I want to draw the diagram on the left in the following image using tikz. Till now I have been able to draw the diagram on the right hand side using the code given below. What I want to do is to cut out the lower half of this diagram and construct a semicircle in the bottom half such that the curved lines start from the boundary of the semicircle.
Along with this major change I would like bold arrow tips on these curved lines and the origin of these lines on the semicircle to be marked with a cross. Thanks. 
\documentclass[convert]{standalone} \usepackage{tikz} \usetikzlibrary{decorations.pathmorphing} \usetikzlibrary{calc} \usetikzlibrary{arrows,decorations.markings} \begin{document} \begin{tikzpicture} \node (I) at ( 4,0) {}; \node (II) at (-4,0) {}; \node (III) at (0, 2.5) {}; \node (IV) at (0,-2.5) {}; \path (II) +(90:4) coordinate[label=90:] (IItop) +(-90:4) coordinate[label=-90:] (IIbot) +(0:4) coordinate (IIright) +(180:4) coordinate[label=180:] (IIleft); \draw (IItop) -- node[midway, below] {} (IIright) -- (IIbot); \draw (IItop) -- (IIbot); \path (I) +(90:4) coordinate (Itop) +(-90:4) coordinate (Ibot) +(180:4) coordinate (Ileft) +(0:4) coordinate (Iright) ; \draw (Ileft) -- node[midway, below] {}(Itop) -- (Ibot) -- (Ileft) -- cycle; \draw[decorate,decoration=zigzag, red, thick] (IItop) -- (Itop) node[midway, above, inner sep=2mm] {}; \draw[decorate,decoration=zigzag, red, thick] (IIbot) -- (Ibot) node[midway, below, inner sep=2mm] {}; \draw[blue, thick] ($(Itop)!.5!(Ileft)$) to[out=210, in=-30, looseness=1.3] ($(IItop)!.5!(IIright)$); \draw[violet, thick] ($(Itop)!.3!(Ileft)$) to[out=210, in=-30, looseness=1.3] ($(IItop)!.3!(IIright)$); \draw[->][magenta] ($(Ibot)!.63!(IIbot)$) to[out=150, in=250, looseness=1.1] ($(Itop)!.60!(IItop)$); \draw[->][orange] ($(Ibot)!.63!(IIbot)$) to[out=110, in=210, looseness=1.05] ($(Itop)!.65!(IItop)$); \draw[fill] ($(Itop)!.5!(Ileft)$) circle [radius=0.05]; \draw[fill] ($(IItop)!.5!(IIright)$) circle [radius=0.05]; \draw[fill] ($(Itop)!.3!(Ileft)$) circle [radius=0.05]; \draw[fill] ($(IItop)!.3!(IIright)$) circle [radius=0.05]; \end{tikzpicture} \end{document} 