Method of accounting for wavelet stretch in seismic data

A method of accounting for angle-dependent wavelet stretch in seismic data, said method comprising:

• applying to the seismic data an operator that relates wavelet stretch to the cosine of a wavelet reflection angle, wherein the operator is expressed in the time domain as:
• ∂
• t
• ∂
• τ
• ⁢
• |
• x
• =
• cos
• ⁡
• (
• θ
• )
• wherein ∂τ is the vertical time difference between two seismic events at an offset distance of zero, ∂t is the vertical time difference between the two seismic events at an offset distance of x, and θ is the wavelet reflection angle measured between a seismic ray and a line normal to a subsurface reflector reflecting the ray at an offset distance of x.

A method of accounting for angle-dependent wavelet stretch in seismic data, said method comprising:

• applying to the seismic data an operator that relates wavelet stretch to the cosine of a wavelet reflection angle, wherein said applying of the operator includes using the operator to correct angle-dependent wavelet stretch resulting from prestack processing of the seismic data, wherein the operator directly relates a wavelet stretch factor to the cosine of the wavelet reflection angle, and wherein the wavelet stretch factor is expressed in the time domain as:
• ∂
• t
• ∂
• τ
• ⁢
• |
• x
• wherein ∂τ is the vertical time difference between two seismic events at an offset distance of zero and ∂t is the vertical time difference between the two seismic events at an offset distance of x.

A method of accounting for angle-dependent wavelet stretch in seismic data, said method comprising:

• applying to the seismic data an operator that relates wavelet stretch to the cosine of a wavelet reflection angle, wherein said applying of the operator includes using the operator to correct angle-dependent wavelet stretch resulting from prestack processing of the seismic data, wherein the operator is expressed in the time domain as:
• ∂
• t
• ∂
• τ
• ⁢
• |
• x
• =
• cos
• ⁡
• (
• θ
• )
• wherein ∂τ is the vertical time difference between two seismic events at an offset distance of zero, ∂t is the vertical time difference between the two seismic events at an offset distance of x, and θ is the wavelet reflection angle measured between a seismic ray and a line normal to a subsurface reflector reflecting the ray at an offset distance of x.

A method of accounting for angle-dependent wavelet stretch in seismic data having a plurality of wavelets, said method comprising:

• (a) determining reflection angles for the wavelets;
• (b) processing the seismic data such that the wavelets are subject to angle-dependent wavelet stretch;
• (c) utilizing an operator to calculate a wavelet stretch factor for at least one wavelet based on the cosine of the wavelet's reflection angle;
• (d) applying the wavelet stretch factor to each corresponding wavelet in the seismic data to correct angle-dependent wavelet stretching;
• and
• (e) after step (d), applying a high-cut frequency filter to the seismic data to prevent amplification of noise at high frequencies.

A method of accounting for angle-dependent wavelet stretch in seismic data having a plurality of wavelets, said method comprising:

• (a) determining reflection angles for the wavelets;
• (b) processing the seismic data such that the wavelets are subject to angle-dependent wavelet stretch;
• (c) utilizing an operator to calculate a wavelet stretch factor for at least one wavelet based on the cosine of the wavelet's reflection angle;
• and
• (d) applying the wavelet stretch factor to each corresponding wavelet in the seismic data to correct angle-dependent wavelet stretching,
• wherein the wavelet stretch factor is expressed in the time domain as:
• ∂
• t
• ∂
• τ
• ⁢
• |
• x
• wherein ∂τ is the vertical time difference between two seismic events at an offset distance of zero and ∂t is the vertical time difference between the two seismic events at an offset distance of x.

A method of accounting for angle-dependent wavelet stretch in seismic data having a plurality of wavelets, said method comprising:

• (a) determining reflection angles for the wavelets;
• (b) processing the seismic data such that the wavelets are subject to angle-dependent wavelet stretch;
• (c) utilizing an operator to calculate a wavelet stretch factor for at least one wavelet based on the cosine of the wavelet's reflection angle and utilizing the operator to determine a stretched wavelet from the estimated unstretched wavelet based on the cosine of the wavelet reflection angle;
• and
• (d) applying the wavelet stretch factor to each corresponding wavelet in the seismic data to correct angle-dependent wave let stretching,
• wherein the operator utilizes a filter to transform the stretched wavelet into the unstretched wavelet, and
• wherein the filter is represented in the frequency domain as:
• (cos θ)V(ω)/V(ω/[cos θ])
• wherein θ is the wavelet reflection angle measured between a seismic ray and a line normal to a subsurface reflector reflecting the ray and V(ω) represents the estimated unstretched wavelet in the frequency domain.