h 2 XTV inversion Rayfract help Page 1 of 6

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1 XTV inersion Rayfract help Page of 6 BXTV inersion Delta-t-V and XTV inersion assume that traces are gathered by Common Mid-Point CMP (Diebold and Stoffa 98). Also, these inersion methods rely on the suppression of layer dip effects on apparent elocity, when sorting traces in a CMP gather by unsigned offset (Diebold and Stoffa 98). This suppression fails at locations of strong refractor curature. Barton and Baker (3) try to obtain improed apparent elocities by regarding the shot direction. To enable the realistic interpretation of sudden apparent elocity increase in CMP sorted traeltime cures, (Winkelmann 998) proposes to extend the Delta-t-V gradient layer inersion (Gebrande 986), with Dix inersion and Intercept Time inersion. These two additional inersion methods allow the modeling of constant-elocity layers. As described by (Winkelmann 998) and (Gawlas ), the XTV inersion reconstructs the D elocity s. depth function (z) below a CMP based on XTV data triples, with alues X = (reduced) unsigned offset, T = (reduced) time and V = apparent elocity. These data triples sample a (reduced) CMP sorted traeltime cure. The inersion is based on the layer stripping principle. With offset we always mean unsigned offset in the following. XTV inersion uses three separate methods, for inersion of a data triple into a model layer : Modified Dix inersion Intercept Time inersion Gradient layer inersion (original Delta-t-V method) The inersion starts with the first XTV triple at the smallest offset X, as determined from the original CMP cure. Once the first layer has been determined by one of aboe methods, offset and time for all other triples are reduced to the bottom of this first layer. Then the XTV triple at the next smallest offset X is inerted into a second layer, and remaining triples are reduced to the bottom of this second layer. This triple inersion process is continued iteratiely, until all XTV triples hae been processed. We first describe each of these three inersion methods in detail. We then describe the oerall XTV algorithm, which decides what inersion method should be applied to the current XTV triple. All inersion methods are described for the two-layer case only. Since the XTV inersion is based on layer stripping, we only need to deal with two layers (current oerburden, current refractor) during each iteration and triple-to-layer inersion step. The modified Dix inersion assumes reflection of a ray. The layer thickness h is determined as follows : h Vt is the unsigned offset X between shot point and receier. t is the traeltime T between shot point and receier, separated by offset. V is the measured apparent elocity, at the bottom of the layer i.e. at offset. ()

2 XTV inersion Rayfract help Page of 6 The aerage layer elocity is obtained with V t () Velocities at the top and at the bottom of the modeled layer are both set to this aerage elocity. The Intercept Time inersion assumes critical refraction of a ray, with both oerburden and basement layer haing a constant elocity. Using intercept time as determined from the XTV triple with t V (3) the layer thickness h is determined with h ( ) ( ) V (4) is the direct wae elocity (for first XTV triple) or the elocity as modeled for the bottom of the preiously determined layer (for reduced XTV triples). Velocities at the top and at the bottom of the modeled layer are both set to. The Gradient layer inersion method or Delta-t-V method assumes a diing wae ray and a constant elocity-gradient equal to a. So the layer's elocity-depth function is ( z) az (5) Since the elocity gradient is assumed constant, the diing first-break ray follows a circular arc, between shot point and receier. Based on the two equations

3 XTV inersion Rayfract help Page 3 of 6 a ( V) V (6) and t( V ) a arch( V ) (7) the elocity at the top of the modeled layer is determined numerically. Then the layer thickness h is h V V (8) and the elocity at the bottom of the modeled layer is set to the measured elocity V. can be smaller than the elocity measured at the bottom of the oerlying layer. So the gradient layer inersion can recognize elocity inersions, at least in some situations. Also, the gradient layer inersion does not use the intercept time. Layer stripping is done using equations as described by Gibson et al. (979). XTV triples are sorted by unsigned offset X, for layer inersion as described here. Winkelmann (998) proposes the following XTV inersion algorithm : Use Intercept Time inersion if the apparent elocity V increases suddenly, between adjacent XTV triples. The Minimum elocity ratio required for application of the Intercept Time layer inersion can be adjusted by the user. Intercept Time inersion can be disabled with XTV parameter Enable Intercept Time layer inersion. Otherwise use Dix inersion if both the aerage elocity (determined with Dix inersion) and the elocity at the top of the modeled layer (determined with Gradient layer inersion) are smaller than the elocity modeled for the bottom of the preiously determined layer. You may disable Dix inersion with XTV parameter Enable Modified Dix layer inersion. Otherwise use Gradient layer inersion. A candidate XTV triple is optionally rejected if its apparent elocity V or intercept time are larger than aerage alues for the next three XTV triples. This triple filtering has the aim of suppressing reflections erroneously picked as first breaks.

4 XTV inersion Rayfract help Page 4 of 6 Intercept Time layer inersion for multiple adjacent XTV triples as required for Intercept Time layer inersion is not clearly defined, especially if the preious layer has been obtained with Intercept Time inersion as well. You may suppress application of our Intercept Time inersion to multiple adjacent XTV triples, with XTV parameter Allow adjacent Intercept time layer inersion. If the preious XTV triple was inerted with Intercept Time layer inersion as well, then the elocity for the bottom of the preious layer may be assumed to be the preious, or the apparent elocity V of the preious XTV triple, or any alue between these two elocities. Alternatiely, can be determined by interpolating between the preious and the apparent elocity V of the current XTV triple. You may specify how should be determined with XTV parameters Oerlying layer elocity step and Current layer elocity step. If the resulting exceeds the preious apparent elocity V, used for inersion of the current XTV triple is reset to V of the preious triple. The XTV inersion ensures that the sum of Oerlying layer elocity step and Current layer elocity step does not exceed %. If you want to use apparent elocities V (from preious and current XTV triples) exclusiely and disregard preious, for determination of the current based on step parameters Oerlying layer elocity step and Current layer elocity step, just enable XTV option Prefer measured layer top elocity oer inerted. If this option is enabled, the apparent elocity V as obtained for the preious XTV triple and layer is taken as an estimate for the elocity at the top of the current layer. In analogy, the elocity at the top of the preious layer is estimated with the apparent elocity V of the preious-preious XTV triple. Parameters for XTV inersion Minimum elocity ratio The minimum elocity ratio (between apparent elocity V of the current XTV triple and the preious triple) required for application of the Intercept time layer inersion. If the actual ratio is smaller, the Intercept Time layer inersion method will not be applied. Instead, Dix inersion or Gradient layer inersion will be applied to the current XTV triple. Valid ratio alues range from. to.5. This ratio is regarded if XTV parameter Enable XTV Intercept Time layer inersion is checked only.

5 XTV inersion Rayfract help Page 5 of 6 Enable Intercept Time layer inersion Check this XTV option if you want to enable XTV Intercept Time layer inersion Enable Modified Dix layer inersion Check this XTV option if you want to enable Dix layer inersion Allow adjacent Intercept time layer inersion Check this XTV option to enable application of our Intercept Time inersion method, for multiple adjacent XTV triples. Oerlying layer elocity step This XTV parameter is used if Allow adjacent Intercept time layer inersion is enabled only. This step parameter may ary between alues % and %. The elocity step determines how needed for Intercept Time inersion of the current XTV triple is obtained, from the preious XTV triple and by interpolation between the preious (step %) and the preious apparent elocity V (step %). Current layer elocity step This XTV parameter is used if Allow adjacent Intercept time layer inersion is enabled only. This step parameter may ary between alues % and 99%. The elocity step determines how needed for Intercept Time inersion of the current XTV triple is obtained, by interpolation between as obtained with step parameter Oerlying layer elocity step (current step %) and the current apparent elocity V (current step %). Prefer measured layer top elocity oer inerted Check this XTV option to use apparent elocities V (belonging to preious and current XTV triples) exclusiely and disregard the preious, for determination of the current, based on step parameters Oerlying layer elocity step and Current layer elocity step. Oerburden elocity is needed for our Intercept Time two-layer case inersion method. If this option is enabled, the apparent elocity V as obtained for the preious XTV triple and layer is taken as an estimate for the elocity at the top of the current layer. Suppress elocity artefacts Enable this option to suppress the generation of processing artefacts, i.e. unrealistic elocity ariations. Use best for medium and high coerage profiles. See (Winkelmann 998), top of page 36. If enabled, a candidate ray will be used for modeling of an incremental layer if the ray specific apparent elocity and intercept time (as modeled by local regression on CMP cure, at ray specific offset) both are lower than the mean of apparent elocity and intercept time, as estimated for the next three higher CMP offsets. This triple filtering has the aim of suppressing reflections erroneously picked as first breaks. If this setting is disabled, no

6 XTV inersion Rayfract help Page 6 of 6 candidate ray selection, i.e. filtering / enforcing of CMP traeltime cure continuity, based on apparent elocity and intercept time will occur. References J. B. Diebold and P. L. Stoffa 98. The traeltime equation, tau-p mapping, and inersion of common midpoint data. SEG Geophysics, olume 46, pp Roland A. Winkelmann 998 Ph. D. Thesis. Entwicklung und Anwendung eines Wellenfelderfahrens zur Auswertung on CMP-sortierten Refraktionseinsaetzen. Akademischer Verlag Muenchen, Munich. ISBN Gawlas, Peter Florian Ph. D. Thesis. Möglichkeiten eines DMO-Prozesses in der CMP- Refraktionsseismik. LMU Munich: Faculty of Geosciences. See H. Gebrande 986. CMP-Refraktionsseismik. Paper presented (in German) at Mintrop Seminar / Uni-Kontakt Ruhr-Uniersitaet Bochum, Expanded abstract "Seismik auf neuen Wegen", pp H. Gebrande and H. Miller 985. Refraktionsseismik (in German). In: F. Bender (Editor), Angewandte Geowissenschaften II. Ferdinand Enke, Stuttgart; pp ISBN Bruce S. Gibson, Mark E. Odegard and George H. Sutton 979. Nonlinear least-squares inersion of traeltime data for a linear elocity-depth relationship. Geophysics, olume 44, pp Barton P. and Barker N. 3. Velocity imaging by tau-p transformation of refracted seismic traeltimes. Geophysical Prospecting, olume 5, pp Copyright (c) Intelligent Resources Inc. All rights resered.