From Impedance to Reflectivity
Learning objectives
- Write the normal-incidence reflection coefficient in terms of impedance
- See that a reflection comes from a contrast in impedance, not impedance itself
- Read the sign of a reflection: hard (positive) versus soft (negative)
- Recognise that equal impedance across a boundary gives no reflection
Where a Reflection Comes From
The convolutional model has two ingredients: a reflectivity series and a wavelet. This section builds the first one. A seismic reflection is created at a boundary where acoustic impedance changes. Impedance is , density times velocity, and at a boundary between a layer of impedance over a layer of impedance the normal-incidence reflection coefficient is
Read that equation carefully, because it is the whole idea. The reflection depends on the difference . A thick, uniform, high-impedance rock reflects nothing from its interior; it is only where impedance jumps that energy comes back.
Reading the Spikes
Edit the impedance profile and three things become clear. First, the sign: when the lower layer is harder (higher impedance) the coefficient is positive, a hard kick; when it is softer the coefficient is negative, a soft kick, and this sign is exactly the polarity you would pick on a trace. Second, the size: bigger contrasts give bigger spikes. Third, and most important, set two adjacent layers to the same impedance and the spike vanishes to zero however large that impedance is. No contrast, no reflection.
The result is a reflectivity series, a spike at every interface with a height and sign set by the contrast there. It is the earth reduced to exactly what normal-incidence seismic responds to. In the next section this spike series meets the wavelet, and their convolution is the synthetic trace.