M. B. Widess, (1973), "HOW THIN IS A THIN BED?," GEOPHYSICS 38: 1176-1180.

widess-1973/README.md

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+# How Thin is a Thin Bed?
+
+This paper has been reproduced by [Altay Sansal](https://github.com/tasansal).
+
+### How to Run
+
+1. Create `conda` environment from `environment.yaml` file.
+2. Install Jupyter or Jupyer Lab; or register environment kernel with global Jupyter Lab.
+3. Run.
+
+### Reference
+
+M. B. Widess, (1973), "HOW THIN IS A THIN BED?," GEOPHYSICS 38: 1176-1180.
+
+<div style="text-align: left; margin: 0 auto;">
+
+|             |                                   |
+|-------------|-----------------------------------|
+| Publication | GEOPHYSICS                        |
+| Published   | December 1973                     |
+| Authors     | M. B. Widess                      |
+| DOI         | https://doi.org/10.1190/1.1440403 |
+
+</div>
+
+
+### Abstract
+
+Based on reflective properties, a thin bed may be conveniently defined as one whose thickness is less than about 𝜆𝑏/8 where 𝜆𝑏 is the (predominant) wavelength computed using the velocity of the bed. The amplitude of a reflection from a thin bed is to the first order of approximation equal to 4𝜋Ab/𝜆𝑏, where b is the thickness of the bed and A is the amplitude of the reflection if the bed were to be very thick. The equation shows that a bed as thin as 10 ft has, for typical frequency and velocity, considerably more reflective power than is usually attributed to it.

widess-1973/environment.yaml

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+name: repro-zoo
+channels:
+  - conda-forge
+dependencies:
+  - appnope=0.1.3=pyhd8ed1ab_0
+  - asttokens=2.2.1=pyhd8ed1ab_0
+  - backcall=0.2.0=pyh9f0ad1d_0
+  - backports=1.0=pyhd8ed1ab_3
+  - backports.functools_lru_cache=1.6.5=pyhd8ed1ab_0
+  - brotli=1.1.0=hb547adb_0
+  - brotli-bin=1.1.0=hb547adb_0
+  - brotli-python=1.1.0=py311ha891d26_0
+  - bzip2=1.0.8=h3422bc3_4
+  - ca-certificates=2023.7.22=hf0a4a13_0
+  - certifi=2023.7.22=pyhd8ed1ab_0
+  - charset-normalizer=3.2.0=pyhd8ed1ab_0
+  - comm=0.1.4=pyhd8ed1ab_0
+  - contourpy=1.1.0=py311he4fd1f5_0
+  - cycler=0.11.0=pyhd8ed1ab_0
+  - debugpy=1.6.8=py311ha891d26_0
+  - decorator=5.1.1=pyhd8ed1ab_0
+  - exceptiongroup=1.1.3=pyhd8ed1ab_0
+  - executing=1.2.0=pyhd8ed1ab_0
+  - fonttools=4.42.1=py311heffc1b2_0
+  - freetype=2.12.1=hd633e50_1
+  - idna=3.4=pyhd8ed1ab_0
+  - importlib-metadata=6.8.0=pyha770c72_0
+  - importlib_metadata=6.8.0=hd8ed1ab_0
+  - ipykernel=6.25.1=pyh5fb750a_0
+  - ipython=8.15.0=pyh31c8845_0
+  - jedi=0.19.0=pyhd8ed1ab_0
+  - jupyter_client=8.3.1=pyhd8ed1ab_0
+  - jupyter_core=5.3.1=py311h267d04e_0
+  - kiwisolver=1.4.5=py311he4fd1f5_0
+  - lcms2=2.15=hd835a16_1
+  - lerc=4.0.0=h9a09cb3_0
+  - libblas=3.9.0=17_osxarm64_openblas
+  - libbrotlicommon=1.1.0=hb547adb_0
+  - libbrotlidec=1.1.0=hb547adb_0
+  - libbrotlienc=1.1.0=hb547adb_0
+  - libcblas=3.9.0=17_osxarm64_openblas
+  - libcxx=16.0.6=h4653b0c_0
+  - libdeflate=1.18=h1a8c8d9_0
+  - libexpat=2.5.0=hb7217d7_1
+  - libffi=3.4.2=h3422bc3_5
+  - libgfortran=5.0.0=12_3_0_hd922786_1
+  - libgfortran5=12.3.0=ha3a6a3e_1
+  - libjpeg-turbo=2.1.5.1=h1a8c8d9_0
+  - liblapack=3.9.0=17_osxarm64_openblas
+  - libopenblas=0.3.23=openmp_hc731615_0
+  - libpng=1.6.39=h76d750c_0
+  - libsodium=1.0.18=h27ca646_1
+  - libsqlite=3.43.0=hb31c410_0
+  - libtiff=4.5.1=h23a1a89_1
+  - libwebp-base=1.3.1=hb547adb_0
+  - libxcb=1.15=hf346824_0
+  - libzlib=1.2.13=h53f4e23_5
+  - llvm-openmp=16.0.6=h1c12783_0
+  - matplotlib=3.7.2=py311ha1ab1f8_0
+  - matplotlib-base=3.7.2=py311h3bc9839_0
+  - matplotlib-inline=0.1.6=pyhd8ed1ab_0
+  - munkres=1.1.4=pyh9f0ad1d_0
+  - ncurses=6.4=h7ea286d_0
+  - nest-asyncio=1.5.6=pyhd8ed1ab_0
+  - numpy=1.25.2=py311hb8f3215_0
+  - openjpeg=2.5.0=hbc2ba62_2
+  - openssl=3.1.2=h53f4e23_0
+  - packaging=23.1=pyhd8ed1ab_0
+  - parso=0.8.3=pyhd8ed1ab_0
+  - pexpect=4.8.0=pyh1a96a4e_2
+  - pickleshare=0.7.5=py_1003
+  - pillow=10.0.0=py311h095fde6_0
+  - pip=23.2.1=pyhd8ed1ab_0
+  - platformdirs=3.10.0=pyhd8ed1ab_0
+  - pooch=1.7.0=pyha770c72_3
+  - prompt-toolkit=3.0.39=pyha770c72_0
+  - prompt_toolkit=3.0.39=hd8ed1ab_0
+  - psutil=5.9.5=py311he2be06e_0
+  - pthread-stubs=0.4=h27ca646_1001
+  - ptyprocess=0.7.0=pyhd3deb0d_0
+  - pure_eval=0.2.2=pyhd8ed1ab_0
+  - pygments=2.16.1=pyhd8ed1ab_0
+  - pyparsing=3.0.9=pyhd8ed1ab_0
+  - pysocks=1.7.1=pyha2e5f31_6
+  - python=3.11.5=h47c9636_0_cpython
+  - python-dateutil=2.8.2=pyhd8ed1ab_0
+  - python_abi=3.11=3_cp311
+  - pyzmq=25.1.1=py311hb1af645_0
+  - readline=8.2=h92ec313_1
+  - requests=2.31.0=pyhd8ed1ab_0
+  - scipy=1.11.2=py311h93d07a4_0
+  - setuptools=68.1.2=pyhd8ed1ab_0
+  - six=1.16.0=pyh6c4a22f_0
+  - stack_data=0.6.2=pyhd8ed1ab_0
+  - tk=8.6.12=he1e0b03_0
+  - tornado=6.3.3=py311heffc1b2_0
+  - traitlets=5.9.0=pyhd8ed1ab_0
+  - typing-extensions=4.7.1=hd8ed1ab_0
+  - typing_extensions=4.7.1=pyha770c72_0
+  - tzdata=2023c=h71feb2d_0
+  - urllib3=2.0.4=pyhd8ed1ab_0
+  - wcwidth=0.2.6=pyhd8ed1ab_0
+  - wheel=0.41.2=pyhd8ed1ab_0
+  - xorg-libxau=1.0.11=hb547adb_0
+  - xorg-libxdmcp=1.1.3=h27ca646_0
+  - xz=5.2.6=h57fd34a_0
+  - zeromq=4.3.4=hbdafb3b_1
+  - zipp=3.16.2=pyhd8ed1ab_0
+  - zstd=1.5.5=h4f39d0f_0
+prefix: /Users/Altay.Sansal/mambaforge/envs/repro-zoo

widess-1973/figures.py

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+import matplotlib.pyplot as plt
+import numpy as np
+from numpy.typing import NDArray
+
+
+def figure1(
+    times: NDArray,
+    amplitude_r1: NDArray,
+    amplitude_r2: NDArray,
+    amplitude_rd: NDArray,
+    shift: float,
+    dpi: int,
+) -> None:
+    """Generate Figure 1 of Widess, 1973."""
+    fig, (fig_1a, fig_1b, fig_1c) = plt.subplots(3, 1, dpi=dpi)
+    arrow_props = dict(facecolor="black", width=0.001, headwidth=5, headlength=5)
+
+    # Panel a.
+    fig_1a.plot(times, amplitude_r1, "black")
+    fig_1a.plot(times, amplitude_r2, "black")
+    fig_1a.fill_between(
+        times,
+        amplitude_r1,
+        amplitude_r2,
+        facecolor="none",
+        edgecolor="black",
+        hatch="|||||",
+    )
+    fig_1a.grid(True, "major", axis="x")
+    fig_1a.set_xticks(np.arange(shift / 2, 1, 0.165) - 0.5)
+    fig_1a.annotate(
+        text="$R_1$",
+        xy=(times[25], amplitude_r1[25]),
+        xytext=(-0.35, 0.5),
+        arrowprops=arrow_props,
+    )
+    fig_1a.annotate(
+        text="$-R_2$",
+        xy=(times[25], amplitude_r2[25]),
+        xytext=(-0.15, -0.5),
+        arrowprops=arrow_props,
+    )
+    # Panel b.
+    fig_1b.plot(times, amplitude_rd, "black")
+    fig_1b.grid(True, "major")
+    fig_1b.set_xticks(np.arange(shift / 2, 1, 0.165) - 0.5)
+    fig_1b.set_yticks([0])
+    fig_1b.annotate(
+        text="$R_d$",
+        xy=(times[40], amplitude_rd[40]),
+        xytext=(-0.25, -0.5),
+        arrowprops=arrow_props,
+    )
+
+    # Panel c (left side)
+    fig_1c.plot([-0.25, -0.25], [-0.5, 0.5], "black")
+    fig_1c.plot(
+        [-0.2, -0.2, -0.15, -0.15, -0.2, -0.2],
+        [-0.5, -0.25, -0.25, 0.25, 0.25, 0.5],
+        "black",
+    )
+    fig_1c.annotate(
+        text="VELOCITY",
+        xy=(-0.1, 1),
+        xytext=(-0.35, 1),
+        arrowprops=arrow_props,
+        verticalalignment="center",
+    )
+    fig_1c.annotate(
+        text="DEPTH",
+        xy=(-0.3, -0.5),
+        xytext=(-0.3, -0.1),
+        arrowprops=arrow_props,
+        horizontalalignment="center",
+        rotation=90,
+    )
+
+    fig_1c.text(x=-0.21, y=0.6, s="$V_1$")
+    fig_1c.text(x=-0.15, y=0.3, s="$V_2=V_b$")
+    fig_1c.text(x=-0.21, y=-0.75, s="$V_3=V_1$")
+
+    fig_1c.text(
+        x=-0.225,
+        y=-1,
+        s="VELOCITY GRAPH",
+        horizontalalignment="center",
+        verticalalignment="center",
+    )
+
+    # Panel c (right side)
+    fig_1c.fill_between(
+        [0.1, 0.4],
+        [0.25, 0.25],
+        [-0.25, -0.25],
+        facecolor="none",
+        edgecolor="black",
+        hatch="//////",
+    )
+    fig_1c.text(x=0.4, y=0.45, s="$V_1$", verticalalignment="center")
+    fig_1c.text(
+        x=0.37,
+        y=0.0,
+        s="$V_2=V_b$",
+        verticalalignment="center",
+        bbox=dict(facecolor="white", edgecolor="none", pad=0),
+    )
+    fig_1c.text(x=0.4, y=-0.45, s="$V_3=V_1$", verticalalignment="center")
+
+    fig_1c.arrow(0.2, 0.45, 0.05, -0.9, head_width=0.01, head_length=0.1, fc="black")
+    fig_1c.arrow(0.21, 0.25, 0.02, 0.4, head_width=0.01, head_length=0.1, fc="black")
+    fig_1c.arrow(0.24, -0.25, 0.044, 0.88, head_width=0.01, head_length=0.1, fc="black")
+
+    fig_1c.text(
+        x=0.25,
+        y=-1,
+        s="REFLECTION RAY DIAGRAM",
+        horizontalalignment="center",
+        verticalalignment="center",
+    )
+
+    # Common plot formatting
+    for ax in [fig_1a, fig_1b, fig_1c]:
+        ax.set_xlim(-0.5, 0.5)
+        ax.set_ylim(-1, 1)
+        ax.set_xticklabels([])
+        ax.set_yticklabels([])
+        ax.tick_params(axis="both", which="both", length=0)
+
+        for spine in ["left", "right", "top", "bottom"]:
+            ax.spines[spine].set_visible(False)