S U M M A R YInvestigating the mechanisms of small seismic sources usually consists of three steps: determining the moment tensor of the source; decomposing the moment tensor into parameters that can be interpreted in terms of physical mechanisms and displaying those parameters. This paper concerns the second and third steps. Two existing methods-the Riedesel-Jordan and Hudson-Pearce-Rogers parameters and displays-are reviewed, compared and contrasted, and advantages and disadvantages of the two methods are discussed. One disadvantage is that neither method takes into consideration the effect of anisotropy on the interpretation. In microseisms, anisotropy can be important. A new procedure based on the biaxial decomposition of the potency tensor is introduced which explicitly allows for anisotropy and interprets the moment tensor in terms of an isotropic pressure change and a displacement discontinuity on a fault. It is shown that this interpretation is always possible for any moment tensor whatever the anisotropy. To compare the pressure change with the displacement discontinuity, it is useful to be able to determine the volume change from the pressure source in any medium. This depends on the embedded bulk modulus, which differs from the normal bulk modulus. The embedded modulus in isotropic media is well known and the equivalent anisotropic result is derived in this paper. Interpreting a seismic source in terms of the volume change due to a pressure change and a displacement discontinuity on a fault allows a simple 3-D graphical glyph to be used to display the interpretation.

To avoid the defocusing effects of propagating waves through salt and overburden with an inaccurate overburden velocity model, we introduce a vertical seismic profiling ͑VSP͒ local elastic reverse-time-migration ͑RTM͒ method for salt-flank imaging by transmitted P-to-S waves. This method back-projects the transmitted PS waves using a local velocity model around the well until they are in phase with the back-projected PP waves at the salt boundaries. The merits of this method are that it does not require the complex overburden and salt-body velocities and it automatically accounts for source-side statics. In addition, the method accounts for kinematic and dynamic effects, including anisotropy, absorption, and all other unknown rock effects outside of this local subsalt velocity model. Numerical tests on an elastic salt model and offset 2D VSP data in the Gulf of Mexico, using a finite-difference time-domain staggered-grid RTM scheme, partly demonstrate the effectiveness of this method over interferometry PS-PP transmission migration and local acoustic RTM. Our method separates elastic wavefields to vector P-and S-wave velocity components at the trial image point and achieves better resolution than local acoustic RTM and interferometric transmission migration. The analytical formulas of migration resolution for local acoustic and elastic RTM show that the migration illumination is limited by data frequency and receiver aperture, and the spatial resolution is lower than standard poststack and prestack migration. This new method can image salt flanks as well as subsalt reflectors.

A B S T R A C TWe describe a method to invert a walkaway vertical seismic profile (VSP) and predict elastic properties (P-wave velocity, S-wave velocity and density) in a layered model looking ahead of the deepest receiver. Starting from Bayes's rule, we define a posterior distribution of layered models that combines prior information (on the overall variability of and correlations among the elastic properties observed in well logs) with information provided by the VSP data. This posterior distribution of layered models is sampled by a Monte-Carlo method. The sampled layered models agree with prior information and fit the VSP data, and their overall variability defines the uncertainty in the predicted elastic properties. We apply this technique first to a zero-offset VSP data set, and show that uncertainty in the long-wavelength P-wave velocity structure results in a sizable uncertainty in the predicted elastic properties. We then use walkaway VSP data, which contain information on the long-wavelength P-wave velocity (in the reflection moveout) and on S-wave velocity and density contrasts (in the change of reflectivity with offset). The uncertainty of the look-ahead prediction is considerably decreased compared with the zero-offset VSP, and the predicted elastic properties are in good agreement with well-log measurements.

A B S T R A C TWe describe a method to invert a walkaway vertical seismic profile (VSP) and predict elastic properties (P-wave velocity, S-wave velocity and density) in a layered model looking ahead of the deepest receiver. Starting from Bayes's rule, we define a posterior distribution of layered models that combines prior information (on the overall variability of and correlations among the elastic properties observed in well logs) with information provided by the VSP data. This posterior distribution of layered models is sampled by a Monte-Carlo method. The sampled layered models agree with prior information and fit the VSP data, and their overall variability defines the uncertainty in the predicted elastic properties. We apply this technique first to a zero-offset VSP data set, and show that uncertainty in the long-wavelength P-wave velocity structure results in a sizable uncertainty in the predicted elastic properties. We then use walkaway VSP data, which contain information on the long-wavelength P-wave velocity (in the reflection moveout) and on S-wave velocity and density contrasts (in the change of reflectivity with offset). The uncertainty of the look-ahead prediction is considerably decreased compared with the zero-offset VSP, and the predicted elastic properties are in good agreement with well-log measurements.