with synthetic data.