Attenuation¶

Power-law tissue attenuation is applied as a causal frequency-domain transfer function multiplied onto the (lossless) SIR spectrum — absorption plus the Kramers-Kronig dispersion phase, so waveforms stay causal. The SIR kernel itself is never modified.

sim = Emission(tx, fs=200e6, excitation=exc,
               alpha0=0.5,      # dB/(MHz^y · cm) — clinical convention
               freq_power=1.1)  # power-law exponent y (tissue 1.0–1.3)
p, coords = sim(field_points, method="auto")

Parameter	Meaning
`alpha0`	Attenuation coefficient in dB/(MHz`^y`·cm); `None` disables it
`freq_power`	Power-law exponent `y` (1.0 = linear-with-frequency)
`fast_attenuation`	`True` uses transducer-centre distance (fast); `False` per-element origin (accurate near-field, slower)

CW field with brain attenuation

Works in monochromatic (amplitude decay at fc) and transient (full spectral distortion) modes, and per-patch one-way in reception. See Example 11 — CW with Attenuation.