去线性趋势#
去线性趋势是指计算出一条最能拟合整个波形数据的直线（即趋势线），并从每个数据点中减去该直线对应的值， 使波形围绕稳定的零基线振动。此操作用于去除由温度变化或地壳形变等因素造成的缓慢漂移与基线偏移。
我们以前一节使用的 2022 年 9 月 22 日墨西哥 Mw 6.8 地震在 ANMO 台站的波形为例。
from obspy import UTCDateTime
from obspy.clients.fdsn import Client
import matplotlib.pyplot as plt
from numpy.polynomial import polynomial as P
client = Client("IRIS")
# 下载 2022 年墨西哥 Mw 6.8 级地震在 ANMO 台站的波形数据
starttime = UTCDateTime("2022-09-22T06:18:00")
endtime = starttime + 720 # 下载 12 分钟数据
st = client.get_waveforms(
network="IU",
station="ANMO",
location="00",
channel="BHZ",
starttime=starttime,
endtime=endtime,
)
st.plot();
---------------------------------------------------------------------------
ModuleNotFoundError Traceback (most recent call last)
Cell In[1], line 1
----> 1 from obspy import UTCDateTime
2 from obspy.clients.fdsn import Client
3 import matplotlib.pyplot as plt
File ~/micromamba/envs/seismo-learn/lib/python3.13/site-packages/obspy/__init__.py:44
41 msg = ('pkg_resources is deprecated as an API')
42 warnings.filterwarnings(
43 'ignore', message=msg, category=DeprecationWarning, module='obspy')
---> 44 from obspy.core.utcdatetime import UTCDateTime # NOQA
45 from obspy.core.util import _get_version_string
46 __version__ = _get_version_string(abbrev=10)
File ~/micromamba/envs/seismo-learn/lib/python3.13/site-packages/obspy/core/__init__.py:120
12 """
13 obspy.core - Core classes of ObsPy
14 ==================================
(...) 117 .. _NumPy: http://www.numpy.org
118 """
119 # don't change order
--> 120 from obspy.core.utcdatetime import UTCDateTime # NOQA
121 from obspy.core.util.attribdict import AttribDict # NOQA
122 from obspy.core.trace import Stats, Trace # NOQA
File ~/micromamba/envs/seismo-learn/lib/python3.13/site-packages/obspy/core/utcdatetime.py:21
18 import warnings
20 import numpy as np
---> 21 from obspy.core.util.deprecation_helpers import ObsPyDeprecationWarning
24 # based on https://www.myintervals.com/blog/2009/05/20/iso-8601, w/ week 53 fix
25 _ISO8601_REGEX = re.compile(r"""
26 ^
27 ([\+-]?\d{4}(?!\d{2}\b))
(...) 40 $
41 """, re.VERBOSE)
File ~/micromamba/envs/seismo-learn/lib/python3.13/site-packages/obspy/core/util/__init__.py:22
20 # import order matters - NamedTemporaryFile must be one of the first!
21 from obspy.core.util.attribdict import AttribDict
---> 22 from obspy.core.util.base import (ALL_MODULES, DEFAULT_MODULES,
23 NATIVE_BYTEORDER, NETWORK_MODULES,
24 NamedTemporaryFile, _read_from_plugin,
25 create_empty_data_chunk, get_example_file,
26 get_script_dir_name, MATPLOTLIB_VERSION,
27 SCIPY_VERSION, NUMPY_VERSION,
28 CARTOPY_VERSION, CatchAndAssertWarnings)
29 from obspy.core.util.misc import (BAND_CODE, CatchOutput, complexify_string,
30 guess_delta, score_at_percentile,
31 to_int_or_zero, SuppressOutput)
32 from obspy.core.util.obspy_types import (ComplexWithUncertainties, Enum,
33 FloatWithUncertainties)
File ~/micromamba/envs/seismo-learn/lib/python3.13/site-packages/obspy/core/util/base.py:26
23 from pathlib import PurePath
25 import numpy as np
---> 26 import pkg_resources
27 from pkg_resources import get_entry_info, iter_entry_points
29 from obspy.core.util.misc import to_int_or_zero, buffered_load_entry_point
ModuleNotFoundError: No module named 'pkg_resources'
进行去线性趋势处理之前，通常需要先进行去均值操作。
tr = st[0]
# 去均值
tr.detrend("demean")
# 计算去线性趋势处理前的斜率
slope_before = P.polyfit(tr.times(), tr.data, deg=1)[1]
print(f"Slope before linear detrend: {slope_before}")
ObsPy 提供了 obspy.core.trace.Trace.detrend() 方法可以实现去线性趋势操作。
# 去线性趋势
tr.detrend("linear")
# 计算去线性趋势处理后的斜率
slope_after = P.polyfit(tr.times(), tr.data, deg=1)[1]
print(f"Slope after linear detrend: {slope_after}")
可以看到，针对去均值后的波形，其斜率从 -1.15 降至 1.96e-14，说明 detrend 方法已成功校正基线。