Try something like
ContourPlot[1/((x - 1500)^2 + (y - 1200)^2) + 1/((x - 1550)^2 + (y - 2000)^2) +
1/((x - 2000)^2 + (y - 1700)^2), {x, 0, 3000}, {y, 0, 3000}]
the peak is not so sharp in the given picture, so it looks rather like
ContourPlot[Log[1/((x - 1500)^2 + (y - 1200)^2)] +
Log[1/((x - 1550)^2 + (y - 2000)^2)] +
Log[1/((x - 2000)^2 + (y - 1700)^2)], {x, 0, 3000}, {y, 0, 3000},
PlotPoints -> 50]
but if you prescribe the contours
ContourPlot[
Log[1/((x - 1500)^2 + (y - 1200)^2)] +
Log[1/((x - 1550)^2 + (y - 2000)^2)] +
Log[1/((x - 2000)^2 + (y - 1700)^2)], {x, 0, 3000}, {y, 0, 3000},
PlotPoints -> 50, Contours -> Range[40, 80, 5]]
you see, that it's not the Log because the result is mono-colored.
