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I propose a two component analytic formula $F(s,t)=F^{(1)}(s,t)+F^{(2)}(s,t)$for $(ab\rightarrow ab) +(a\bar{b}\rightarrow a\bar{b})$ scattering at energies$\ge 100 GeV$ ,where $s,t$ denote squares of c.m. energy and momentumtransfer.It saturates the Froissart-Martin bound and obeysAuberson-Kinoshita-Martin (AKM) \cite{AKM1971} scaling. I choose $ImF^{(1)}(s,0)+Im F^{(2)}(s,0)$ as given by Particle Data Group (PDG) fits tototal cross sections. The PDG formula is extended to non-zero momentumtransfers using partial waves of $Im F^{(1)}$ and $Im F^{(2)}$ motivated byPomeron pole and 'grey disk' amplitudes . $Re F(s,t)$ is deduced from realanalyticity: I prove that $Re F(s,t)/ImF(s,0) \rightarrow (\pi/\ln{s}) d/d\tau(\tau Im F(s,t)/ImF(s,0) )$ for $s\rightarrow \infty$ with $\tau=t (ln s)^2$fixed, and apply it to $F^{(2)}$.Using also the forward slope fit bySchegelsky-Ryskin , the model gives real parts,differential cross sections for$(-t)<.3 GeV^2$, and inelastic cross sections in good agreement with data at$546 GeV, 1.8 TeV,7 TeV$ and $ 8 TeV $. It predicts for inelastic crosssections for $pp$ or $\bar{p} p$, $\sigma_{inel}=72.7\pm 1.0 mb$ at $7TeV$ and$74.2 \pm 1.0mb$ at $8 TeV$ in agreement with $pp$ Totem experimental values$73.1\pm 1.3 mb $ and $74.7\pm 1.7 mb$ respectively, and with Atlas values$71.3\pm 0.9 mb$ and $71.7\pm 0.7mb$ respectively. The predictions at $546 GeV$and $1800 GeV$ also agree with $\bar{p} p$ experimental results of Abe et al\cite{Abe} at $546 GeV$ and $1800 GeV$.  The model yields for $\sqrt{s}> 0.5 TeV$, with PDG2013 total cross sections ,and Schegelsky-Ryskin slopes as input, $\sigma_{inel} (s) =22.6 + .034 ln s +.158 (ln s)^2 mb , and \sigma_{inel} / \sigma_{tot} \rightarrow 0.56,s\rightarrow \infty ,$ where $s$ is in $GeV^2$

Pomeron pole plus grey disk model: real parts, inelastic cross sections and LHC data