--- title: "Seismic Reflections II: Beyond the Flat-Layer Model" week: 3 lecture: 9 date: "2026-04-22" topic: "Dipping-layer travel time, multiples, diffractions, AVO, noise filtering, and deep learning processing" course_lo: ["LO-1", "LO-2", "LO-3", "LO-4", "LO-5", "LO-7"] learning_outcomes: ["LO-OUT-A", "LO-OUT-B", "LO-OUT-C", "LO-OUT-D", "LO-OUT-G", "LO-OUT-H"] open_sources: - "Lowrie & Fichtner 2020 Ch. 6 Β§6.5 (free via UW Libraries)" - "Sheriff & Geldart 1995 Ch. 4 Β§4.2, Ch. 6 Β§6.1 (cite only)" - "Shuey 1985 Geophysics doi:10.1190/1.1441936 (open)" - "Rutherford & Williams 1989 Geophysics doi:10.1190/1.1442696 (open)" --- # Seismic Reflections II: Beyond the Flat-Layer Model :::{seealso} πŸ“Š **Lecture slides** β€” open in new tab β†— ::: :::::{dropdown} Learning Objectives :color: primary :icon: target By the end of this lecture, students will be able to: - **[LO-9.1]** Derive the dipping-layer travel-time equation and explain how the asymmetric linear term in $x$ distinguishes dipping from flat-layer hyperbolas; compute up-dip and down-dip apparent velocities. - **[LO-9.2]** Identify the physical origin of multiple reflections, predict the TWTT and NMO velocity of a long-path surface multiple, and explain why NMO stacking alone cannot remove it. - **[LO-9.3]** Explain the Huygens-principle origin of diffraction hyperbolae, state the diffraction equation, and describe qualitatively what migration accomplishes. - **[LO-9.4]** Apply the Shuey approximation $R(\theta) \approx R(0) + G\sin^2\theta$; classify a reflection event into AVO Classes I–IV from the signs of intercept and gradient. - **[LO-9.5]** Explain the purpose of f–k velocity filtering for ground-roll suppression; describe the architecture and training strategy of a U-Net denoising model applied to seismic data. - **[LO-9.6]** Critically evaluate a claim that a deep-learning seismic denoiser has "recovered" true geology, identifying at least two failure modes. ::::: :::::{dropdown} Syllabus Alignment :color: secondary :icon: list-task | | | |---|---| | **Course LOs addressed** | LO-1 (multiples, diffractions, AVO physics), LO-2 (dipping-layer t-x math, Shuey coefficients), LO-3 (DMO concept, velocity analysis for dipping layers), LO-4 (flat-layer assumptions and when they break), LO-5 (figure generation in Lab 3), LO-7 (AI/ML tools evaluated critically) | | **Learning outcomes** | LO-OUT-A through D, G, H | | **Prior lecture** | Lecture 8 β€” Introduction to Seismic Reflection (flat-layer travel time, NMO, CMP stacking, velocity analysis) | | **Next lecture** | Lecture 10 β€” Migration & Velocity–Image Duality | | **Lab connection** | Lab 3 Part 6 (dipping-layer CMP gather; measure up-dip/down-dip velocities; apply f-k filter) | ::::: ## Prerequisites Students should be comfortable with Snell's law (Lecture 5), acoustic impedance, the normal-incidence reflection coefficient $R(0) = (Z_2-Z_1)/(Z_2+Z_1)$, and the flat-layer two-way travel-time hyperbola derived in Lecture 8. --- ## 1. From Ideal to Real: Five Assumptions That Fail In Lecture 8, the CMP stacking pipeline β€” sort, NMO correct, stack β€” produced a sharp zero-offset section from multi-offset data. That pipeline rested on five simplifying assumptions: 1. **Reflectors are horizontal** β€” the NMO hyperbola has no linear term in $x$ 2. **Only primary reflections** reach the receiver β€” every event in the gather is a single-bounce wave 3. **Reflecting interfaces are continuous** β€” reflections come from planar surfaces, not isolated point scatterers 4. **The recorded wavefield is noise-free** β€” no ground roll, no air blast, no source-generated surface waves 5. **Only travel times matter** β€” amplitudes are constant with offset None of these holds in a real survey. In the Cascadia accretionary wedge, fold-and-thrust structures produce reflectors dipping at 5–25Β°. Shallow water-bottom multiples dominate marine gathers. Fault-tip diffractions obscure thrust geometry. Ground roll overwhelms land data. And amplitude varies with incidence angle β€” carrying information about fluid content that travel times alone cannot provide. This lecture relaxes each assumption in turn. For every complication, we follow the same progression: > **Why it matters β†’ What breaks β†’ The math β†’ How to fix it** --- ## 2. Complication 1: Dipping Reflectors > **Assumption that fails:** *Reflectors are horizontal.* In the Cascadia accretionary wedge, fold-and-thrust structures produce reflectors dipping at 5–25Β°, invalidating the symmetric NMO hyperbola from Lecture 8. ### 2.1 Why It Matters: The Geometry of Dip A reflector dipping at angle $\delta$ from horizontal presents a different reflection geometry in the up-dip and down-dip directions from a common surface source. For **down-dip shooting** (receiver in the down-dip direction), each successive receiver is above a progressively deeper part of the reflector, and the two-way path increases faster than for a flat reflector at the same perpendicular depth $h$. For **up-dip shooting**, the receiver looks toward the shallower part of the reflector, shortening the two-way path. The result is an asymmetric travel-time curve: the same source–receiver configuration produces different arrival times depending on the survey direction. ### 2.2 What Breaks: CMP Reflection-Point Smear For a flat reflector, every trace in a CMP gather reflects from the same subsurface point β€” directly below the surface midpoint. For a **dipping reflector**, the reflection point migrates up-dip as offset increases (Fig. {numref}`fig-cmp-smear-l9`). A CMP gather over a dipping layer therefore samples a laterally smeared zone, not a single point. Standard NMO stacking produces a spatially blurred image in the presence of dip. ```{figure} ../assets/figures/fig_cmp_dipping_scatter.png :name: fig-cmp-smear-l9 :alt: Two-panel figure. Left panel shows a flat horizontal reflector at 1000 m depth; all ray paths for different offsets in a CMP gather converge on the same single reflection point directly below the surface midpoint. Right panel shows a dipping reflector at 15 degrees; the reflection points are smeared up-dip at shallower depths as offset increases. :width: 100% **CMP reflection-point geometry for flat (left) and dipping (right) reflectors.** For a flat reflector, all traces in the CMP gather share the same reflection point. For a dipping reflector ($\delta = 15Β°$), the reflection point migrates up-dip with increasing offset. Stacking without a dip-moveout (DMO) correction averages over a spatially extended zone. [Python-generated: `assets/scripts/fig_cmp_dipping_scatter.py`] ``` ### 2.3 Exact Travel-Time Equation Using the image-point method, the exact two-way travel-time for a source at the origin and receiver at offset $x$, with a reflector whose perpendicular distance from the source is $h$ and dip angle $\delta$, is ```{math} :label: eq-l9-tx-down t_d(x) = \frac{1}{V_1}\sqrt{x^2 + 4h x\sin\delta + 4h^2} \quad \text{(down-dip)} ``` ```{math} :label: eq-l9-tx-up t_u(x) = \frac{1}{V_1}\sqrt{x^2 - 4h x\sin\delta + 4h^2} \quad \text{(up-dip)} ``` Both curves share the same zero-offset intercept $t_0 = 2h/V_1$. ### 2.4 The Linear Term and Asymmetry Squaring and expanding: ```{math} :label: eq-l9-t2x2-dip t^2(x) = t_0^2 + \frac{x^2}{V_1^2} \pm \frac{2 t_0 \sin\delta}{V_1}\cdot x ``` The $\pm(2 t_0 \sin\delta / V_1) \cdot x$ term β€” linear in $x$ and absent in the flat-layer case β€” is the mathematical signature of dip. It produces: - **Down-dip** (+ sign): MORE moveout than flat β†’ shallower apparent NMO velocity when fit with a flat-layer model - **Up-dip** (βˆ’ sign): LESS moveout than flat β†’ deeper apparent NMO velocity The $t^2$–$x^2$ relationship is therefore **non-linear** for dipping reflectors, making the linear regression incorrect. ```{figure} ../assets/figures/fig_dipping_layer_geometry.png :name: fig-dipping-geom-l9 :alt: Three-panel figure. Panel A shows geometry with source, up-dip and down-dip receivers, a green dipping reflector and ray paths. Panel B shows travel-time curves for flat (grey dashed), down-dip (orange), and up-dip (blue) shooting sharing the same t0. Panel C shows the t-squared x-squared relationship with curved non-linear trends for the dipping cases and a green dotted tangent showing V_NMO = V1/cos-delta. :width: 100% **Dipping-layer travel-time asymmetry.** (A) Geometry. (B) $t(x)$ curves: down-dip arrivals are delayed relative to the flat-layer case; up-dip arrivals are early. (C) $t^2$–$x^2$ plot: non-linear trends for dipping cases contrast with the straight flat-layer line. The green dotted tangent has slope $1/V_\mathrm{NMO}^2 = \cos^2\delta/V_1^2$. [Python-generated: `assets/scripts/fig_dipping_layer_geometry.py`] ``` ### 2.5 What Breaks: NMO Velocity for Dipping Layers Taylor-expanding $t_d(x)$ around $x = 0$, the quadratic coefficient gives: ```{math} :label: eq-l9-vnmo-dip V_\mathrm{NMO,dip} = \frac{V_1}{\cos\delta} ``` This is **larger** than $V_1$; fitting a flat-layer NMO model to data over a dipping reflector overestimates the subsurface velocity. ### 2.6 The Fix: Recovering True Velocity and Dip From two surveys β€” one down-dip and one up-dip β€” the true velocity and dip angle can be recovered: ```{math} :label: eq-l9-v1-dip-recover V_1 = \frac{2\,V_d\,V_u}{V_d + V_u}, \qquad \sin\delta = \frac{V_u - V_d}{V_u + V_d} ``` In practice, **dip-moveout (DMO) correction** is applied after NMO correction to reposition the reflection points to a common location before stacking. *With dip accounted for, the next complication is unwanted energy from waves that bounce more than once.* --- ## 3. Complication 2: Multiple Reflections > **Assumption that fails:** *Only primary reflections reach the receiver.* In reality, seismic energy bounces multiple times between the free surface and subsurface reflectors, generating coherent events that mimic primaries. A **multiple** is a seismic event that has undergone more than one reflection before reaching the receiver. Multiples are coherent and appear as hyperbolic events in the CMP gather; they are a primary source of false structure in seismic sections. ### 3.1 Types of Multiples ```{figure} ../assets/figures/fig_multiple_types.png :name: fig-multiples-l9 :alt: Three-panel figure. Panel A shows ray-path diagrams for four multiple types: primary P, long-path multiple M, peg-leg PL, and interbed IB. Panel B shows the synthetic CMP gather with four hyperbolic events. Panel C shows the t-squared x-squared plot where the long-path multiple and primary have the same slope (same V_rms) but the multiple has double the intercept. :width: 100% **Multiple reflection types.** (A) Ray paths: primary (P), long-path surface multiple (M), peg-leg (PL), and interbed (IB). (B) Synthetic CMP gather. (C) $t^2$–$x^2$ plot: the long-path multiple and its parent primary have **identical slopes** (same $V_\mathrm{rms}$) β€” this is the central challenge for NMO stacking. [Python-generated: `assets/scripts/fig_multiple_types.py`] ``` The **long-path (surface) multiple** travel-time is: ```{math} :label: eq-l9-multiple-twtt t_\mathrm{mult}^2(x) = (2\,t_0)^2 + \frac{x^2}{V_\mathrm{rms}^2} ``` This has the **same NMO velocity** as the primary but double the zero-offset TWTT. Because NMO correction simultaneously flattens both, stacking will not suppress the multiple. ### 3.2 The Fix: Multiple Suppression Modern workflows use **surface-related multiple elimination (SRME)**: the observed wavefield is autocorrelated with itself to predict the multiple waveforms, which are then adaptively subtracted. Deep-learning approaches train encoder-decoder networks to separate primaries from multiples in the $\tau$-$p$ domain. *With multiples suppressed, we turn to energy scattered by point-like discontinuities rather than planar interfaces.* --- ## 4. Complication 3: Diffractions > **Assumption that fails:** *Reflecting interfaces are continuous surfaces.* At sharp discontinuities β€” fault tips, unconformity edges, channel boundaries β€” the wavefront scatters in all directions. ### 4.1 Huygens Principle and Point Scatterers Every point on a wavefront acts as a secondary source of spherical wavelets (Huygens's principle). At a sharp subsurface discontinuity β€” a fault tip, an unconformity edge, a channel boundary β€” the incident wave excites new secondary spherical waves. These **diffractions** carry energy in all directions equally. For a point scatterer at $(x_s, z_s)$ in a medium of velocity $V_1$, the diffraction travel time is: ```{math} :label: eq-l9-diffraction t_\mathrm{diff}(x) = \frac{2}{V_1}\sqrt{(x - x_s)^2 + z_s^2} ``` This is a hyperbola with vertex at $(x_s,\, 2z_s/V_1)$. ```{figure} ../assets/figures/fig_diffraction_hyperbola.png :name: fig-diffraction-l9 :alt: Three-panel figure. Panel A shows a depth cross-section with a flat blue-dashed reflector at 600 m and a fault-tip scatterer at 1000 m with orange ray paths fanning to surface receivers. Panel B shows the t(x) curves for the flat-reflector primary (blue dashed) and fault-tip diffraction (red solid). Panel C shows the synthetic zero-offset section with the flat primary and diffraction hyperbola visible. :width: 100% **Point diffraction from a fault-tip scatterer.** (A) Subsurface model. (B) Travel-time curves: the diffraction hyperbola extends uniformly across the entire receiver array. (C) Synthetic zero-offset section. Migration collapses the hyperbola to the fault-tip point, recovering the true geometry. [Python-generated: `assets/scripts/fig_diffraction_hyperbola.py`] ``` ### 4.2 The Fix: Migration An **unmigrated** seismic section displays the hyperbolic diffraction rather than the point; fault terminations appear as fan-shaped energy patches. A syncline bounded by two dipping reflectors produces a "bowtie" pattern. **Seismic migration** β€” the topic of Lecture 10 β€” collapses diffractions and repositions dipping events to their true subsurface locations. *Diffractions will be collapsed by migration (Lecture 10). Meanwhile, another class of unwanted energy β€” coherent noise from surface waves β€” must be removed before stacking.* --- ## 5. Complication 4: Coherent Noise and Signal Enhancement > **Assumption that fails:** *The recorded wavefield contains only reflected body waves.* A raw shot gather is dominated by surface waves (ground roll), direct arrivals, and other coherent noise that masks the reflections we seek. ### 5.1 Coherent Noise Types A raw shot gather contains several coherent noise types alongside desired reflections: - **Direct wave** ($V \approx V_1$): linear first arrival, easily muted - **Ground roll** (Rayleigh wave; $V \approx 200$–500 m/s): high amplitude, low frequency (5–20 Hz), dispersive; dominates land gathers at short and medium offsets - **Air blast** ($V \approx 340$ m/s): muted by velocity filter - **Head wave** ($V > V_1$): muted before NMO correction ### 5.2 The Fix: f–k Velocity Filtering In the frequency-wavenumber ($f$–$k$) domain, events with apparent velocity $V_\mathrm{app}$ map to the line $k = f/V_\mathrm{app}$. Ground roll occupies the high-$|k|$ fan region. A **velocity filter** rejects all $|k| > f/V_\mathrm{cutoff}$: ```{math} :label: eq-l9-fk-mask \mathcal{M}(f, k) = \begin{cases} 1 & |k| < f / V_\mathrm{cutoff} \\ 0 & \text{otherwise} \end{cases} ``` ```{figure} ../assets/figures/fig_ground_roll_fk.png :name: fig-fk-filter-l9 :alt: Three-panel figure. Panel A shows a raw shot gather with labelled ground roll, direct wave, and hyperbolic reflection. Panel B shows the f-k amplitude spectrum with velocity fan lines at 300, 600, and 2000 m/s. Panel C shows the filtered gather with ground roll removed and the reflection hyperbola now clearly visible. :width: 100% **Ground-roll suppression by f–k velocity filtering.** (A) Raw gather: ground roll dominates at small offsets. (B) f–k spectrum: the slow fan of ground roll is separated from fast reflection events; filter mask at $V_\mathrm{cutoff} = 600$ m/s shown in orange. (C) Filtered gather: ground roll attenuated, reflection hyperbola visible. [Python-generated: `assets/scripts/fig_ground_roll_fk.py`] ``` ### 5.3 Stacking Fold and SNR After NMO correction and noise filtering, the stacked trace SNR improves as: ```{math} :label: eq-l9-snr-fold \mathrm{SNR}_\mathrm{stack} = \sqrt{N_\mathrm{fold}} \times \mathrm{SNR}_\mathrm{single} ``` A 48-fold survey improves SNR by a factor of $\approx 7$. Modern dense 3D surveys achieve fold $> 200$. *With noise suppressed and travel times corrected, we can finally examine what the amplitudes themselves reveal about subsurface rock and fluid properties.* --- ## 6. Complication 5: Amplitude Versus Offset > **Assumption that fails:** *Only travel times carry useful information.* In fact, how the reflection amplitude changes with incidence angle reveals the fluid content of subsurface rocks β€” information invisible to NMO velocity analysis alone. ### 6.1 Oblique-Incidence Reflectivity For a plane P-wave incident at angle $\theta_i$ on a planar interface, the reflected and transmitted amplitudes are governed by the **Zoeppritz equations**. For moderate angles ($\theta_i < 30Β°$), the Shuey (1985) two-term approximation gives: ```{math} :label: eq-l9-shuey R(\theta_i) \approx R(0) + G\,\sin^2\theta_i ``` where $R(0) = (Z_2 - Z_1)/(Z_2 + Z_1)$ is the normal-incidence reflection coefficient (intercept) and $G$ is the **AVO gradient**, sensitive to the contrast in $V_P/V_S$ ratio across the interface. Gas substitution strongly lowers $V_P$ while leaving $V_S$ nearly unchanged, producing a large distinctive change in $G$. ### 6.2 AVO Classes ```{figure} ../assets/figures/fig_avo_classes.png :name: fig-avo-l9 :alt: Two-panel figure. Panel A shows reflection coefficient R versus incidence angle for AVO Classes I through IV and IIp. Class I starts positive and decreases. Class II starts near zero with polarity reversal. Class III starts negative and brightens with offset (gas sand). Class IV starts negative and dims. Panel B shows the AVO crossplot of intercept R(0) versus gradient G with scatter clusters for each class and background trend line. :width: 100% **AVO classes and the $R(0)$–$G$ crossplot.** (A) $R(\theta)$ curves: Class III gas sands brighten with offset ($R(0) < 0$, $G < 0$); Class I tight sands dim. (B) Crossplot: wet sands and shales cluster along the background trend; gas sands deviate toward the lower left. [Python-generated: `assets/scripts/fig_avo_classes.py`] ``` - **Class I** ($R(0) > 0$, $G < 0$): Hard sand or cemented rock; amplitude decreases with offset. - **Class II** ($R(0) \approx 0$, $G < 0$): Near-zero normal-incidence contrast; polarity reversal at intermediate angle. - **Class III** ($R(0) < 0$, $G < 0$): Soft gas sand; amplitude increases with offset β€” the classical **bright spot** direct hydrocarbon indicator (DHI). - **Class IV** ($R(0) < 0$, $G > 0$): Amplitude decreases with offset despite a negative intercept; overpressured or very shallow gas sands. ### 6.3 The AVO Crossplot and Fluid Discrimination Plotting $R(0)$ against $G$ for all reflection events in a 3D survey produces the **AVO crossplot**. Background wet sands and shales cluster along a "fluid line" ($G \approx -R(0)$). Gas-saturated sands deviate toward more negative $G$ values (Classes II, III). The deviation from the background trend is the primary diagnostic for fluid content beyond what impedance alone resolves. --- ## 7. Worked Example: Dipping-Layer Survey **Given:** A 2D survey over a thrust-fault reflector. Perpendicular depth $h = 800$ m, $V_1 = 2000$ m/s, $\delta = 10Β°$. | Quantity | Formula | Result | |---|---|---| | Zero-offset TWTT | $t_0 = 2h/V_1$ | 0.80 s | | NMO velocity (dipping) | $V_\mathrm{NMO} = V_1/\cos\delta$ | 2031 m/s | | Down-dip at $x = 2400$ m | Eq. {eq}`eq-l9-tx-down` | 1.553 s | | Up-dip at $x = 2400$ m | Eq. {eq}`eq-l9-tx-up` | 1.322 s | **Check apparent velocities:** $V_d \approx 1704$ m/s, $V_u \approx 2421$ m/s β†’ $\sin\delta = (2421-1704)/(2421+1704) = 0.174 \approx \sin10Β°$ βœ“ ```{admonition} Concept Check :class: tip 1. A CMP gather over a 12Β° dipping reflector is NMO-corrected using the flat-layer formula $V_\mathrm{NMO} = V_1$. Will the corrected reflectors be over- or under-corrected? Explain using Eq. {eq}`eq-l9-vnmo-dip`. 2. A long-path multiple arrives at $t = 1.4$ s at zero offset with $V_\mathrm{rms} = 2400$ m/s. At what zero-offset time does its parent primary arrive? Compute the depth to the reflecting horizon. 3. A seismic section shows a hyperbolic event that broadens uniformly across all offsets without attenuating. Is this a primary reflection or a diffraction? What must be done to recover the true geological feature? ``` --- ## 8. SOTA: Deep Learning in Reflection Seismic Processing ### 8.1 Supervised Denoising with U-Nets The dominant deep-learning architecture for seismic denoising is the **U-Net** β€” a fully convolutional encoder-decoder network trained to map a noisy seismic gather to a denoised output: $$\hat{\mathbf{d}}_\mathrm{clean} = f_\theta(\mathbf{d}_\mathrm{noisy}), \qquad \theta^* = \arg\min_\theta \|\mathbf{d}_\mathrm{clean}^\mathrm{train} - f_\theta(\mathbf{d}_\mathrm{noisy}^\mathrm{train})\|^2$$ Skip connections between the encoder and decoder layers preserve fine spatial detail that would otherwise be lost in the downsampling path. ```{figure} ../assets/figures/fig_dl_denoising_concept.png :name: fig-dl-denoise-l9 :alt: Three-panel figure. Panel A shows a U-Net architecture schematic with encoder (green boxes), bottleneck (orange box), decoder (blue boxes), and red skip connections. Panel B shows a noisy synthetic CMP gather. Panel C shows the denoised output with improved SNR. :width: 100% **U-Net architecture for seismic denoising.** (A) Encoder-decoder with skip connections. (B) Noisy input gather. (C) Denoised output. A real U-Net learns the noise distribution from training data; band-pass filtering is shown here as a proxy. [Python-generated: `assets/scripts/fig_dl_denoising_concept.py`] ``` ### 8.2 Self-Supervised and Foundation Models A limitation of supervised U-Nets is the need for paired clean/noisy training data, which is unavailable for real field datasets. **Self-supervised** methods train entirely on the observed noisy data by exploiting the statistical property that noise is spatially uncorrelated while signal is coherent. **Seismic foundation models** (e.g. SeisFoundation, SegFM) are large pretrained vision transformers fine-tuned on seismic images that can perform multiple tasks β€” denoising, horizon picking, facies classification β€” from a single model backbone. ### 8.3 Open Challenges - **Domain shift:** networks trained on synthetic gathers frequently fail on field data because real noise is non-stationary and geologically correlated. - **Physics inconsistency:** a denoised gather may violate reciprocity, polarity conventions, or AVO relationships physically present in the original data. - **Interpretability:** it is difficult to determine whether an amplitude anomaly in a DL-denoised section is a true DHI or a network artifact. --- ## 9. Course Connections The dipping-layer travel-time equation (Β§2) is the direct extension of the flat-layer hyperbola ($\delta \to 0$ recovers the standard reflection hyperbola). The additional linear term motivates DMO correction, which is a special case of the migration operator discussed in Lecture 10. Diffraction hyperbolae (Β§4) are the building block of Kirchhoff migration (Lecture 10, Β§3): migration collapses diffractions by summing amplitudes along the diffraction curve. The AVO gradient $G$ involves $V_P/V_S$, which connects to density constraints available from the gravity module (Lectures 18–22): density is related to both impedance ($Z = \rho V_P$) and AVO ($G$ depends on $\Delta\rho/\rho$). --- ## 10. Research Horizon :::{admonition} Current Research Highlights (2022–2025) :class: seealso **Learned multiple suppression** uses deep learning in the $\tau$-$p$ domain to achieve adaptive subtraction without the wave-equation modelling required by SRME, reducing computational cost by 1–2 orders of magnitude (Xiong et al. 2023). **Sparse-shot acquisition and DL interpolation** trains networks to reconstruct densely sampled shot gathers from sparse acquisitions, enabling 4D time-lapse surveys at a fraction of traditional acquisition cost (Mosher et al. 2023). **Physics-informed AVO inversion** embeds Zoeppritz boundary conditions as hard constraints in a neural-network inversion, ensuring that recovered $V_P/V_S$ profiles satisfy the governing physics rather than merely fitting observed amplitudes (Zhang et al. 2024). *For students interested in graduate research: EarthScope SSBW workshops and the SCOPED project (scoped.codes) are entry points. The IRIS/EarthScope AVO module provides open datasets.* ::: --- ## 11. Societal Relevance :::{admonition} Why It Matters Beyond the Classroom :class: note **Direct Hydrocarbon Indicators:** The AVO Class III "bright spot" is the most widely used DHI in exploration. False positive identifications β€” attributing a bright reflection to gas when it is caused by a shallow coal seam, a hard carbonate layer, or a DL denoising artifact β€” have led to costly dry wells. The $R(0)$–$G$ crossplot uncertainties directly inform decisions worth hundreds of millions of dollars. **Carbon Capture and Storage (CCS):** AVO analysis is now central to characterizing COβ‚‚ storage reservoirs and monitoring injection plumes β€” where accurate fluid discrimination directly affects the long-term security of millions of tonnes of stored COβ‚‚. **Cascadia:** The updip extent of the dΓ©collement's seismic coupling is constrained by the impedance contrast between unconsolidated accretionary sediment and the overriding plate. Whether a bright spot at the plate interface is a fluid-saturated zone (Class III AVO) or a cemented carbonate zone (Class I) affects estimates of seismic moment release and future Cascadia rupture magnitude. **For further exploration:** IRIS/EarthScope AVO educational module (CC-BY, iris.edu/hq/inclass/lesson/avo); Shuey (1985) is freely accessible and remains the canonical reference. ::: --- ## AI Literacy β€” Epistemics: Interrogating a Seismic Interpretation :::{admonition} AI Prompt Lab :class: tip Ask an AI assistant to interpret: *"A bright, negative-polarity reflection at 1.8 s TWTT with amplitude that increases strongly with offset on a marine gather acquired over a Paleogene sandstone reservoir."* Before accepting the response, apply the epistemics framework: 1. **What evidence distinguishes this from a multiple?** (If it were a long-path multiple, what would its parent primary TWTT be? Does a primary exist at 0.9 s on the section?) 2. **What evidence distinguishes it from a hard kick at the base of a fast layer?** (Negative polarity can also come from impedance decreasing from dense limestone into soft shale.) 3. **What data would confirm the gas interpretation?** (Well control, fluid substitution modelling, 4D time-lapse survey, CSEM/MT resistivity data.) Document: (a) what the AI identified correctly; (b) what the AI failed to flag as an alternative explanation; (c) what additional data the AI suggested or failed to suggest. ::: --- ## Further Reading 1. Lowrie, W. & Fichtner, A. (2020). *Fundamentals of Geophysics*, 3rd ed. Ch. 6, Β§6.5. [Free via UW Libraries] 2. Shuey, R.T. (1985). A simplification of the Zoeppritz equations. *Geophysics*, 50(4), 609–614. [doi:10.1190/1.1441936](https://doi.org/10.1190/1.1441936) 3. Rutherford, S.R. & Williams, R.H. (1989). Amplitude-versus-offset variations in gas sands. *Geophysics*, 54(6), 680–688. [doi:10.1190/1.1442696](https://doi.org/10.1190/1.1442696) 4. Birnie, C. et al. (2021). Analysis and application of unsupervised deep learning for seismic noise attenuation. *Geophysical Prospecting*, 69(8). doi:10.1111/1365-2478.13095 *(⚠ this DOI leads to the 2021 Erratum, not the original article β€” verify manually)* 5. Haeni, F.P. (1988). USGS Open-File Report 88-296. [Public domain] ```{bibliography} :filter: docname in docnames ```