Calculation of the amplitudes of elastic waves in anisotropic media in Cartesian or ray-centred coordinates

Studia Geophysica et Geodaetica - We derive various expressions for the amplitude of the ray-theory approximation of elastic waves in heterogeneous anisotropic media, and show their mutual...     

Resolution of prestack depth migration

The resolution of a general 3-D common-shot elastic prestack depth migration in a heterogeneous anisotropic medium is studied approximately, using the ray theory. It is demonstrated that the migrated section can approximately be represented by the convolution of the reflectivity function with the corresponding local resolution function. Alternatively, it can also be approximately represented by the convolution of the spatial distribution of the weak-contrast displacement reflection-transmission coefficient with the corresponding local resolution function. The derived explicit approximate equations enable us to predict the migration resolution approximately without doing the whole and expensive migration. The equations are applicable to 3-D elastic migrations in 3-D isotropic or anisotropic, heterogeneous velocity models. Both the reflectivity function and the spatial distribution of the weak-contrast displacement reflection-transmission coefficient approximately determine the linear combination of the perturbations of elastic moduli and density to which the migrated section is sensitive. The imaged linear combination of the perturbations of elastic parameters depends on the selection of the polarizations (wave types) of the incident and back-propagated wavefields and on the directions of propagation. The resolution of the linear combination of the perturbations of elastic moduli and density in the migrated section is determined by the above mentioned local resolution functions. The local resolution functions depend on the aperture and on the imaging function. The imaging function is determined by the source time function and by the form of the imaging functional. The local resolution functions are considerably sensitive to heterogeneities. The local resolution functions in elastic media differ from their acoustic counterparts, especially by the existence of converted scattered waves in elastic media.     

Ray tracing and geodesic deviation of the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. If we know that a medium is close to uniaxial (transversely isotropic), it may be advantageous to trace reference rays which resemble the SH–wave and SV–wave rays. This paper is devoted to defining and tracing these SH and SV reference rays of elastic S waves in a heterogeneous generally anisotropic medium which is approximately uniaxial (approximately transversely isotropic), and to the corresponding equations of geodesic deviation (dynamic ray tracing). All presented equations are simultaneously applicable to ordinary and extraordinary reference rays of electromagnetic waves in a generally bianisotropic medium which is approximately uniaxially anisotropic. The improvement of the coupling–ray–theory seismograms calculated along the proposed SH and SV reference rays, compared to the coupling–ray–theory seismograms calculated along the anisotropic common reference rays, has already been numerically demonstrated by the authors in four approximately uniaxial velocity models.     

Arrival-time residuals and hypocentre mislocation

It is shown that the arrival-time residuals and hypocentre mislocation are two mutually independent consequences of the inaccurate seismic model and inaccurately measured arrival times. The minimum residuals resulting from the kinematic hypocentre determination contain no information on the accuracy in determining the hypocentre position.     

Optimization of the shape of Gaussian beams of a fixed length

Summary The procedure of choosing the shape of Gaussian beams in order to minimize a given object function of a certain kind is proposed. The general form of the object function enables both the average square of the quadratic variation of the phase and the average square of the beamwidth to be minimized along the central ray. The error of the transformation of the Gaussian beams at the structural interfaces may also be taken into account. Most of the hitherto published suggestions of how to choose the shape of Gaussian beams are special cases of the described procedure. The aim of this paper is not to propose the object function to be minimized, but only to describe the minimization of a given object function. The minimization assumes the a priori known lengths of the central rays of the Gaussian beams (i.e. the lengths of the beams are not free parameters in the minimization procedure).

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The relation between Gaussian beams and Maslov asymptotic theory

Summary The application of Maslov asymptotic theory in a general 3-D mixed subspace of 6-D complex phase space is proposed to obtain the integral superpositions of Gaussian packets and beams. The ray method and the superposition of plane waves (Maslov method of Chapman and Drummond [7]) are special limiting cases of the above mentioned approach. The same high-frequency asymptotic expansion formulae for seismic body waves were derived previously in [8] using the Gaussian beam method.

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Correction of twilight measurements of influence of night sky

Studia Geophysica et Geodaetica -