Phase-array decomposition of a seismic section

A seismic re fraction/wide-angle reflection profile is analysed for the presence of correlated events ('phases'). The correlation problem is formulated in terms of temporally, spatially and frequency-local complex covariances. For robustness, the method concentrates on phase rather than amplitude information. This allows a computationally efficient algorithm that can make allowance for signal correlation length and can model curved wavefronts. A statistical test based on residual phase misfit across the analysed subarray is used to assess the probability that a detected event represents a real correlated signal.
With our chosen analysis parameters and confidence level (over 99.9 per cent). 1222 events were detected in the data. Using simple techniques based on 1-D earth models, detected events are associated with a small number of particular wave types. In this way, we have succeeded in classifying almost 95 per cent of the detected events. Those that remain describe those components of the data that are inconsistent with our simple ray paths in the 1-D assumption and with our prescribed tolerance. These include reverberations, near-surface guided waves and reflected waves from strongly laterally inhomogeneous structures. According to our modelling, about 25 per cent of the detected events are consistent with simple P -wave reflected energy, and these are to a very large extent (over 85 per cent) distinct from all the other wave-type models we have used. A direct mapping of the detected events into the offset-depth domain reveals dear internal and external consistencies among the detections for the various wave types. Estimated earth structure is consistent with models from previous analyses based on much larger data sets.
We have thus succeeded in extracting correlated events from the data and decomposing these, approximately but meaningfully, into distinct classes (ray paths)     

Inversion of seismic attributes for velocity and attenuation structure

We have developed an inversion formuialion for velocity and attenuation structure using seismic attributes, including envelope amplitude, instantaneous frequency and arrival times of selected seismic phases. We refer to this approach as AFT inversion for amplitude, (instantaneous) frequency and time. Complex trace analysis is used to extract the different seismic attributes. The instantaneous frequency data are converted to t * using a matching procedure that approximately removes the effects of the source spectra. To invert for structure, ray-perturbation methods are used to compute the sensitivity of the seismic attributes to variations in the model. An iterative inversion procedure is then performed from smooth to less smooth models that progressively incorporates the shorter-wavelength components of the model. To illustrate the method, seismic attributes are extracted from seismic-refraction data of the Ouachita PASSCAL experiment and used to invert for shallow crustal velocity and attenuation structure. Although amplitude data are sensitive to model roughness, the inverted velocity and attenuation models were required by the data to maintain a relatively smooth character. The amplitude and t * data were needed, along with the traveltimes, at each step of the inversion in order to fit all the seismic attributes at the final iteration.     

Kirchhoff synthetics for seismic reflections and diving waves in two dimensions and application to the D" layer

The Kirchhoff-Helmholtz (KH) integration has been used to model the reflected and the diving waves from an interface with a positive velocity gradient. The modelling is carried out for a spherical boundary and for a sinusoidal topography with a long-scale wavelength.
An artefact, which is a major problem in modelling the seismic response using the KH integration, has been reduced by introducing a Hilbert transform sign manipulation. Cleaner synthetic seismograms with correct amplitudes have been produced by this method. A discretization in larger surface elements has been made possible by introducing a smoothing factor that suppresses the noise that normally follows the constructed signal if a large element size is taken.     

The effects of seismic rotations on inertial sensors

With the important increase in the number of instruments, especially in the near field of quite significant earthquakes, unsaturated traces have led seismologists to question what they are really measuring. We have performed a review of previous studies related to the effects of rotations on both horizontal and vertical components of various sensors. Illustrations of near-field records show that the recovering static displacement requires an accurate rotation estimation that present-day seismometers cannot achieve. Estimations of coseismic tilts (rotation around an horizontal axis) using seismometers cannot be achieved independently of translational motion. Therefore, for specific configurations such as near-field or long-period far-field, reconstruction of the ground motion requires specific rotation measurements. Effects of the Chi-Chi earthquake (1999) on accelerograms make the static displacement estimation unreliable. For long-period background noise, far-field horizontal seismic signals present unexpected N45° polarization, which is explained by the similar influence of the rotation around the vertical axis on the two horizontal components. For the GEOSCOPE network, this feature has been seen for stations with a Streckeisen STS-1 sensor, while those with a Streckeisen STS-2 sensor do not show this polarization feature. This study suggests that sensor installation should follow a protocol that will better guarantee the verticality of the sensors. Moreover, rotational recordings with ad hoc sensors are necessary, and by adequately correcting the traces, they will enable us to reconstruct the translational motion from recorded seismic signals.     

On reduction of long-period horizontal seismic noise using local barometric pressure

Tilt from atmospheric loading has long been known to be the major source of long-period horizontal seismic noise. We try to quantify these effects for seismic data from the Black Forest Observatory (BFO), which is known to be a very quiet station. Experimental transfer functions between local barometric pressure and horizontal seismic noise are estimated for two long time-series by standard methods. Two simple analytical physical models are developed: the local deformation model (LDM) and the acoustic-gravity wave model (TWM). Subsequently these models, with only two free parameters are fit using least squares to the observed seismic noise for time-series of widely differing lengths. The results are variable, sometimes rather dramatic variance reductions are obtained and sometimes the reduction is hardly significant. The method produces the best results when barometrically induced noise is high. The resulting admittances for the LDM are compared to finite element calculations. Since the methods are simple and can result in conspicuous reductions in noise we provide one more reason for installing barometers at even the best broad-band seismic stations.     

Refining seismic structure models by the systematic phase identification of late-arriving groups

We develop a systematic approach to the phase identification of late-arriving groups in 2-D seismic data. Waveforms in the same traveltime branch are grouped, and synthetic traveltimes for all phases are calculated using an initial approximation to the 2-D structure. For each group, we identify the two synthetic phases providing the smallest RMS residuals. If their ratio is less than some predetermined threshold, then the group's phase is ambiguous and both assignments must be tested by traveltime inversion. If there are n unidentified groups, we construct 2 ⁿ phase tables and perform a traveltime inversion on every plausible phase assignment. The phase table that provides the highest value of the posterior probability density is taken as correct, and a 2-D velocity model is constructed from the data. This approach is shown to be effective and efficient on both simulated and real data. In addition, the residuals associated with late-arriving groups provide a means of identifying deficiencies in the initial model.     

Noise reduction and detection of weak, coherent signals through phase-weighted stacks

We present a new tool for efficient incoherent noise reduction for array data employing complex trace analysis. An amplitude-unbiased coherency measure is designed based on the instantaneous phase, which is used to weight the samples of an ordinary, linear stack. The result is called the phase-weighted stack (PWS) and is cleaned from incoherent noise. PWS thus permits detection of weak but coherent arrivals. The method presented can easily be extended to phase-weighted cross-correlations or be applied in the τ p domain. We illustrate and discuss the advantages and disadvantages of PWS in comparison with other coherency measures and present examples. We further show that our non-linear stacking technique enables us to detect a weak lower-mantle P -to- S conversion from a depth of approximately 840 km on array data. Hints of an 840 km discontinuity have been reported; however, such a discontinuity is not yet established due to the lack of further evidence.