Absorption decreases the amplitude of waves propagating in the earth. In ad
dition, it narrows the bandwidth and modifies the phase. Obtaining true-amp
litude migration and acceptable resolution in dissipative media requires a
migration algorithm that corrects these effects. To achieve this, a reverse
-time prestack depth migration technique is used. This uses a stable amplif
ying finite-difference wavefield extrapolation that compensates for the att
enuating propagation of the wavefields in the real earth. Numerical tests o
n synthetic VSP data illustrate how dissipation destroys the amplitude, pha
se and resolution in the migration images, and how our algorithm corrects t
hese effects. The tests also show that the method is stable with respect to
noise, and does not require a very detailed macro-model for dissipation.