New insights into the P- and S-wave velocity structure of the D" discontinuity beneath the Cocos plate

Broad-band P - and S -waves from earthquakes in South America recorded at Californian network stations are analysed to image lateral variations of the D"-discontinuity beneath the Cocos plate. We apply two array processing methods to the data set: a simplified migration method to the P -wave data set and a double-array method to both the P - and S -wave data sets, allowing us to compare results from the two methods. The double-array method images a dipping reflector at a depth range from 2650 to 2700 km in the southern part of the study area. We observe a step-like topography of 100 km to a shallower reflector at about 2600 km depth to the north, as well as evidence for a second (deeper) reflector at a depth range from 2700 to 2750 km in the north. Results from the simplified migration agree well with those from the double-array method, similarly locating a large step in reflector depth in a similar location (about 2650 km depth in the south and about 2550 km in the north) as well as the additional deeper reflector at the depth of about 2750 km in the north. Waveform modelling of the reflected waves from both methods suggests a positive velocity contrast for S waves, but a negative velocity contrast for P waves for the upper reflector in agreement with predictions from mineral physical calculations for a post-perovskite phase transition. The data also show some evidence for the existence of another deeper reflector that could indicate a double intersection of the geotherm with the post-perovskite stability field, that is, the back-transformation of post-perovskite to perovskite close to the core–mantle boundary.     

Solution of the inverse problem of seismology for laterally inhomogeneous media

Summary. The Backus-Gilbert method has been extended to the estimation of the seismic wave velocity distribution in 2-D or 3-D inhomogeneous media from a finite set of travel-time data. The method may be applied to the inversion of body wave as well as surface wave data. The problem of determining a local average of the unknown velocity corrections may be reduced to a choice of a suitable δ-ness criterion for the averaging kernel. For 2-D and 3-D inhomogeneous media the simplest criterion is to minimize a sum of 'spreads' over all the coordinates. The use of this criterion requires the solution (the averaged velocity corrections) to be represented as a sum of functions, each of which depends only on one coordinate. This is a basic restriction of the method. In practice it is possible to achieve good agreement between the solution and a real velocity distribution by a reasonable choice of the coordinate system.
Numerical tests demonstrate the efficiency of the method. Some examples of the application of the method to the inversion of real seismological data for body and surface waves are given.     

Modelling and inversion of single-ended refraction data from the shot gathers of multifold deep seismic reflection profiling—an approach for deriving the shallow velocity structure

A multifold crustal-scale deep seismic near-vertical reflection profile generates a large number of single-ended shot gathers, which provide redundant data sets because of overlapping coverage of the shallow refractors. We present an approach for deriving the shallow velocity structure by modelling and inversion of single-ended seismic refraction first arrival traveltime data. We apply this method to a data set acquired with a 12-km long spread with 100 m spacing of shots and receivers, of the Neoproterozoic Marwar basin in the NW Indian shield. The approach is shown to be quite successful for delineating the shallow refractor depths, steep dips and velocities, even in the absence of regular reverse refraction profiles. The study reveals two-layered sedimentary formations, Malani volcanics and a complicated basement configuration of the Marwar basin, and provides a measure of resolution and uncertainty of the estimated model parameters. A seismic section of the near-trace gather is found to be qualitatively consistent with the derived structural features of the basin. The relative highs and lows, observed in the Bouguer gravity profile, further corroborate the derived velocity model. The present approach can be especially useful in offshore areas and elsewhere, where the single-ended multifold seismic profiles are the only available data sets.     

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.     

Slowness-backazimuth weighted migration: A new array approach to a high-resolution image

We have developed a new array method combining conventional migration with a slowness-backazimuth deviation weighting scheme. All seismic traces are shifted based on the theoretical traveltime of the scattered wave from specific gridpoints in a 3-D volume. Observed slowness and backazimuth are calculated for each raypath and compared with theoretical values in order to estimate slowness and backazimuth deviations. Subsequently, stacked energy calculated by a conventional migration method is weighted by the slowness and backazimuth deviations to suppress any arrival energy whose slowness and backazimuth are inconsistent with the expected theoretical values. This new method was applied to two P- wave data sets which comprise (1) underside reflections at the 410 and 660 km mantle discontinuities and (2) D" reflections as well as their corresponding synthetic data sets. The results show that the weighting scheme dramatically increases the resolution of the migrated images and enables us to obtain well-constrained, focused images, making upper-mantle discontinuities and D" reflections more distinct by reducing their surrounding energy.     

Accurate hypocentre determination in the seismogenic zone of the subducting Nazca Plate in northern Chile using a combined on-/offshore network

The coupled plate interface of subduction zones—commonly called the seismogenic zone—has been recognized as the origin of fatal earthquakes. A subset of the after-shock series of the great Antofagasta thrust-type event (1995 July 30; M _w = 8.0) has been used to study the extent of the seismogenic zone in northern Chile. To achieve reliable and precise hypocentre locations we applied the concept of the minimum 1-D model, which incorporates iterative simultaneous inversion of velocity and hypocentre parameters. The minimum 1-D model is complemented by station corrections which are influenced by near-surface velocity heterogeneity and by the individual station elevations. By relocating mine blasts, which were not included in the inversion, we obtain absolute location errors of 1  km in epicentre and 2  km in focal depth. A study of the resolution parameters ALE and DSPR documents the importance of offshore stations on location accuracy for offshore events. Based on precisely determined hypo-centres we calculate a depth of 46  km for the lower limit of the seismogenic zone, which is in good agreement with previous studies for this area. For the upper limit we found a depth of 20  km. Our results of an aseismic zone between the upper limit of the seismogenic zone and the surface correlates with a detachment zone proposed by other studies; the results are also in agreement with thermal studies for the Antofagasta forearc region.     

Seismic imaging of the laterally varying D" region beneath the Cocos Plate

We use an axisymmetric, spherical Earth finite difference algorithm to model SH -wave propagation through cross-sections of laterally varying lower mantle models beneath the Cocos Plate derived from recent data analyses. Synthetic seismograms with dominant periods as short as 4 s are computed for several models: (1) a D" reflector 264 km above the core–mantle boundary with laterally varying S -wave velocity increases of 0.9–2.6 per cent, based on localized structures from a 1-D double-array stacking method; (2) an undulating D" reflector with large topography and uniform velocity increase obtained using a 3-D migration method and (3) cross-sections through the 3-D mantle S -wave velocity tomography model TXBW. We apply double-array stacking to assess model predictions of data. Of the models explored, the S -wave tomography model TXBW displays the best overall agreement with data. The undulating reflector produces a double Scd arrival that may be useful in future studies for distinguishing between D" volumetric heterogeneity and D" discontinuity topography. Synthetics for the laterally varying models show waveform variability not observed in 1-D model predictions. It is challenging to predict 3-D structure based on localized 1-D models when lateral structural variations are on the order of a few wavelengths of the energy used, particularly for the grazing geometry of our data. Iterative approaches of computing synthetic seismograms and adjusting model characteristics by considering path integral effects are necessary to accurately model fine-scale D" structure.     

Non-linear crustal corrections in high-resolution regional waveform seismic tomography

We compare 3-D upper mantle anisotropic structures beneath the North American continent obtained using standard and improved crustal corrections in the framework of Non-linear Asymptotic Coupling Theory (NACT) applied to long period three component fundamental and higher mode surface waveform data. Our improved approach to correct for crustal structure in high-resolution regional waveform tomographic models goes beyond the linear perturbation approximation, and is therefore more accurate in accounting for large variations in Moho topography within short distances as observed, for instance, at ocean–continent margins. This improved methodology decomposes the shallow-layer correction into a linear and non-linear part and makes use of 1-D sensitivity kernels defined according to local tectonic structure, both for the forward computation and for the computation of sensitivity kernels for inversion. The comparison of the 3-D upper mantle anisotropic structures derived using the standard and improved crustal correction approaches shows that the model norm is not strongly affected. However, significant variations are observed in the retrieved 3-D perturbations. The largest differences in the velocity models are present below 250 km depth and not in the uppermost mantle, as would be expected. We suggest that inaccurate crustal corrections preferentially map into the least constrained part of the model and therefore accurate corrections for shallow-layer structure are essential to improve our knowledge of parts of the upper mantle where our data have the smallest sensitivity.     

Sequential integrated inversion of refraction and wide-angle reflection traveltimes and gravity data for two-dimensional velocity structures

A new algorithm is presented for the integrated 2-D inversion of seismic traveltime and gravity data. The algorithm adopts the 'maximum likelihood' regularization scheme. We construct a 'probability density function' which includes three kinds of information: information derived from gravity measurements; information derived from the seismic traveltime inversion procedure applied to the model; and information on the physical correlation among the density and the velocity parameters. We assume a linear relation between density and velocity, which can be node-dependent; that is, we can choose different relationships for different parts of the velocity–density grid. In addition, our procedure allows us to consider a covariance matrix related to the error propagation in linking density to velocity. We use seismic data to estimate starting velocity values and the position of boundary nodes. Subsequently, the sequential integrated inversion (SII) optimizes the layer velocities and densities for our models. The procedure is applicable, as an additional step, to any type of seismic tomographic inversion.
We illustrate the method by comparing the velocity models recovered from a standard seismic traveltime inversion with those retrieved using our algorithm. The inversion of synthetic data calculated for a 2-D isotropic, laterally inhomogeneous model shows the stability and accuracy of this procedure, demonstrates the improvements to the recovery of true velocity anomalies, and proves that this technique can efficiently overcome some of the limitations of both gravity and seismic traveltime inversions, when they are used independently.
An interpretation of field data from the 1994 Vesuvius test experiment is also presented. At depths down to 4.5 km, the model retrieved after a SII shows a more detailed structure than the model obtained from an interpretation of seismic traveltime only, and yields additional information for a further study of the area.     

Two-dimensional PP/PS-stereotomography: P- and S-waves velocities estimation from OBC data

We present the extension of stereotomography to P - and S -wave velocity estimation from PP - and PS -reflected/diffracted waves. In this new context, we greatly benefit from the use of locally coherent events by stereotomography. In particular, when applied to S -wave velocity estimation from PS -data, no pairing of PP - and PS -events is a priori required. In our procedure the P -wave velocity model is obtained first using stereotomography on PP -arrivals. Then the S -wave velocity model is obtained using PS -stereotomography on PS -arrivals fixing the P -wave velocity model. We present an application to an 'ideal' synthetic data set demonstrating the relevance of the approach, which allows us to recover depth consistent P - and S -waves velocity models even if no pairing of PP - and PS -events is introduced. Finally, results to a real data set from the Gulf of Mexico are presented demonstrating the potential of the method in a noisy data context.     

Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency–time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.     

Crosshole seismic waveform tomography – I. Strategy for real data application

The frequency-domain version of waveform tomography enables the use of distinct frequency components to adequately reconstruct the subsurface velocity field, and thereby dramatically reduces the input data quantity required for the inversion process. It makes waveform tomography a computationally tractable problem for production uses, but its applicability to real seismic data particularly in the petroleum exploration and development scale needs to be examined. As real data are often band limited with missing low frequencies, a good starting model is necessary for waveform tomography, to fill in the gap of low frequencies before the inversion of available frequencies. In the inversion stage, a group of frequencies should be used simultaneously at each iteration, to suppress the effect of data noise in the frequency domain. Meanwhile, a smoothness constraint on the model must be used in the inversion, to cope the effect of data noise, the effect of non-linearity of the problem, and the effect of strong sensitivities of short wavelength model variations. In this paper we use frequency-domain waveform tomography to provide quantitative velocity images of a crosshole target between boreholes 300 m apart. Due to the complexity of the local geology the velocity variations were extreme (between 3000 and 5500 m s⁻¹), making the inversion problem highly non-linear. Nevertheless, the waveform tomography results correlate well with borehole logs, and provide realistic geological information that can be tracked between the boreholes with confidence.     

A crustal seismic velocity model for the UK, Ireland and surrounding seas

A regional model of the 3-D variation in seismic P -wave velocity structure in the crust of NW Europe has been compiled from wide-angle reflection/refraction profiles. Along each 2-D profile a velocity–depth function has been digitised at 5 km intervals. These 1-D velocity functions were mapped into three dimensions using ordinary kriging with weights determined to minimise the difference between digitised and interpolated values. An analysis of variograms of the digitised data suggested a radial isotropic weighting scheme was most appropriate. Horizontal dimensions of the model cells are optimised at 40 × 40 km and the vertical dimension at 1 km. The resulting model provides a higher resolution image of the 3-D variation in seismic velocity structure of the UK, Ireland and surrounding areas than existing models. The construction of the model through kriging allows the uncertainty in the velocity structure to be assessed. This uncertainty indicates the high density of data required to confidently interpolate the crustal velocity structure, and shows that for this region the velocity is poorly constrained for large areas away from the input data.     

P- and S-velocity images of the lithosphere–asthenosphere system in the Central Andes from local-source tomographic inversion

About 50 000 P and S arrival times and 25 000 values of t * recorded at seismic arrays operated in the Central Andes between 20°S and 25°S in the time period from 1994 to 1997 have been used for locating more than 1500 deep and crustal earthquakes and creating 3-D P , S velocity and Qp models. The study volume in the reference model is subdivided into three domains: slab, continental crust and mantle wedge. A starting velocity distribution in each domain is set from a priori information: in the crust it is based on the controlled sources seismic studies; in slab and mantle wedge it is defined using relations between P and S velocities, temperature and composition given by mineral physics. Each iteration of tomographic inversion consists of the following steps: (1) absolute location of sources in 3-D velocity model using P and S arrival times; (2) double-difference relocation of the sources and (3) simultaneous determination of P and S velocity anomalies, P and S station corrections and source parameters by inverting one matrix. Velocity parameters are computed in a mesh with the density of nodes proportional to the ray density with double-sided nodes at the domain boundaries. The next iteration is repeated with the updated velocity model and source parameters obtained at the previous step. Different tests aimed at checking the reliability of the obtained velocity models are presented. In addition, we present the results of inversion for Vp and Vp/Vs parameters, which appear to be practically equivalent to Vp and Vs inversion. A separate inversion for Qp has been performed using the ray paths and source locations in the final velocity model. The resulting Vp , Vs and Qp distributions show complicated, essentially 3-D structure in the lithosphere and asthenosphere. P and S velocities appear to be well correlated, suggesting the important role of variations of composition, temperature, water content and degree of partial melting.     

Simultaneous velocity and interface tomography of normal-incidence and wide-aperture seismic traveltime data

A tomographic inversion technique that inverts traveltimes to obtain a model of the subsurface in terms of velocities and interfaces is presented. It uses a combination of refraction, wide-angle reflection and normal-incidence data, it simultaneously inverts for velocities and interface depths, and it is able to quantify the errors and trade-offs in the final model. The technique uses an iterative linearized approach to the non-linear traveltime inversion problem. The subsurface is represented as a set of layers separated by interfaces, across which the velocity may be discontinuous. Within each layer the velocity varies in two dimensions and has a continuous first derivative. Rays are traced in this medium using a technique based on ray perturbation theory, and two-point ray tracing is avoided by interpolating the traveltimes to the receivers from a roughly equidistant fan of rays. The calculated traveltimes are inverted by simultaneously minimizing the misfit between the data and calculated traveltimes, and the roughness of the model. This 'smoothing regularization' stabilizes the solution of the inverse problem. In practice, the first iterations are performed with a high level of smoothing. As the inversion proceeds, the level of smoothing is gradually reduced until the traveltime residual is at the estimated level of noise in the data. At this point, a minimum-feature solution is obtained, which should contain only those features discernible over the noise.
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion.     

Controls on Rayleigh wave amplitudes: attenuation and focusing

A large data set of amplitude measurements of minor and major arc Rayleigh waves in the period range 73–171 s is collected. By comparing these amplitudes with the amplitudes of synthetic waveforms calculated by mode summation, maps of lateral variations in the apparent attenuation structure of the Earth are constructed. An existing formalism for predicting the effects of focusing is employed to calculate amplitude perturbations for the same data set. These perturbations are used to construct 'pseudo‐attenuation' maps and these results are compared with the apparent attenuation maps calculated from the data. It is shown that variations in Rayleigh wave amplitude perturbations in the Earth are dominated by attenuation at long wavelengths (below about degree 8) and by elastic structure at shorter wavelengths. It is also shown that the linear approximation for focusing is successful at predicting Rayleigh wave amplitudes using existing phase velocity maps. These results indicate that future attempts to model the velocity structure of the Earth would be assisted by incorporating amplitude data and by jointly inverting for Q structure.     

Wavepath traveltime tomography

The elastic-wave equation is used to construct sensitivity kernels relating perturbations in elastic parameters to traveltime deviations. Computation of the functions requires a correlation of the forward-propagating seismic wavefield with a backward propagation of the residual wavefield. The computation of the wavefields is accomplished using a finite difference algorithm and is efficiently executed on a CM-2 parallel processor. The source and receiver locations have maximum sensitivity to velocity structure. The sensitivity kernels or wavepaths are well suited for transmission traveltime inversion such as cross-borehole tomography and vertical seismic profiling. Conventional ray tomography and wavepath tomography are applied to a set of P -wave arrival times, from a cross-borehole experiment at Kesterson, California. Because the wavepaths have increased sensitivity near the source and receiver there are differences in resolution of the velocity structure. Both techniques recover the same relative variations in velocity where the coverage is adequate. The wavepath solution is more laterally continuous and the dominant variation is vertical, as is expected for the layered sediments in this region.     

Secular trend of the Earth's rotation pole: consideration of motion of the latitude observatories

Secular polar motion has been recorded in ILS data over the past 75 years, an amount greater by a factor of ten than the 'true polar wandering' deduced from paleomagnetic data. In this work, the possibility that the secular trend is an observational artifact of the continental drift of the ILS stations is directly examined by consideration of several absolute plate velocity models earlier proposed by Minster et al. (1974), Kaula (1975), and Solomon, Sleep & Richardson (1975). The assumptions underlying those models are discussed; in general, the absolute velocity models are more likely to be valid when geologically short timescales are considered.
The corrections to the ILS data due to the stations' motion fail by an order of magnitude to explain the ILS trend; even by taking into account possible plate hyperactivity and non-rigidity, the corrections could explain no more than 30 per cent of the trend. The corrections are small because the absolute plate velocities of North America and Eurasia are small and primarily east—west. Consequently, the rotation pole is undergoing significant motion of its own relative to the surface of the Earth.
The Kimura z term found by the ILS observations provides an independent means of estimating the relative motion between Eurasia and North America. It also contains other geophysical information; the 7.5-yr periodicity discovered by Naito & Ishii (1974) may be widespread.
Lastly, tectonically induced changes in the zenith direction, such as at Mizusawa, are probably too small to be detected, contrary to earlier proposals.     

The relationship between seismic velocity and density in the continental crust — a useful constraint?

Summary . Plots of seismic velocity and density of rock samples show that a range of densities is possible for rocks of each seismic velocity and vice versa. although a single linear relationship is often assumed in crustal gravity calculations. Because of the scatter, whenever rocks of known seismic velocity are converted to density using this relationship, a reduction is made to the resolving power of the resulting gravity calculation. If these rocks reach thicknesses of more than a few kilometres, then the uncertainties become significant when compared with the size of commonly observed gravity anomalies. Examples are considered from the North Sea, Mississippi and Carolina Trough. It is concluded that the use of a seismic velocity measurement as the only indication of rock density does not provide a useful constraint when attempting to reproduce observed gravity variations. An appropriate model for isostatic compensation is probably the most important factor for successful predictions of crustal structure on the basis of gravity data.     

Array analysis using circular-wave-front geometry:an application to locate the nearby seismo-volcanic source

The zero-lag cross-correlation technique, used for array analysis in the hypothesis of plane waves, has been modified to allow the wave front to be circular. Synthetic tests have been performed to check the capability of the method, which returns the input test data when the source–array distances are not greater than two or three times the array aperture. For this distance range the method furnishes an estimate of the apparent velocity and the epicentral coordinates of the source. For more distant sources the method becomes equivalent to that based on the planar-wave approximation, which gives an estimate of the backazimuth to the source and the apparent velocity. The method has been applied to seismic data recorded at the active volcano located at Deception Island, Antarctica. 35 volcanic long-period events occurring in a small swarm were selected. Results show that the epicentres are close to the array (between 0.4 and 2 km) and aligned in a SW direction, in agreement with one of the main directions of the fracture system of Deception volcano.