A new method of solution of Hallén’s problem

1995 ◽  
Vol 36 (8) ◽  
pp. 4087-4099 ◽  
Author(s):  
G. Miano ◽  
L. Verolino ◽  
V. G. Vaccaro
Keyword(s):  
New Method ◽  
Method Of Solution

On the resolution of statics, structure, and residual normal moveout

Geophysics ◽  
1981 ◽  
Vol 46 (7) ◽  
pp. 984-993 ◽  
Author(s):  
Michael O. Marcoux
Keyword(s):  
White Noise ◽  
Explicit Solution ◽  
New Method ◽  
Two Dimensional ◽  
Static Structure ◽  
Spatial Variables ◽  
Practical Consequence ◽  
Common Depth Point ◽  
Method Of Solution ◽  
Selection Of

The problem of separation of reflection times into the component parts of source static, receiver static, structure time, and residual normal moveout (RNMO) is presented. A new solution is derived which is valid for wavelengths ranging from a group interval at the short end to a distance equal to the separation between the full‐fold positions at the long end. In the absence of RNMO, this solution, though not unique, is, however, optimum with regard to stability against noise in general. In the presence of RNMO, the solution is most stable against white noise. Additionally, it is concluded that the underconstrained nature of the problem is of minor practical consequence. The new method is based on the two‐dimensional (2-D) spectrum of the reflection times considered as a function of the spatial variables of common depth point (CDP) and offset. The resultant equations yield a simple, explicit solution for each separate wavelength. The computation is rapid and directly controllable by selection of the desired wavelengths. Synthetic examples are used to demonstrate the properties of this method of solution.

A new method of solution for one-dimensional quasi-neutral bounded plasmas

2010 ◽  
Vol 76 (3-4) ◽  
pp. 617-625 ◽  
Author(s):  
M. KAMRAN ◽  
S. KUHN
Keyword(s):  
Present Method ◽  
Analytic Solution ◽  
Ion Source ◽  
New Method ◽  
Ion Density ◽  
One Dimensional ◽  
Plasma Equation ◽  
Neutrality Condition ◽  
Bounded Plasma ◽  
Method Of Solution

AbstractA new method is proposed for calculating the potential distribution Φ(z) in a one-dimensional quasi-neutral bounded plasma; Φ(z) is assumed to satisfy a quasi-neutrality condition (plasma equation) of the form ni{Φ(z)} = ne(Φ), where the electron density ne is a given function of Φ and the ion density ni is expressed in terms of trajectory integrals of the ion kinetic equation. While previous methods relied on formally solving a global integral equation (Riemann, Phys. Plasmas, vol. 13, 2006, paper no. 013503; Kos et al., Phys. Plasmas, vol. 16, 2009, paper no. 093503), the present method is characterized by piecewise analytic solution of the plasma equation in reasonably small intervals of z. As a first concrete application, Φ(z) is found analytically through order z4 near the center of a collisionless Tonks–Langmuir discharge with a cold-ion source.

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