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.     

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.     

Geocentre motion from the DORIS space system and laser data to the Lageos satellites: comparison with surface loading data

Surface mass redistribution within the Earth system, especially in the atmosphere, oceans, continents and ice sheets, causes the position of the centre of mass to vary in a reference frame attached to the solid Earth. Space techniques are now precise enough to measure the centre of mass motion. Here we present a determination of the centre of mass coordinates at regular monthly intervals using DORIS data on SPOT‐2, SPOT‐3 and Topex–Poseidon (1993–1997) and laser data on Lageos‐1 and Lageos‐2 (1993–1996). The amplitude and phase of the space‐geodesy‐derived annual cycle for each coordinate are further compared to estimates based on surface mass redistribution at the Earth surface derived from various climatic data sources: surface pressure, soil moisture, snow depth and ocean mass variations.     

From ACH tomographic models to absolute velocity models

The ACH method, a widely used tomographic inverse method, is characterized by the use of relative residuals in order to avoid possible biases coming from outside the target volume. The ACH method thus does not really retrieve the 3-D structure of the target volume, but instead leads to velocity contrasts relative to the layer average of the velocity, this average value remaining unknown ( Aki et al. 1977 ). Two artefacts derive from this particularity: (1) velocity contrasts are known only in the horizontal direction and it is not possible, in a strict mathematical sense, to estimate the contrasts in the vertical direction with ACH alone; (2) negative anomalies are often interpreted as low velocities, whereas negative anomalies may correspond to high velocities if the average value of the corresponding layer is sufficiently high. The converse is true of positive anomalies. We show with synthetic data how these artefacts can affect the interpretation of tomographic images. We propose to correct the artefacts by reintroducing the 1-D regional average model, and show in synthetic experiments how effective this correction can be.
  The application of this procedure to data recorded in the Kunlun region shows that the retrieval of the absolute values of the 3-D velocity model is helpful for interpreting the tomographic images and better defining which features are anomalous.