Facies classification using machine learning techniques

Contact author: Paolo Bestagini

In the following, we provide a possible solution to the facies classification problem described at https://github.com/seg/2016-ml-contest.

The proposed algorithm is based on the use of random forests combined in one-vs-one multiclass strategy. In particular, we would like to study the effect of:

  • Robust feature normalization.
  • Feature imputation for missing feature values.
  • Well-based cross-validation routines.
  • Feature augmentation strategies.

Script initialization

Let us import the used packages and define some parameters (e.g., colors, labels, etc.).


In [1]:
# Import
from __future__ import division
%matplotlib inline
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rcParams['figure.figsize'] = (20.0, 10.0)
inline_rc = dict(mpl.rcParams)
from classification_utilities import make_facies_log_plot

import pandas as pd
import numpy as np
import seaborn as sns

from sklearn import preprocessing
from sklearn.model_selection import LeavePGroupsOut
from sklearn.metrics import f1_score
from sklearn.multiclass import OneVsOneClassifier
from sklearn.ensemble import RandomForestClassifier

from scipy.signal import medfilt

In [2]:
import sys, scipy, sklearn
print('Python:  ' + sys.version.split('\n')[0])
print('         ' + sys.version.split('\n')[1])
print('Pandas:  ' + pd.__version__)
print('Numpy:   ' + np.__version__)
print('Scipy:   ' + scipy.__version__)
print('Sklearn: ' + sklearn.__version__)


Python:  2.7.13 (default, Dec 18 2016, 07:03:39) 
         [GCC 4.2.1 Compatible Apple LLVM 8.0.0 (clang-800.0.42.1)]
Pandas:  0.19.2
Numpy:   1.11.3
Scipy:   0.18.1
Sklearn: 0.18.1

In [3]:
# Parameters
feature_names = ['GR', 'ILD_log10', 'DeltaPHI', 'PHIND', 'PE', 'NM_M', 'RELPOS']
facies_names = ['SS', 'CSiS', 'FSiS', 'SiSh', 'MS', 'WS', 'D', 'PS', 'BS']
facies_colors = ['#F4D03F', '#F5B041','#DC7633','#6E2C00', '#1B4F72','#2E86C1', '#AED6F1', '#A569BD', '#196F3D']

Load data

Let us load training data and store features, labels and other data into numpy arrays.


In [4]:
# Load data from file
data = pd.read_csv('../facies_vectors.csv')

In [5]:
# Store features and labels
X = data[feature_names].values  # features
y = data['Facies'].values  # labels

In [6]:
# Store well labels and depths
well = data['Well Name'].values
depth = data['Depth'].values

Data inspection

Let us inspect the features we are working with. This step is useful to understand how to normalize them and how to devise a correct cross-validation strategy. Specifically, it is possible to observe that:

  • Some features seem to be affected by a few outlier measurements.
  • Only a few wells contain samples from all classes.
  • PE measurements are available only for some wells.

In [7]:
# Define function for plotting feature statistics
def plot_feature_stats(X, y, feature_names, facies_colors, facies_names):
    
    # Remove NaN
    nan_idx = np.any(np.isnan(X), axis=1)
    X = X[np.logical_not(nan_idx), :]
    y = y[np.logical_not(nan_idx)]
    
    # Merge features and labels into a single DataFrame
    features = pd.DataFrame(X, columns=feature_names)
    labels = pd.DataFrame(y, columns=['Facies'])
    for f_idx, facies in enumerate(facies_names):
        labels[labels[:] == f_idx] = facies
    data = pd.concat((labels, features), axis=1)

    # Plot features statistics
    facies_color_map = {}
    for ind, label in enumerate(facies_names):
        facies_color_map[label] = facies_colors[ind]

    sns.pairplot(data, hue='Facies', palette=facies_color_map, hue_order=list(reversed(facies_names)))

In [8]:
# Feature distribution
plot_feature_stats(X, y, feature_names, facies_colors, facies_names)
mpl.rcParams.update(inline_rc)



In [9]:
# Facies per well
for w_idx, w in enumerate(np.unique(well)):
    ax = plt.subplot(3, 4, w_idx+1)
    hist = np.histogram(y[well == w], bins=np.arange(len(facies_names)+1)+.5)
    plt.bar(np.arange(len(hist[0])), hist[0], color=facies_colors, align='center')
    ax.set_xticks(np.arange(len(hist[0])))
    ax.set_xticklabels(facies_names)
    ax.set_title(w)



In [10]:
# Features per well
for w_idx, w in enumerate(np.unique(well)):
    ax = plt.subplot(3, 4, w_idx+1)
    hist = np.logical_not(np.any(np.isnan(X[well == w, :]), axis=0))
    plt.bar(np.arange(len(hist)), hist, color=facies_colors, align='center')
    ax.set_xticks(np.arange(len(hist)))
    ax.set_xticklabels(feature_names)
    ax.set_yticks([0, 1])
    ax.set_yticklabels(['miss', 'hit'])
    ax.set_title(w)


 Feature imputation

Let us fill missing PE values. Different strategies could be used. We simply substitute them with the average PE value.


In [11]:
imp = preprocessing.Imputer(missing_values='NaN', strategy='mean', axis=0)
imp.fit(X)
X = imp.transform(X)

Feature augmentation

Our guess is that facies do not abrutly change from a given depth layer to the next one. Therefore, we consider features at neighboring layers to be somehow correlated. To possibly exploit this fact, let us perform feature augmentation by:

  • Aggregating features at neighboring depths.
  • Computing feature spatial gradient.

In [12]:
# Feature windows concatenation function
def augment_features_window(X, N_neig):
    
    # Parameters
    N_row = X.shape[0]
    N_feat = X.shape[1]

    # Zero padding
    X = np.vstack((np.zeros((N_neig, N_feat)), X, (np.zeros((N_neig, N_feat)))))

    # Loop over windows
    X_aug = np.zeros((N_row, N_feat*(2*N_neig+1)))
    for r in np.arange(N_row)+N_neig:
        this_row = []
        for c in np.arange(-N_neig,N_neig+1):
            this_row = np.hstack((this_row, X[r+c]))
        X_aug[r-N_neig] = this_row

    return X_aug

In [13]:
# Feature gradient computation function
def augment_features_gradient(X, depth):
    
    # Compute features gradient
    d_diff = np.diff(depth).reshape((-1, 1))
    d_diff[d_diff==0] = 0.001
    X_diff = np.diff(X, axis=0)
    X_grad = X_diff / d_diff
        
    # Compensate for last missing value
    X_grad = np.concatenate((X_grad, np.zeros((1, X_grad.shape[1]))))
    
    return X_grad

In [14]:
# Feature augmentation function
def augment_features(X, well, depth, N_neig=1):
    
    # Augment features
    X_aug = np.zeros((X.shape[0], X.shape[1]*(N_neig*2+2)))
    for w in np.unique(well):
        w_idx = np.where(well == w)[0]
        X_aug_win = augment_features_window(X[w_idx, :], N_neig)
        X_aug_grad = augment_features_gradient(X[w_idx, :], depth[w_idx])
        X_aug[w_idx, :] = np.concatenate((X_aug_win, X_aug_grad), axis=1)
    
    # Find padded rows
    padded_rows = np.unique(np.where(X_aug[:, 0:7] == np.zeros((1, 7)))[0])
    
    return X_aug, padded_rows

In [15]:
# Augment features
X_aug, padded_rows = augment_features(X, well, depth)

Generate training, validation and test data splits

The choice of training and validation data is paramount in order to avoid overfitting and find a solution that generalizes well on new data. For this reason, we generate a set of training-validation splits so that:

  • Features from each well belongs to training or validation set.
  • Training and validation sets contain at least one sample for each class.

In [16]:
# Initialize model selection methods
lpgo = LeavePGroupsOut(2)

# Generate splits
split_list = []
for train, val in lpgo.split(X, y, groups=data['Well Name']):
    hist_tr = np.histogram(y[train], bins=np.arange(len(facies_names)+1)+.5)
    hist_val = np.histogram(y[val], bins=np.arange(len(facies_names)+1)+.5)
    if np.all(hist_tr[0] != 0) & np.all(hist_val[0] != 0):
        split_list.append({'train':train, 'val':val})
            
# Print splits
for s, split in enumerate(split_list):
    print('Split %d' % s)
    print('    training:   %s' % (data['Well Name'][split['train']].unique()))
    print('    validation: %s' % (data['Well Name'][split['val']].unique()))


Split 0
    training:   ['SHRIMPLIN' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['ALEXANDER D' 'CHURCHMAN BIBLE']
Split 1
    training:   ['SHRIMPLIN' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'NOLAN' 'Recruit F9' 'NEWBY'
 'CHURCHMAN BIBLE']
    validation: ['ALEXANDER D' 'CROSS H CATTLE']
Split 2
    training:   ['SHRIMPLIN' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['ALEXANDER D' 'KIMZEY A']
Split 3
    training:   ['SHRIMPLIN' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['ALEXANDER D' 'NOLAN']
Split 4
    training:   ['SHRIMPLIN' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['ALEXANDER D' 'SHANKLE']
Split 5
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['CROSS H CATTLE' 'CHURCHMAN BIBLE']
Split 6
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['KIMZEY A' 'CHURCHMAN BIBLE']
Split 7
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['LUKE G U' 'CHURCHMAN BIBLE']
Split 8
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'NOLAN' 'Recruit F9']
    validation: ['NEWBY' 'CHURCHMAN BIBLE']
Split 9
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'Recruit F9' 'NEWBY']
    validation: ['NOLAN' 'CHURCHMAN BIBLE']
Split 10
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'NOLAN' 'NEWBY']
    validation: ['Recruit F9' 'CHURCHMAN BIBLE']
Split 11
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['SHANKLE' 'CHURCHMAN BIBLE']
Split 12
    training:   ['ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'NEWBY']
    validation: ['SHRIMPLIN' 'CHURCHMAN BIBLE']
Split 13
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['KIMZEY A' 'CROSS H CATTLE']
Split 14
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'NOLAN'
 'Recruit F9' 'CHURCHMAN BIBLE']
    validation: ['CROSS H CATTLE' 'NEWBY']
Split 15
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'NOLAN' 'NEWBY'
 'CHURCHMAN BIBLE']
    validation: ['CROSS H CATTLE' 'Recruit F9']
Split 16
    training:   ['ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'NOLAN' 'Recruit F9' 'NEWBY'
 'CHURCHMAN BIBLE']
    validation: ['SHRIMPLIN' 'CROSS H CATTLE']
Split 17
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['LUKE G U' 'KIMZEY A']
Split 18
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'CHURCHMAN BIBLE']
    validation: ['KIMZEY A' 'NEWBY']
Split 19
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE'
 'Recruit F9' 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['KIMZEY A' 'NOLAN']
Split 20
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['KIMZEY A' 'Recruit F9']
Split 21
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['SHANKLE' 'KIMZEY A']
Split 22
    training:   ['ALEXANDER D' 'SHANKLE' 'LUKE G U' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['SHRIMPLIN' 'KIMZEY A']
Split 23
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'Recruit F9' 'CHURCHMAN BIBLE']
    validation: ['NOLAN' 'NEWBY']
Split 24
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'Recruit F9' 'CHURCHMAN BIBLE']
    validation: ['SHANKLE' 'NEWBY']
Split 25
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['NOLAN' 'Recruit F9']
Split 26
    training:   ['ALEXANDER D' 'SHANKLE' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE'
 'Recruit F9' 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['SHRIMPLIN' 'NOLAN']
Split 27
    training:   ['SHRIMPLIN' 'ALEXANDER D' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['SHANKLE' 'Recruit F9']
Split 28
    training:   ['ALEXANDER D' 'LUKE G U' 'KIMZEY A' 'CROSS H CATTLE' 'NOLAN' 'Recruit F9'
 'NEWBY' 'CHURCHMAN BIBLE']
    validation: ['SHRIMPLIN' 'SHANKLE']

Classification parameters optimization

Let us perform the following steps for each set of parameters:

  • Select a data split.
  • Normalize features using a robust scaler.
  • Train the classifier on training data.
  • Test the trained classifier on validation data.
  • Repeat for all splits and average the F1 scores.

At the end of the loop, we select the classifier that maximizes the average F1 score on the validation set. Hopefully, this classifier should be able to generalize well on new data.


In [17]:
# Parameters search grid (uncomment parameters for full grid search... may take a lot of time)
N_grid = [100]  # [50, 100, 150]
M_grid = [10]  # [5, 10, 15]
S_grid = [25]  # [10, 25, 50, 75]
L_grid = [5] # [2, 3, 4, 5, 10, 25]
param_grid = []
for N in N_grid:
    for M in M_grid:
        for S in S_grid:
            for L in L_grid:
                param_grid.append({'N':N, 'M':M, 'S':S, 'L':L})

In [18]:
# Train and test a classifier
def train_and_test(X_tr, y_tr, X_v, well_v, param):
    
    # Feature normalization
    scaler = preprocessing.RobustScaler(quantile_range=(25.0, 75.0)).fit(X_tr)
    X_tr = scaler.transform(X_tr)
    X_v = scaler.transform(X_v)
    
    # Train classifier
    clf = OneVsOneClassifier(RandomForestClassifier(n_estimators=param['N'], criterion='entropy',
                             max_features=param['M'], min_samples_split=param['S'], min_samples_leaf=param['L'],
                             class_weight='balanced', random_state=0), n_jobs=-1)

    clf.fit(X_tr, y_tr)
    
    # Test classifier
    y_v_hat = clf.predict(X_v)
    
    # Clean isolated facies for each well
    for w in np.unique(well_v):
        y_v_hat[well_v==w] = medfilt(y_v_hat[well_v==w], kernel_size=5)
    
    return y_v_hat

In [19]:
# For each set of parameters
score_param = []
for param in param_grid:
    
    # For each data split
    score_split = []
    for split in split_list:
    
        # Remove padded rows
        split_train_no_pad = np.setdiff1d(split['train'], padded_rows)
        
        # Select training and validation data from current split
        X_tr = X_aug[split_train_no_pad, :]
        X_v = X_aug[split['val'], :]
        y_tr = y[split_train_no_pad]
        y_v = y[split['val']]
        
        # Select well labels for validation data
        well_v = well[split['val']]

        # Train and test
        y_v_hat = train_and_test(X_tr, y_tr, X_v, well_v, param)
        
        # Score
        score = f1_score(y_v, y_v_hat, average='micro')
        score_split.append(score)
        
    # Average score for this param
    score_param.append(np.mean(score_split))
    print('F1 score = %.3f %s' % (score_param[-1], param))
          
# Best set of parameters
best_idx = np.argmax(score_param)
param_best = param_grid[best_idx]
score_best = score_param[best_idx]
print('\nBest F1 score = %.3f %s' % (score_best, param_best))


F1 score = 0.562 {'S': 25, 'M': 10, 'L': 5, 'N': 100}

Best F1 score = 0.562 {'S': 25, 'M': 10, 'L': 5, 'N': 100}

Predict labels on test data

Let us now apply the selected classification technique to test data.


In [20]:
# Load data from file
test_data = pd.read_csv('../validation_data_nofacies.csv')

In [21]:
# Prepare training data
X_tr = X
y_tr = y

# Augment features
X_tr, padded_rows = augment_features(X_tr, well, depth)

# Removed padded rows
X_tr = np.delete(X_tr, padded_rows, axis=0)
y_tr = np.delete(y_tr, padded_rows, axis=0)

In [22]:
# Prepare test data
well_ts = test_data['Well Name'].values
depth_ts = test_data['Depth'].values
X_ts = test_data[feature_names].values

# Augment features
X_ts, padded_rows = augment_features(X_ts, well_ts, depth_ts)

In [23]:
# Predict test labels
y_ts_hat = train_and_test(X_tr, y_tr, X_ts, well_ts, param_best)

In [24]:
# Save predicted labels
test_data['Facies'] = y_ts_hat
test_data.to_csv('well_data_with_facies_try02.csv')

In [25]:
# Plot predicted labels
make_facies_log_plot(
    test_data[test_data['Well Name'] == 'STUART'],
    facies_colors=facies_colors)

make_facies_log_plot(
    test_data[test_data['Well Name'] == 'CRAWFORD'],
    facies_colors=facies_colors)
mpl.rcParams.update(inline_rc)