Seismic Reflection — Source Gather Geometry, Multi-Layer Arrivals and Multiple Suppression: 18-Geol-A7 Applied Geophysics, December 2018, Q10

Question 10: Seismic Reflection — Source Gather Geometry, Multi-Layer Arrivals and Multiple Suppression (16.66% of paper)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Source and sensor layout. A single source is placed at the centre of a symmetric "split spread" of geophones extending an equal distance to either side; every geophone records the shot simultaneously, giving a source gather in which travel time is plotted as a function of offset on both sides of the source.

Split-spread source gather over three horizontal layers (layer 3 is the underlying half-space, so there are two reflecting interfaces): symmetric reflected raypaths from the layer 1/2 interface (red) and layer 2/3 interface (blue) to geophones on either side of the source.

Reflected arrivals for three horizontal layers. For each of the two reflecting interfaces the two-way travel time as a function of offset $x$ follows a hyperbola,

$$t(x)=\sqrt{t_0^2+\dfrac{x^2}{V_{rms}^2}}$$

where $t_0$ is the zero-offset (vertical) two-way time to that interface and $V_{rms}$ is the root-mean-square velocity of the layers above it. Because the deeper (layer 2/3) interface has a larger $t_0$ and generally a higher overlying $V_{rms}$, its hyperbola sits below and is flatter (less moveout with offset) than the shallower (layer 1/2) interface's hyperbola; being a split spread, both hyperbolas are symmetric about $x=0$ at the source.

Two-way travel time (increasing downward, seismic convention) vs. offset for the source gather: symmetric hyperbolas, one per interface, flattening and deepening with depth.

Multiples. A multiple is energy that has reflected more than once before reaching a receiver. A surface (long-path) multiple, such as a marine water-bottom multiple, reverberates between the free surface and a strong reflector (e.g. the seabed) one or more extra times, arriving at close to an integer multiple of that reflector's primary zero-offset time. A peg-leg multiple takes one short extra bounce within a shallow layer (e.g. the water layer, or between the top and base of a hard limestone bed) on the way to or from a deeper reflector, so it arrives a little after that deeper primary. An interbed multiple bounces between two internal strong reflectors (e.g. a coal seam and an overlying limestone) and can closely mimic — and be mistaken for — a genuine deeper primary reflection.

Multiples (schematic): primary reflection from the deep interface (solid); a first-order surface multiple of the shallow interface (red dashed) that reflects off it twice with an extra bounce at the surface, arriving at about twice that primary's zero-offset time; and a peg-leg multiple (blue dashed) with one extra short bounce between the two interfaces, arriving just after the deep primary.

Suppression. Multiples are attenuated during processing by exploiting the two properties in which they differ from primaries. Predictive deconvolution exploits their periodic timing (surface and peg-leg multiples repeat at a regular period set by the two-way time in the reverberating layer) to predict and subtract the repeating energy. Radon-transform (moveout-based) demultiple exploits the fact that, having travelled through more of the shallow, lower-velocity section per unit depth, a multiple has a distinctly different (typically lower) stacking velocity than the primary at the same travel time, so after NMO correction with the primary velocity the multiple is under- or over-corrected and separable in the velocity/offset (Radon) domain, where it can be muted before being transformed back. Finally, simple CMP stacking itself provides partial multiple attenuation, since a multiple imperfectly flattened by the primary's NMO velocity destructively interferes across the offset range of the gather, while the correctly-flattened primary stacks constructively.

Circumstances for use. Reflection surveying is used wherever detailed imaging of layered structure at depth is required — hydrocarbon and coal exploration and reservoir characterization, deep crustal/tectonic studies, and geotechnically for mapping bedrock structure, fault zones or buried channels too deep or geologically complex for refraction's simpler layered-velocity assumptions to resolve; its higher cost and more elaborate acquisition/processing are justified whenever fine structural or stratigraphic detail, not just a single depth-to-bedrock number, is the actual objective.

Concept & Theory

Topic. Split-spread reflection source-gather geometry, hyperbolic multi-layer reflection moveout, and multiple identification/suppression.

Key relations. Reflection moveout $t(x)=\sqrt{t_0^2+x^2/V_{rms}^2}$; multiples separated from primaries by differential (typically lower) stacking velocity and/or periodic arrival timing.

Why this works. A multiple necessarily travels through more of the (generally slower) shallow section per unit of two-way time than a primary reaching the same time from directly below, which is exactly the velocity difference that Radon-domain demultiple and stacking itself exploit to attenuate it.

Common pitfall. Picking stacking velocity purely to flatten the strongest hyperbola in a gather without checking for multiple contamination — a well-developed multiple can present a coherent hyperbola of its own and be mistaken for, or bias the velocity pick away from, the true primary.

Source. Telford, Geldart & Sheriff, Applied Geophysics, Ch. 4 (seismic reflection).

Question 10 of 10: Seismic Reflection — Source Gather Geometry, Multi-Layer Arrivals and Multiple Suppression

Question 10: Seismic Reflection — Source Gather Geometry, Multi-Layer Arrivals and Multiple Suppression (16.66% of paper)