2D inversion of refraction traveltime curves using homogeneous functions

Abstract

A method using simple inversion of refraction traveltimes for the determination of 2D velocity and interface structure is presented. The method is applicable to data obtained from engineering seismics and from deep seismic investigations. The advantage of simple inversion, as opposed to ray‐tracing methods, is that it enables direct calculation of a 2D velocity distribution, including information about interfaces, thus eliminating the calculation of seismic rays at every step of the iteration process. The inversion method is based on a local approximation of the real velocity cross‐section by homogeneous functions of two coordinates. Homogeneous functions are very useful for the approximation of real geological media. Homogeneous velocity functions can include straight‐line seismic boundaries. The contour lines of homogeneous functions are arbitrary curves that are similar to one another. The traveltime curves recorded at the surface of media with homogeneous velocity functions are also similar to one another. This is true for both refraction and reflection traveltime curves. For two reverse traveltime curves, non‐linear transformations exist which continuously convert the direct traveltime curve to the reverse one and vice versa. This fact has enabled us to develop an automatic procedure for the identification of waves refracted at different seismic boundaries using reverse traveltime curves. Homogeneous functions of two coordinates can describe media where the velocity depends significantly on two coordinates. However, the rays and the traveltime fields corresponding to these velocity functions can be transformed to those for media where the velocity depends on one coordinate. The 2D inverse kinematic problem, i.e. the computation of an approximate homogeneous velocity function using the data from two reverse traveltime curves of the refracted first arrival, is thus resolved. Since the solution algorithm is stable, in the case of complex shooting geometry, the common‐velocity cross‐section can be constructed by applying a local approximation. This method enables the reconstruction of practically any arbitrary velocity function of two coordinates. The computer program, known as godograf, which is based on this theory, is a universal program for the interpretation of any system of refraction traveltime curves for any refraction method for both shallow and deep seismic studies of crust and mantle. Examples using synthetic data demonstrate the accuracy of the algorithm and its sensitivity to realistic noise levels. Inversions of the refraction traveltimes from the Salair ore deposit, the Moscow region and the Kamchatka volcano seismic profiles illustrate the methodology, practical considerations and capability of seismic imaging with the inversion method.

The Sea of Okhotsk crust from deep seismic sounding data

“…This method of interpretation and a "GODOGRAF" computer program had been developed at the Moscow State University [Piip, 1991[Piip, , 2001]. This method is based on the local approximation of real velocity fields using homogeneous two-coordinate functions.…”

“…We digitized these travel-time data and interpreted them using moderntechnology computer means, namely, a method of homogeneous functions [Piip, 1991[Piip, , 1997[Piip, , 2001]. Detailed seismic sections were obtained to depths of 30-60 km.…”

Application of 2d Homogeneous Function Method to Study the Subsurface Geologic Section in the Northwestern Part of the Kharga Oasis Area, Western Desert, Egypt.

“…Interpretation of the collected seismic data was done using 2D inversion algorithm (GODOGRAF software). This algorithm is based on a local approximation of the real velocity distribution by homogeneous functions of two coordinates (Piip, 2001;Piip and El-Haddad 2008). In this inversion the preliminary distinguishing and identification of waves on travel time curves from different interfaces are automatically performed.…”

“…At Moscow State University, a 2D tomographic inversion method of refraction traveltimes curves, i.e. the homogeneous function method, was proposed and firstly used in the 1980s (Piip, 2001). This method is based on a local approximation of the real velocity distribution by homogeneous functions of two coordinates (Piip, 2001).…”

“…the homogeneous function method, was proposed and firstly used in the 1980s (Piip, 2001). This method is based on a local approximation of the real velocity distribution by homogeneous functions of two coordinates (Piip, 2001). In this inversion the preliminary distinguishing and identification of waves on travel time curves from different interfaces are automatically performed.…”