Karşılıklı kuyu yer radarı verilerinin modellenmesi

Year 2016, Volume: 22 Issue: 6, 581 - 596, 20.12.2016

Çağlayan Balkaya , Gökhan Göktürkler

Abstract

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.

Keywords

Eikonal çözücü, Modelleme, Karşılıklı kuyu, Seyahat zamanı, Sonlu farklar, Yer radarı

Modeling of crosshole ground-penetrating radar data

Abstract

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, first-arrival
traveltimes being essential for tomographic inversion of crosshole GPR data
sets were calculated by a finite-difference time-domain (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 low- and 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.

Keywords

Eikonal solver, Modeling, Crosshole, Traveltime, Finite differences, Ground-penetrating radar

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