GEOLOGY 724Quiz #3 (TAKE HOME)(100 points)Name: ____________________________________________________________1. (a) Write a finite difference approximation for the following equation using a Crank-Nicolson implicit approximation:(20 points)tcxcvxcDL22-2-(b) Write a fully implicit approximation for the following equation:(10 points)tcxcvxcDL22(c) Rewrite your finite difference equation in part b so that it is in the form appropriate for solving the equation using Gauss-Seidel iteration. Change your notation so that an “n” subscript represents the time level and an “m” superscript represents the iteration level.(10 points)-3-2. (a) Consider the mathematical model shown below. KRdxhdEGo2:..222Ro2022HxKLRxKRhoo0dxdhh = Ho(analytical solution for the water table) x = 0 x = LSuppose that the above steady-state model represents the state of the system at t = 0. Now, consider a transient simulation such that when t > 0, the head at x = 0 is decreased to HT and the recharge rate is decreased from Ro to RT. Write a mathematical model that describes the transient problem. Use mathematical symbols (not words) to describe the boundaries completely.(30 points)-4-(b) To compute a water balance check for the system in part (a) under transient conditions, we must consider inflows and outflows to and from the system. Describe the inflows andoutflows using representative mathematical expressions for each type of water flow. Put these mathematical expressions, along with a few words describing the nature of the inflow or outflow, in the appropriate column below.(20 points)INFLOWS OUTFLOWS3. Define Storage Coefficient:(5 points) Define Specific Storage:(5
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