Yer içinin modellenmesi amacıyla sismik kırılma verilerinin tersçözümü

Abstract

ÖZET Jeolojik yapıların model 1enmesi nde iki tür yaklaşım uygulanmaktadır. Birinci tur yaklaşım, parametreleri önce den belirlenen jeolojik modelin tepkisini bulma işlemidir. Bu yaklaşıma `Düzçözüm(Forward) adı verilir. ikinci tür yaklaşım, gözlemsel verilerden ve oluşturulan bir model tep kisinden yararlanarak belirlenen model aracılığı ile aranı lan Jeolojik modelin parametrelerini bulma işlemidir. Bu yaklaşıma `Tersçözüm (Invertion) ` adı verilir. Tersinir (reversed) sismik kırılma zaman-uzaklık ve rileri kullanılarak herbir Jeofon altında refraktör yüzeyi ne kadar olan düşey derinlikler ile refraktör hızı yaklaşık olarak saptanarak refraktör yüzeyi tersçözüm yaklaşımı ile haritalanabilir. Bu amaçla, in-line tipi açılımlarda uygu lanan tersinir sismik kırılma zaman-uzaklık verilerine Doğ rusal olmayan Enküçük Kareler Tersçözüm Tekniği (Marquardt Algoritması) uygulanarak tek katmanlı bir ortam için herbir Jeofon altında refraktör yüzeyine kadar olan düşey derin likler ile refraktör hızı kestirimi yapılarak refraktör yü zeyi haritalanmaya çalışılmıştır. Geliştirilen zaman-uzaklık bağıntısında, kırılma ışınlarının çıktığı refraktör yüzeyi üzerindeki noktalarda refraktör eğimleri, tersinir zaman-uzaklık verisinden, her bir iterasyon adımında kestirilen refraktör hızları kulla nılarak yaklaşık olarak belir lenebilmekte ve düzensiz r&f- raktörlerin hari talamasında yeni bir yaklaşım getirilmekte dir. Geliştirilen iteratif Tersçözüm Tekniği (ITT) Genel leştirilmiş Resiprok Yöntemi (Generalized Reciprocal Method /GRMD ile birlikte bir dizi yapay ve gerçek sismik kırılma verilerine uygulanmıştır. Karşılaştırmalı sonuçlara göre, ITT ile elde edilen refraktör derinlik kestirimleri oldukça sağlıklıdır. Refraktör yüzeyinin düzensizliği arttıkça hız kestirimi ndeki hata yüzdesi artmaya başlamak tadır. Hız kontrastının yüksek olduğu modellerde parametre kestirimle ri gerçek değerlere cok yakın olarak elde edilmiştir. Ref raktör yüzeyinin düzensizliği arttıkça hız parametresi ger çek değerden uzaklaşmaktadır. Geliştirilen iteratif Terscözüm Tekniği (ITT) ile Genelleştirilmiş Resiprok Yöntemi (GRMD) nden elde edilen sonuçlar birbirleriyle oldukça iyi uyum sağlamıştır.

SUMMARY INVERSION OF SEISMIC REFRACTION DATA FOR SUBSURFACE MODELLING Seismie methods are employed for two different types of investigations. Seismic reflection method is most widely employed for hydrocarbon exploration such as oil and gass. Seismic refraction method on the other hand is widely used in site investigation studies, groundwater exploration, bedrock mapping, environmental site investi gations, etc. Most refraction work involves in-line profiling with forward and reverse shooting. It involves a long linear spread of many geophone groups shot from each end. Refraction method is suitable when a lower speed layer lies on a high-speed layer. If the purpose is to determine the depth and shape of a sedimentary basin by mapping the basement surface, and if the sedimentary rocks have a lower speed than the basement formations, then the refraction method can be a highly effective and economical approach for this purpose. Seismie headwaves, which emerge from a refractor surface for various source and detector distances, give information on the velocities and depths of the subsurface formations. Thus, depths from surface to interfaces, velocity of layer and relation between velocity and density of the medium can be deter mined. The refraction data which are obtained in the field, using unreversed or reversed shooting, are interpreted for refractor mapping and refractor velocity estimation. There are many methods to estimate the refractor depths and refractor velocity. These methods were developed using the delay times of critically refracted waves or by graphical solution of wavefront reconstruction. Delay time methods assume that an arrival time of critically refracted wave involves shot delay time and geophone delay time for a given source-detector pair. Thus, using delay times, depths from surface to refractor and refractor velocity can be estimated for each detector. In these methods, the refractor dip should be less than about lO degrees for more accurate results. VIThe wavefront methods are graphical solutions which involve reconstructing the portion of emerging wavefronts from the arrival times at a spread of geophones from a shot of critically refracted waves. The Generalized Reciprocal Method is used for ref ractor depths mapping and refractor velocity estimation in shallow seismic profiling. In this method, for each geo- phone position, the refractor depths are estimated using the reciprocal time recorded as a maximum arrival time along a reversed profile, time-depths formed from arrival times, refractor velocity determined from velocity analysis curve, and depth conversion factor formed from the refrac tor velocity. Generalized Reciprocal Method requires velo city analysis function to determine the optimum XY spacing. It is relatively insensitive to dip angles up to about 20 degrees. Two different approaches are used for modelling the geological structures. These are forward and inverse problem solutions. The former is known as the model response. The latter on the other hand is known as the parameter estimation. In this approach, one tries to es timate the best model which fits the observed data. The basic strategy in geophysical inversion is an operation to fit the response of an idealized geological model to finite set of actual observations. The model response consists of the synthetic data produced by a particular realization of the model. The basic strategy of inversion is to minimize the sum of squares of the errors between the model response and the observations. A model response can be either a linear or a nonlinear function of the model parameters. Nonlinear problems, using the Taylor series expansion, can be converted to linear problems. The least-squares approximation in estimation of the unknown model parame ters is one of the methods used in inversion. Many geophysical model responses are nonlinear func tions of the model parameters. The Marquardt-Levenberg approach provides a power full and sufficient method to esti mate the unknown model parameters in an iterative manner. In this study, the forward and inverse solutions of the traveltime data of critically refracted waves have been considered. For this purpose, a procedure for forward solution of the traveltime data has been derived by using the Shell's Law and the Fermat's Principle along with the ray tracing method, and then, an iterative inversion tech nique has been developed for the inverse solution of the traveltime data. The algorithm for forward solution assumes that the irregular refractor surface consists of a set of planar and VIIdipping segments. Each segment is independent of the others. It is also assumed that the refractor surface is continuous in physical manner even though it is considered as being consisted of several segmental surfaces. The algorithm of the forward solution for single layer case for which the arrival times of refracted waves have been computed considers the following the initial and boundary conditions: - The topography of the refractor surface is continu ous almost everywhere in physical sense. - The refractor surface is a homogeneous and isotropic medi urn. - Each raypath between every source-detector pair is independent of the others; hence, the ray-tracing is not greatly affected by gross errors in the neighboring source- detector pairs data. - Overburden velocity is constant everywhere, and is less than the refractor velocity. - The refractor medium can contain lateral velocity di scant i nui ti es. This algorithm is suitable for computer applications. In this study, for single-layer case, an iterative inversion technique has been applied to reversed shooting seismic refraction data collected by in-line profiling. The iterative inversion technique used in the present study is based on ray tracing in homogeneous and isotropic media. The assumptions used in forward modelling are also applicable in inversion procedure. The unknown parameters which should be estimated by the inversion process are the depths to the refractor beneath each geophone, and the velocity of the semi -infinite medium below the refractor. Since, we have used ray tracing to compute the t ravel t i me of seismic waves, the algorithm is also suitable in general to the case of existence of lateral velocity changes. However, in constructing our synthetic models, we have only used homogeneous top layer with constant velocity. Certainly, the method can be applied to both P and S wave refraction data. Under these considerations, a velocity-depth func tion has been derived, and Damped Least-Square Inversion technique which is also known as the Marquardt's Algorithm has been applied to estimate the model parameters. The unknown parameters which are vertical depths to refractor, and the refractor velocity are the components of the para meter vector. The number of obsevations exceeds the number VIIIof unknown parameters, e.g., the linearised system of equa tions is over deter mined. The optimum solution in least-squ ares sense can be obtained minimizing the sum of squares of the differences between model response and the observed data. The inversion technique has been applied to two different set of data. The first set of data are the synthetic travel time data for several irregularly-shaped single-layer models following the forward modelling technique. The second set of data is the actual field data borrowed from Belirti Eng. & Consulting Co. The experiments done with several data sets indicate that the geological models derived from inversion procedure are consistent with those constructed for forward modelling. Similarly, comparison of the results of the inversion with those obtained by the Generalized Reciprocal Method showed that they are very similar. However, if the refractor surface is quite rough and the velocity contrast between the overburden and the ref ractor velocity is low, it might be difficult to find reli able solution. The following results have been obtained from the results of tests undertaken on both synthetic and actual field data: - The inversion technique used in the present study is an iterative technique. As a result, it requires ini tial values for the parameter vector components. - It assumes that the refractor surface between two points, on which the refracted rays emerge to arrive to two consecutive detectors, is planar; hence, it smoothes out the irregularity on the refractor surface. - Eaeh raypath between every source-detector pairs is independent of the others. - It can be only applied to the reversed travel time data. - The algorithm used in the present study has been developed for single layer case. The basic theory, however, is suitable for multilayered case. On the other hand, in order to handle this problem, the Jacobian matrix of the system of linear equations has to be constructed accordingly. - Apparent dips of the refractor, on which the refrac ted rays emerge to arrive to the detectors, are computed from traveltime data by use of refractor velocity which is estimated in the iteration steps. These parameters are the quantities that are modified during the iterative process. IX- The problems associated with low-velocity layer and hidden layer in the medium can not be solved by the present technique. - The effect of ambient noise on the inversion process has been investigated. The results on noise added travel - time data indicated that the convergence of the iterative solution is not affected by the noise. However, we have obtained a noisy interface topography coherent with the noisy data. It is our opinion that it is going to be very useful if the present approach is extended to apply to multilayered case. And, in addition, we also believe that more sophis ticated algorithms can be developed to perform near-surface seismic tomography to investigate the lateral changes in lithology, texture and the structure for engineering appli cations. X