  Dependence of $a/r_c$ (inverse Sommer parameter in units of lattice spacing
$a$) on $am_q$ (quark mass in lattice unit) has been observed in all lattice
QCD simulations with sea quarks including the ones with improved actions. How
much of this dependence is a scaling violation has remained an intriguing
question. Our approach has been to investigate the issue with an action with
known lattice artifacts, i.e., the standard Wilson quark and gauge action with
$\beta=5.6$ and 2 degenerate flavors of sea quarks on $ 16^3 \times 32 $
lattices. In order to study in detail the sea quark mass dependence,
measurements are carried out at eight values of the Wilson hopping parameter
$\kappa$ in the range 0.156 - 0.158 corresponding to PCAC quark mass values
$am_q$ from about 0.07 to below 0.015. We analyze the static potential by
fitting to the familiar phenomenological form and extract $a/r_c$. Though
scaling violations may indeed be present for relatively large $am_q$, a
consistent scenario at sufficiently small $am_q$ seems to emerge in the
mass-independent scheme where for a fixed $\beta$, $1/r_0$ and $\sqrt{\sigma}$
have linear dependence on $m_q$ as physical effects similar to the quark mass
dependence of the rho mass. We present evidence for this scenario and
accordingly extract the lattice scale $a$ by chiral extrapolation to the
physical point. Care has been exercised to determine optimal values of all
fitting parameters and accuracy of the chiral extrapolation. An independent
determination of the scale $a$ by chiral extrapolation of the rho mass is
consistent with the scale obtained above ($a$ = 0.08041(12)(77) fm, $a^{-1}$ =
2.454(4)(23) GeV).
