Geology topics

R. Snieder

Publications and source records attributed to R. Snieder.

6 recordsLinked to original sources

USGS2021

Inter-source interferometry of seismic body waves: Required conditions and examples

Seismic interferometry is widely applied to retrieve wavefields propagating between receivers. Another version of seismic interferometry, called inter-source interferometry, uses the principles of seismic reciprocity and expands interferometric applications to retrieve waves that propagate between two seismic sources. Previous studies of inter-source interferometry usually involve surface-wave and coda-wave estimations. We use inter-source interferometry to estimate the P-waves propagating between two sources rather than the estimation of surface waves and coda waves. We show that the recovered arrival times are dependent on the accuracy of the earthquake catalog of the two sources. Using inter-source interferometry, one can recover the waveform of the direct body waves and potentially reconstruct the waveform of coda waves, depending on the source-receiver geometry. The retrieval of these waveforms is accurate only when the wavefield is sampled with approximately 4 receivers per wavelength in the stationary phase zone. We show that using only receivers inside the stationary phase region for inter-source interferometry introduces the phase error of approximately 0.3 radians. In our study, we show an example of the P-wavefield reconstruction between two earthquakes using the seismic records from an array along San Andreas Fault. The retrieved P waves give a qualitative estimation of the thickness of the low-velocity zone of San Andreas Fault of approximately 4 km.

Pure and Applied Geophysics↗

USGS2008

The critical angle in seismic interferometry

Limitations with respect to the characteristics and distribution of sources are inherent to any field seismic experiment, but in seismic interferometry these lead to spurious waves. Instead of trying to eliminate, filter or otherwise suppress spurious waves, crosscorrelation of receivers in a refraction experiment indicate we can take advantage of spurious events for near-surface parameter extraction for static corrections or near-surface imaging. We illustrate this with numerical examples and a field experiment from the CSM/Boise State University Geophysics Field Camp.

Conference Paper↗

USGS2008

Cancellation of spurious arrivals in Green's function extraction and the generalized optical theorem

The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. ?? 2008 The American Physical Society.

Physical Review E - Statistical, Nonlinear, and So↗

USGS2007

Spectral element modelling of fault-plane reflections arising from fluid pressure distributions

The presence of fault-plane reflections in seismic images, besides indicating the locations of faults, offers a possible source of information on the properties of these poorly understood zones. To better understand the physical mechanism giving rise to fault-plane reflections in compacting sedimentary basins, we numerically model the full elastic wavefield via the spectral element method (SEM) for several different fault models. Using well log data from the South Eugene Island field, offshore Louisiana, we derive empirical relationships between the elastic parameters (e.g. P-wave velocity and density) and the effective-stress along both normal compaction and unloading paths. These empirical relationships guide the numerical modelling and allow the investigation of how differences in fluid pressure modify the elastic wavefield. We choose to simulate the elastic wave equation via SEM since irregular model geometries can be accommodated and slip boundary conditions at an interface, such as a fault or fracture, are implemented naturally. The method we employ for including a slip interface retains the desirable qualities of SEM in that it is explicit in time and, therefore, does not require the inversion of a large matrix. We performa complete numerical study by forward modelling seismic shot gathers over a faulted earth model using SEM followed by seismic processing of the simulated data. With this procedure, we construct post-stack time-migrated images of the kind that are routinely interpreted in the seismic exploration industry. We dip filter the seismic images to highlight the fault-plane reflections prior to making amplitude maps along the fault plane. With these amplitude maps, we compare the reflectivity from the different fault models to diagnose which physical mechanism contributes most to observed fault reflectivity. To lend physical meaning to the properties of a locally weak fault zone characterized as a slip interface, we propose an equivalent-layer model under the assumption of weak scattering. This allows us to use the empirical relationships between density, velocity and effective stress from the South Eugene Island field to relate a slip interface to an amount of excess pore-pressure in a fault zone. ?? 2007 The Authors Journal compilation ?? 2007 RAS.

Geophysical Journal International↗

USGS2007

Downhole receiver function: A case study

Receiver function is defined as the spectral ratio of the radial component and the vertical component of the ground motion. It is used to characterize converted waves. We extend the use of the receiver function to downhole data using waves recorded in a borehole, excited by an earthquake of magnitude 4.0 near San Francisco, California, on 26 June 1994. The focal depth of the event was 6.6 km and the epicenter was located at a distance of 12.6 km from the borehole array. Six three-component sensors were located at different depths in a borehole. To extract a coherent response of the near-surface from the incoherent earthquake waves, we deconvolve the waves recorded by the sensors at different depths with the waves recorded by the sensor on the surface. Deconvolution applied to the waves in the S-time window recorded by the radial component result in an upgoing and a downgoing wave propagating with S-wave velocity. For the waves in the P-time window recorded by the radial component, deconvolution also gives an upgoing and a down-going wave propagating with S-wave velocity. This interesting result suggests a P-to-S conversion at a depth below the deepest sensor. To diagnose this we compute the receiver function for the borehole recording of the earthquake waves. The receiver function shows an upgoing wave with an arrival close to time t = 0 for the deepest sensor. The agreement of the upgoing wave in the receiver function with the travel-time curve for the P-to-S converted wave, calculated using the P- and the S-wave velocity profile, supports the hypothesis of a pronounced P-to-S conversion. We present a synthetic example to illustrate that the first arrival of the receiver function applied to borehole data gives the upward-propagating P-to-S converted wave. To corroborate the observation of the mode conversion, we apply receiver function to a different earthquake data recorded by the same borehole array in 1998. The focal depth of the event was 6.9 km and the epicenter was located at a distance of 13 km from the borehole array. The receiver function for these data also show an upgoing wave with a pulse close to time t = 0 at the deepest sensor. The moveout of the upgoing wave agrees with the travel-time curve for the P-to-S converted wave, hence supporting our observation of the mode conversion.

Bulletin of the Seismological Society of America↗

USGS2006

Extracting the building response using seismic interferometry: Theory and application to the Millikan Library in Pasadena, California

The motion of a building depends on the excitation, the coupling of the building to the ground, and the mechanical properties of the building. We separate the building response from the excitation and the ground coupling by deconvolving the motion recorded at different levels in the building and apply this to recordings of the motion in the Robert A. Millikan Library in Pasadena, California. This deconvolution allows for the separation of instrinsic attenuation and radiation damping. The waveforms obtained from deconvolution with the motion in the top floor show a superposition of one upgoing and one downgoing wave. The waveforms obtained by deconvolution with the motion in the basement can be formulated either as a sum of upgoing and downgoing waves, or as a sum over normal modes. Because these deconvolved waves for late time have a monochromatic character, they are most easily analyzed with normal-mode theory. For this building we estimate a shear velocity c = 322 m/sec and a quality factor Q = 20. These values explain both the propagating waves and the normal modes.

Bulletin of the Seismological Society of America↗