Jeodezik ölçüler ile deprem kaynak mekanizması ilişkisi için belirli varsayımlar altında fonksiyonel ilişkiler kurulabilir. Bu şekilde belirli bir fay geometrisi ve kayma değerleri kullanarak yüzeyde meydana gelen yer değiştirmeleri “direkt modelleme” ile hesaplamak olanaklıdır. Ancak jeodezik ölçüler ile yüzeyde hesaplanan yer değiştirmelere en iyi uyan fay geometrisi ve kayma değerlerinin bulunması için karmaşık analitik ilişkiler yanında gelişmiş optimizasyon yöntemlerine ihtiyaç duyulmaktadır. Fay geometrisi ve kayma vektörünün yüzeyde gerçekleştirilen ölçüler yardımıyla bulunması “ters modelleme” olarak adlandırılmakta olup, söz konusu ilişkiyi sağlayan fonksiyon çok sayıda yerel minimuma sahiptir. Parametrelere ait başlangıç değerlerinin iyi bilinmediği durumlarda ters modelleme ile tümel minimum elde edilememektedir. Jeolojik yüzey gözlemleri ve jeofizik odak mekanizması çözümleri, fay geometrisi ve kayma vektörüne ilişkin belirli doğrulukta başlangıç değerleri sağlamakla birlikte özellikle yüzey kırıklarının gelişmediği ve sismik ağların sık olmadığı göreli olarak küçük depremlerde fay geometrisi ve kayma vektörüne ilişkin yeterli doğrulukta bilgi mevcut olmamaktadır. Bu çalışmada ters modelleme için uygun yöntem araştırması yapılmış, geliştirilen yazılım araçları yardımıyla en uygun olduğu değerlendirilen “benzetimli yaklaşım” yöntemi 17 Ağustos 1999 İzmit Depremi için test edilmiştir. Elde edilen sonuçlar farklı gruplarca yapılan çözümlerle karşılaştırıldığında bulunan fay geometrisi ve kayma değerlerinin jeodezik ölçüler ile bulunan yüzey yer değiştirme değerlerine diğer mevcut çalışmalardan daha iyi uyum sağladığı görülmüş-tür. Jeodezik yüzey ölçüleri ile yapılan ters çözümlerde özellikle başlangıç değerlerinin iyi bilinmediği durumlarda kullanılan optimizasyon yönteminin daha fazla önem kazandığı değerlendirilmektedir.

Functional relations can be established between geodetic observations and earthquake source mechanism under certain assumptions. In this way, it is possible to compute surface displacements with direct modeling using certain fault geometry and slip values. However, computation of fault geometry and slip values which best fit to the surface displacements requires advanced optimization methods together with complicated analytical functions. Although, geological surface observations and seismic focal mechanism solutions provide first-order information about fault geometry and slip vector, they are particularly inadequate for relatively small earthquakes where no surface ruptures are formed and seismic networks are not sufficiently dense. For this type of inversion situations, classical parameter estimation methods such as least-squares and derivative-based optimization methods may fail depending on the a priori values of parameters and produce local estimates of a global optimization problem. Monte-Carlo methods which have been in use for years in other fields of engineering are quite slow for large optimization problems. However, statistical mechanisms behind such methods are particularly useful for investigating complicated problems which intrinsically contain many local minima. In such cases, these heuristic methods provide sufficient convergence when iteration number is kept high. Other methods such as exhaustive searches or grid approximations prove to be inefficient when number of parameters is more than three. This study employs Simulated Annealing for determining fault geometry parameters from a set of surface geodetic observations. In this method, Monte-Carlo runs are controlled by a parameter called critical temperature. When the cost is lower than the previous iteration, new set of parameters are always accepted while the cost is higher than the previous iteration new set of parameters are only accepted if the temperature is sufficiently cool. Critical temperature decreases with according the pre-assumed probability distribution. In terms of inverting geodetic observations for fault parameters, a standard normal distribution was found to be sufficiently efficient. This procedure is analogous to cooling of metals after being exposed to high temperature heat which gives the name of the algorithm. Determination and modeling of seismic displacements can be considered a two-fold phenomenon. One is dispersing such effects from geodetic networks and the other one is quantifying the effects of earthquakes at cm level precision which are inevitable for Turkey and presenting them as input to the other disciplines. Turkish National Horizontal Control Network (TNHCN) has been serving surveying community for more than half a century. However, seismic deformations of 20th century are predicted to have distorted the network up to 10 meters. Considering the relatively less geometrical precision, TNHCN is often regarded as inappropriate for demanding applications. Nevertheless, most cadastral maps and other plans are expressed in TNHCN and TNHCN has to be accurate at a specified level. İzmit Earthquake which occurred on August 17th, 1999 has been an interest of geosciences community for years. While the efforts to quantify the related deformation was mostly focused on the geodynamical aspects of surface deformation. Considering that the region of earthquake is a dense population area involving intensive cadastral applications, deformation of geodetic networks due to earthquakes is an equally important topic. Restoration and re-organization studies which immediately begin after an earthquake need a well-maintained geodetic re-infrastructure which is also subject to displacements of a few meters.In this study, possible methods of inverse modeling using various geodetic observations ranging from Global Positioning System to high-precision spirit leveling were investigated and simulated annealing, which is considered the most appropriate method, was tested for 1999 İzmit Earthquake, using the software tools developed within the study. Comparison of results with other studies shows that vertical components are noisier in terms of dynamical modeling than horizontal components up to an order of ten implying non-earthquake vertical deformation. Results also reveal that computed fault geometry and slip values fit geodetic surface displacements are largely dependent on the optimization method. A new set of fault geometry and slip parameters for İzmit Earthquake are considered to better fit to the data than any other available studies.