Gökhan Göktürkler

Inversion of self-potential anomalies caused by simple-geometry bodies using global optimization algorithms

Three naturally inspired meta-heuristic algorithms—the genetic algorithm (GA), simulated annealing (SA) and particle swarm optimization (PSO)—were used to invert some of the self-potential (SP) anomalies originated by some polarized bodies with simple geometries. Both synthetic and field data sets were considered. The tests with the synthetic data comprised of the solutions with both noise-free and noisy data; in the tests with the field data some SP anomalies observed over a copper belt (India), graphite deposits (Germany) and metallic sulfide (Turkey) were inverted. The model parameters included the electric dipole moment, polarization angle, depth, shape factor and origin of the anomaly. The estimated parameters were compared with those from previous studies using various optimization algorithms, mainly least-squares approaches, on the same data sets. During the test studies the solutions by GA, PSO and SA were characterized as being consistent with each other; a good starting model was not a requirement to reach the global minimum. It can be concluded that the global optimization algorithms considered in this study were able to yield compatible solutions with those from widely used local optimization algorithms.

3D resistivity imaging from an archaeological site in south-western Anatolia, Turkey: a case study

A large-scale resistivity imaging survey was performed in the acropolis area of Archaic Cnidos, south-western Turkey. This survey was a part of the geophysical studies conducted between 1999 and 2004. Two-dimensional resistivity data were acquired along a number of parallel lines using a pole–pole array. The data was processed using a 3D inversion algorithm based on a robust technique. We also applied shaded-relief processing to enhance the representation of the images of apparent-resistivity data and inversion results. In addition, the inverted resistivity data were visualized by a volumetric representation technique to display both the horizontal and the vertical extents of the archaeological structures. The inversion results revealed that a rectangular gridding pattern and a dense structuring existed in the depth range 0.35–1.5 m in the acropolis. Moreover, the bedrock was the base of the archaeological structures in the area. Based on the resistivity survey, four test excavations were carried out in various localities in the acropolis in 2004. These excavations yielded results supporting those obtained by the resistivity inversion. This indicated that large-scale 3D resistivity imaging can be a useful tool in archaeological prospection.

A hybrid approach for tomographic inversion of crosshole seismic first-arrival times

A sequential hybrid approach was presented here to invert crosshole seismic first-arrival times. The proposed tomographic scheme combined a simple simulated annealing algorithm with a linearized smoothness-constrained least-squares inversion. The simulated annealing was implemented to obtain a background velocity distribution used by the linearized inversion for the initial guess. The linearized component was based on the functional description of traveltimes. This indicates a nonlinear function, the eikonal equation, providing traveltimes for a given slowness model. Thus an explicit ray tracing was not required by the linearized scheme. The velocity updates were obtained by a matrix inversion based on an iterative conjugate gradient-like LSQR algorithm. Second-difference regularization was used to stabilize the solutions. The Jacobian matrix giving the partial derivatives with respect to the model parameters was constructed by a finite-difference approximation based on the perturbation of the cell slowness. The traveltimes for both the hybrid and linearized schemes were calculated by a fast finite-difference eikonal solver. The hybrid scheme was tested by using both synthetic and field data sets based on the crosshole geometry. According to the tests studies, the tomograms resulted from the hybrid approach better imaged the subsurface velocity distribution. Also the hybrid optimization was characterized by quicker convergence rate than the conventional optimization based on only the linearized inversion. The tests with the synthetic data set also showed that the hybrid approach yielded a solution having lower rms residual, smaller Euclidean distance and lower relative errors in the cell velocities.

Mapping aquifer geometry using electrical resistivity tomography: a case study from Şanlıurfa, south-eastern Turkey

A shallow aquifer system was investigated with 2D electrical resistivity tomography (ERT) to determine the hydrogeological setting of the Balikli Lake region, Şanliurfa, Turkey. Many spring waters are found in the study area where groundwater flow paths merge and reach the surface. A recreation complex was planned near the Balikli Lake by the Municipality of Şanliurfa. Therefore, an ERT survey was carried out to reveal the subsurface characterization, particularly to investigate the possible shallow aquifer system beneath the recreation area. Consequently, 2D resistivity data along thirteen profiles were acquired in the study area and the data were inverted by a tomographic inversion technique. The conductive layers in the ERT results indicated a shallow aquifer zone probably related to a karstic environment. The high conductivity observed in this layer might be caused by pollution resulting from the industrial and domestic wastes of the residential areas. The high resistive bottom layer was considered to be the basement in the study area. The geometry of the shallow aquifer environment was confirmed by slicing maps obtained from the ERT data. To build the conceptual geological model, a 2D forward resistivity modelling study was also achieved after the inversion studies. The inversion parameters and borehole result underlie the background of the forward model. Field and synthetic data were compared to each other and tested in means of calculation of the misfits to determine the reliability of these models.

Seismic first-arrival tomography with functional description of traveltimes

A two-dimensional smoothness-constrained least-squares inversion scheme was applied to seismic first-arrival time data. The inversion scheme was based on the functional description of traveltimes; thus, it did not require a step of ray tracing, and traveltimes were obtained by a finite-difference eikonal solver. The Laplacian difference of cell slownesses was used for the smoothness constraint. Model velocities were obtained by matrix inversion including the QR decomposition and iterative LSQR method. The Jacobian matrix of the partial derivatives was constructed by a finite-difference approximation based on the perturbation of the cell slowness. Since the construction of the Jacobian matrix was the most time-consuming step of the inversion scheme, Broydens update was used for this matrix, and it was replaced by its numerical approximation obtained from Broydens method after the third iteration and for all subsequent iterations to expedite the inversion process. This significantly improved the computational performance of the scheme by reducing the computer time for the calculation of the Jacobian matrix. The algorithm was tested by using a number of synthetic and field data sets. The test studies included both surface seismic refraction and crosshole seismic data acquisition configurations. Also image appraisal analyses were performed for the solutions obtained from both surface and crosshole field data sets by calculating model covariance and model resolution matrices. The presented algorithm yielded satisfactory results during the test studies. The stability and fast convergence rate were the main characteristics of the algorithm.

A Comparison of Two Travel-time Tomography Schemes for Crosshole Radar Data: Eikonal-equation-based Inversion Versus Ray-based Inversion

Some test studies were performed for comparison of two travel-time inversion schemes for tomographic evaluation of crosshole ground-penetrating radar (GPR) data. The first scheme was a linearized inversion based on Tikhonov regularization (Method 1). In this scheme, ray tracing was not a part of the inversion algorithm and the Jacobian matrix was calculated by numerical differentiation. Travel-time calculations were performed by a finite-difference eikonal equation solver. Model velocity fields were updated by matrix inversion techniques using iterative conjugate gradient solvers. The inversion process was stabilized by a smoothness-constrained regularization. The second scheme was based on a ray tracing algorithm (Method 2) and velocities were updated by a simultaneous iterative reconstruction technique (SIRT) using both straight- and curved-ray approximations. The test studies included synthetic travel-time data sets generated from the models with various velocity distributions. Broyden’s update was imp...

Modeling of crosshole ground-penetrating radar data

Uygulamalı jeofiziğin girişimsel olmayan elektromanyetik yöntemlerinden biri olan yer radarı sığ yeraltının oldukça yüksek çözünürlükle görüntülenmesi için yaygın olarak kullanılmaktadır. Bir yer radarı çalışmasında iki önemli unsur olan çözünürlük ve derinlik, zeminlerin su, kil, çözülebilir tuz içeriklerinden ve antenin merkez frekansından etkilenir. Elektriksel iletkenliğin yüksek olduğu alanlarda istenilen çözünürlük ve hedeflenen derinlikte iyi bir yeraltı görüntüsü elde etmek zor olabilir. Bu nedenle, karşılıklı kuyu dizilimine dayanan bir yer radarı çalışması daha detaylı bir yeraltı radar hız dağılımının elde edilmesi için iyi bir alternatif yaklaşım olabilir. Bu çalışmada, karşılıklı kuyu yer radarı veri kümelerinin tomografik ters çözümü için gerekli olan ilk varış seyahat süreleri Maxwell denklemlerinin zaman ortamı sonlu farklar ve gridlenmiş bir hız alanı boyunca Eikonal denkleminin sonlu farklar çözümünden hesaplanmıştır. Modellemede iki kuramsal yeraltı modeli kullanılmıştır. İlk modelde yeraltı iki tabakadan oluşmaktadır. İkinci model tekdüze bir ortam içerisinde gömülü düşük ve yüksek hızlı bloklar içermektedir. Yer-hava arayüzeyinin modellemedeki etkisi ve bir kuyu içi radar çalışmasında kuyuların derinliği ve mesafesi arasındaki oranının önemi test çalışmalarında gösterilmiştir. Tüm alıcı konumlarında zamanda kaydedilmiş elektrik alanın düşey bileşenini (Ez) içeren radargramlar zaman ortamı sonlu farklar modellemesinden elde edilmiştir. Farklı derinlikteki kaynak konumları için seyahat süresi kontur haritaları hızlı bir sonlu farklar Eikonal çözücüsünden elde edilmiştir. Daha sonra, minimum seyahat süresine sahip ışın yolları alıcıdan kaynağa en dik iniş doğrultusunda izlenerek hesaplanmıştır. Sonuç olarak, her iki modelleme yaklaşımından elde edilen seyahat süreleri birbirleriyle oldukça uyumludur. Zaman ortamı sonlu farklar modellemesi ilk varışlarla ilişkili dalga fazlarının belirlenmesi ve değerlendirilmesi için önemli bir araçtır. Diğer taraftan, Eikonal denklemi temelli modelleme ilk varış sürelerinin doğrudan hesaplanması için oldukça etkili bir yaklaşım sunmaktadır. The ground-penetrating radar (GPR) that is one of the non-invasive electromagnetic methods of applied geophysics is widely used to image shallow subsurface with extremely high resolution. The resolution and depth being two important aspects in a GPR survey are affected by the water, clay, soluble salt contents of soils and the center frequency of antenna. It may be difficult to obtain a good subsurface image at desired resolution and targeted depth in the areas characterized by high electrical conductivity. Therefore, a GPR survey based on the crosshole configuration can be a good alternative approach to achieve more detailed subsurface radar velocity distribution. In this study, firstarrival traveltimes being essential for tomographic inversion of crosshole GPR data sets were calculated by a finite-difference timedomain (FDTD) solutions of Maxwell’s equations and finite-difference solution of the Eikonal equation throughout a gridded velocity field. Two theoretical subsurface models were used in modeling. In the first model, the subsurface divided into two layers. The second model includes lowand high-velocity blocks embedded in a homogenous medium. The effect of ground-air interface in modeling and the importance of the ratio between separation and depth of boreholes in a crosshole radar survey were also shown during the test studies. Radargrams consisting of the vertical component of the electric field (Ez) recorded in time at the entire receiver locations were acquired from FDTD modeling. Traveltime contour maps for source locations with different depths were obtained from a fast finite-difference Eikonal solver. Raypaths having the minimum traveltime were then calculated by following the steepest gradient direction from the receiver to the transmitter. As a result, the first-arrival traveltimes obtained from both modeling approaches are quite compatible with each other. FDTD modeling is an important tool to determine and evaluate of the wave phases corresponding to the first arriving wave. On the other hand, Eikonal-equation-based modeling presents an approach being highly effective for directly computing first-arrival traveltimes.