def calculate_rho_minmax(z_object=None, z_array=None, periods=None): """ Determine 2 arrays of Niblett-Bostick transformed aparent resistivities: minumum and maximum values for respective periods. Values are calculated from the 1D and 2D parts of an impedance tensor array Z. input: - Z (object or array) - periods (mandatory, if Z is just array) output: - n x 3 array, depth/rho_nb/angle for rho_nb max - n x 3 array, depth/rho_nb/angle for rho_nb min The calculation is carried out by : 1) Determine the dimensionality of the Z(T), discard all 3D parts 2) loop over periods * rotate Z and calculate app_res_NB for off-diagonal elements * find maximum and minimum values * write out respective depths and rho values Note: No propagation of errors implemented yet! """ #deal with inputs #if zobject: #z = z_object.z #periods = 1./z_object.freq #else: z = z_array periods = periods dimensions = MTge.dimensionality(z) angles = MTge.strike_angle(z) #reduce actual Z by the 3D layers: z2 = z[np.where(dimensions != 3)[0]] angles2 = angles[np.where(dimensions != 3)[0]] periods2 = periods[np.where(dimensions != 3)[0]] lo_nb_max = [] lo_nb_min = [] rotsteps = 360 rotangles = np.arange(rotsteps) * 180. / rotsteps for i, per in enumerate(periods2): z_curr = z2[i] temp_vals = np.zeros((rotsteps, 4)) for j, d in enumerate(rotangles): new_z = MTcc.rotatematrix_incl_errors(z_curr, d)[0] #print i,per,j,d res = MTz.z2resphi(new_z, per)[0] phs = MTz.z2resphi(new_z, per)[1] te_rho, te_depth = rhophi2rhodepth(res[0, 1], phs[0, 1], per) tm_rho, tm_depth = rhophi2rhodepth(res[1, 0], phs[1, 0], per) temp_vals[j, 0] = te_depth temp_vals[j, 1] = te_rho temp_vals[j, 2] = tm_depth temp_vals[j, 3] = tm_rho column = (np.argmax([np.max(temp_vals[:, 1]), np.max(temp_vals[:, 3])])) * 2 + 1 maxidx = np.argmax(temp_vals[:, column]) max_rho = temp_vals[maxidx, column] max_depth = temp_vals[maxidx, column - 1] max_ang = rotangles[maxidx] #alternative 1 min_column = (np.argmin( [np.max(temp_vals[:, 1]), np.max(temp_vals[:, 3])])) * 2 + 1 if max_ang <= 90: min_ang = max_ang + 90 else: min_ang = max_ang - 90 minidx = np.argmin(np.abs(rotangles - min_ang)) min_rho = temp_vals[minidx, min_column] min_depth = temp_vals[minidx, min_column - 1] lo_nb_max.append([max_depth, max_rho, max_ang]) lo_nb_min.append([min_depth, min_rho]) return np.array(lo_nb_max), np.array(lo_nb_min)
def find_distortion(z_object, lo_dims = None): """ find optimal distortion tensor from z object automatically determine the dimensionality over all frequencies, then find the appropriate distortion tensor D """ z_obj = z_object if lo_dims is None : lo_dims = MTge.dimensionality(z_object = z_obj) try: if len(lo_dims) != len(z_obj.z): lo_dims = MTge.dimensionality(z_object = z_obj) except: pass #dictionary of values that should be no distortion in case distortion #cannot be calculated for that component dis_dict = {(0,0):1, (0,1):0, (1,0):0, (1,1):1} lo_dis = [] lo_diserr = [] if 1 in lo_dims: idx_1 = np.where(np.array(lo_dims) == 1)[0] for idx in idx_1: realz = np.real(z_obj.z[idx]) imagz = np.imag(z_obj.z[idx]) mat1 = np.matrix([[0, -1],[1, 0]]) gr = np.sqrt(np.linalg.det(realz)) gi = np.sqrt(np.linalg.det(imagz)) lo_dis.append(1./gr*np.dot(realz,mat1)) lo_dis.append(1./gi*np.dot(imagz,mat1)) if z_obj.zerr is not None: #find errors of entries for calculating weights lo_diserr.append(1./gr*\ np.array([[np.abs(z_obj.zerr[idx][0,1]), np.abs(z_obj.zerr[idx][0,0])], [np.abs(z_obj.zerr[idx][1,1]), np.abs(z_obj.zerr[idx][1,0])]])) lo_diserr.append(1./gi*\ np.array([[np.abs(z_obj.zerr[idx][0,1]), np.abs(z_obj.zerr[idx][0,0])], [np.abs(z_obj.zerr[idx][1,1]), np.abs(z_obj.zerr[idx][1,0])]])) else: #otherwise go for evenly weighted average lo_diserr.append(np.ones((2, 2))) lo_diserr.append(np.ones((2, 2))) dis = np.identity(2) diserr = np.identity(2) for i in range(2): for j in range(2): try: dis[i,j], dummy = np.average(np.array([k[i, j] for k in lo_dis]), weights=np.array([1./(k[i,j])**2 for k in lo_diserr]), returned=True) diserr[i,j] = np.sqrt(1./dummy) #if the distortion came out as nan set it to an appropriate #value if np.nan_to_num(dis[i,j]) == 0: dis[i, j] = dis_dict[i, j] diserr[i, j] = dis_dict[i, j] except ZeroDivisionError: print ('Could not get distortion for dis[{0}, {1}]'.format( i, j)+' setting value to {0}'.format(dis_dict[i,j])) dis[i, j] = dis_dict[i, j] diserr[i, j] = dis_dict[i, j]*1e-6 return dis, diserr if 2 in lo_dims: idx_2 = np.where(np.array(lo_dims) == 2)[0] #follow bibby et al. 2005 first alternative: P = 1 P = 1 lo_strikes = MTge.strike_angle(z_object = z_obj) lo_tetms = [] lo_t = [] lo_tetm_errs =[] for idx in idx_2: mat = z_obj.z[idx] ang = -lo_strikes[idx][0] if np.isnan(ang): ang = 0. errmat = None if z_obj.zerr is not None: errmat = z_obj.zerr[idx] tetm_mat, tetm_err = MTcc.rotatematrix_incl_errors(mat, ang, inmatrix_err=errmat) lo_tetms.append(tetm_mat) lo_tetm_errs.append(tetm_err) realz = np.real(tetm_mat) imagz = np.imag(tetm_mat) lo_t.append(-4*P*realz[0,1]*realz[1,0]/np.linalg.det(realz) ) lo_t.append(-4*P*imagz[0,1]*imagz[1,0]/np.linalg.det(imagz) ) #since there is no 'wrong' solution by a different value of T, no #error is given/calculated for T ! try: #just add 0.1% for avoiding numerical issues in the squareroots #later on T = np.sqrt(max(lo_t))+0.001 except: T = 2 for idx in range(len(lo_tetms)): realz = np.real(lo_tetms[idx]) imagz = np.imag(lo_tetms[idx]) errmat = lo_tetm_errs[idx] sr = np.sqrt(T**2+4*P*realz[0, 1]*realz[1, 0]/np.linalg.det(realz)) si = np.sqrt(T**2+4*P*imagz[0, 1]*imagz[1, 0]/np.linalg.det(imagz)) par_r = 2*realz[0, 1]/(T-sr) orth_r = 2*realz[1, 0]/(T+sr) par_i = 2*imagz[0, 1]/(T-si) orth_i = 2*imagz[1, 0]/(T+si) mat2_r = np.matrix([[0, 1./orth_r], [1./par_r, 0]]) mat2_i = np.matrix([[0, 1./orth_i], [1./par_i ,0]]) lo_dis.append(np.dot(realz,mat2_r)) lo_dis.append(np.dot(imagz,mat2_i)) if z_obj.zerr is not None: #find errors of entries for calculating weights sigma_sr = np.sqrt((-(2*P*realz[0,1]*realz[1,0]*\ realz[1,1]*errmat[0,0])/\ (np.linalg.det(realz)**2*sr))**2+\ ((2*P*realz[0,0]*realz[1,0]*\ realz[1,1]*errmat[0,1])/\ (np.linalg.det(realz)**2*sr))**2+\ ((2*P*realz[0,0]* realz[0,1]*\ realz[1,1]*errmat[1,0])/\ (np.linalg.det(realz)**2*sr))**2 +\ (-(2*P*realz[0,1]* realz[1,0]*\ realz[0,0]*errmat[1,1])/\ (np.linalg.det(realz)**2*sr))**2) sigma_dr_11 = 0.5*sigma_sr sigma_dr_22 = 0.5*sigma_sr sigma_dr_12 = np.sqrt((mat2_r[0,1]/realz[0,0]*errmat[0,0])**2+\ (mat2_r[0,1]/realz[1,0]*errmat[1,0])**2+\ (0.5*realz[0,0]/realz[1,0]*sigma_sr)**2) sigma_dr_21 = np.sqrt((mat2_r[1,0]/realz[1,1]*errmat[1,1])**2+\ (mat2_r[1,0]/realz[0,1]*errmat[0,1])**2+\ (0.5*realz[1,1]/realz[0,1]*sigma_sr)**2) lo_diserr.append(np.array([[sigma_dr_11, sigma_dr_12], [sigma_dr_21, sigma_dr_22]])) sigma_si = np.sqrt((-(2*P*imagz[0,1]*imagz[1,0]*\ imagz[1,1]*errmat[0,0])/\ (np.linalg.det(imagz)**2*sr))**2+\ ((2*P*imagz[0,0]*imagz[1,0]*\ imagz[1,1]*errmat[0,1])/\ (np.linalg.det(imagz)**2*sr))**2+\ ((2*P*imagz[0,0]*imagz[0,1]*\ imagz[1,1]*errmat[1,0])/\ (np.linalg.det(imagz)**2*sr))**2+\ (-(2*P*imagz[0,1]*imagz[1,0]*\ imagz[0,0]*errmat[1,1])/\ (np.linalg.det(imagz)**2*sr))**2) sigma_di_11 = 0.5*sigma_si sigma_di_22 = 0.5*sigma_si sigma_di_12 = np.sqrt((mat2_i[0,1]/imagz[0,0]*errmat[0,0])**2+\ (mat2_i[0,1]/imagz[1,0]*errmat[1,0])**2+\ (0.5*imagz[0,0]/imagz[1,0]*sigma_si)**2) sigma_di_21 = np.sqrt((mat2_i[1,0]/imagz[1,1]*errmat[1,1])**2+\ (mat2_i[1,0]/imagz[0,1]*errmat[0,1])**2+\ (0.5*imagz[1,1]/imagz[0,1]*sigma_si)**2) lo_diserr.append(np.array([[sigma_di_11, sigma_di_12], [sigma_di_21, sigma_di_22]])) else: #otherwise go for evenly weighted average lo_diserr.append(np.ones((2, 2))) lo_diserr.append(np.ones((2, 2))) dis = np.zeros((2, 2)) diserr = np.zeros((2, 2)) for i in range(2): for j in range(2): dis[i, j], dummy = np.average(np.array([k[i, j] for k in lo_dis]), weights=np.array([1./(k[i,j])**2 for k in lo_diserr]), returned=True ) diserr[i, j] = np.sqrt(1./dummy) return dis, diserr #if only 3D, use identity matrix - no distortion calculated dis = np.identity(2) diserr = diserr = np.zeros((2, 2)) return dis, diserr
def calculate_rho_minmax(z_object = None, z_array = None, periods = None): """ Determine 2 arrays of Niblett-Bostick transformed aparent resistivities: minumum and maximum values for respective periods. Values are calculated from the 1D and 2D parts of an impedance tensor array Z. input: - Z (object or array) - periods (mandatory, if Z is just array) output: - n x 3 array, depth/rho_nb/angle for rho_nb max - n x 3 array, depth/rho_nb/angle for rho_nb min The calculation is carried out by : 1) Determine the dimensionality of the Z(T), discard all 3D parts 2) loop over periods * rotate Z and calculate app_res_NB for off-diagonal elements * find maximum and minimum values * write out respective depths and rho values Note: No propagation of errors implemented yet! """ #deal with inputs #if zobject: #z = z_object.z #periods = 1./z_object.freq #else: z = z_array periods = periods dimensions = MTge.dimensionality(z) angles = MTge.strike_angle(z) #reduce actual Z by the 3D layers: z2 = z[np.where(dimensions != 3)[0]] angles2 = angles[np.where(dimensions != 3)[0]] periods2 = periods[np.where(dimensions != 3)[0]] lo_nb_max = [] lo_nb_min = [] rotsteps = 360 rotangles = np.arange(rotsteps)*180./rotsteps for i,per in enumerate(periods2): z_curr = z2[i] temp_vals = np.zeros((rotsteps,4)) for jj,d in enumerate(rotangles): new_z = MTcc.rotatematrix_incl_errors(z_curr, d)[0] #print i,per,jj,d res = MTz.z2resphi(new_z,per)[0] phs = MTz.z2resphi(new_z,per)[1] te_rho, te_depth = rhophi2rhodepth(res[0,1], phs[0,1], per) tm_rho, tm_depth = rhophi2rhodepth(res[1,0], phs[1,0], per) temp_vals[jj,0] = te_depth temp_vals[jj,1] = te_rho temp_vals[jj,2] = tm_depth temp_vals[jj,3] = tm_rho column = (np.argmax([ np.max(temp_vals[:,1]), np.max(temp_vals[:,3])]))*2 + 1 maxidx = np.argmax(temp_vals[:,column]) max_rho = temp_vals[maxidx,column] max_depth = temp_vals[maxidx,column-1] max_ang = rotangles[maxidx] #alternative 1 min_column = (np.argmin([ np.max(temp_vals[:,1]), np.max(temp_vals[:,3])]))*2 + 1 if max_ang <= 90: min_ang = max_ang + 90 else: min_ang = max_ang - 90 minidx = np.argmin(np.abs(rotangles-min_ang)) min_rho = temp_vals[minidx,min_column] min_depth = temp_vals[minidx,min_column-1] lo_nb_max.append([max_depth, max_rho, max_ang]) lo_nb_min.append([min_depth, min_rho]) return np.array(lo_nb_max), np.array(lo_nb_min)
def find_distortion(z_object, g='det', num_freq=None, lo_dims=None): """ find optimal distortion tensor from z object automatically determine the dimensionality over all frequencies, then find the appropriate distortion tensor D Parameters ---------- **z_object** : mtpy.core.z object **g** : [ 'det' | '01' | '10 ] type of distortion correction *default* is 'det' **num_freq** : int number of frequencies to look for distortion from the index 0 *default* is None, meaning all frequencies are used **lo_dims** : list list of dimensions for each frequency *default* is None, meaning calculated from data Returns ------- **distortion** : np.ndarray(2, 2) distortion array all real values **distortion_err** : np.ndarray(2, 2) distortion error array Examples -------- :Estimate Distortion: :: >>> import mtpy.analysis.distortion as distortion >>> dis, dis_err = distortion.find_distortion(z_obj, num_freq=12) """ if num_freq is not None: if num_freq > z_object.freq.size: num_freq = z_object.freq.size print('Number of frequencies to sweep over is too high for z') print('setting num_freq to {0}'.format(num_freq)) else: num_freq = z_object.freq.size z_obj = MTz.Z(z_object.z[0:num_freq], z_object.z_err[0:num_freq], z_object.freq[0:num_freq]) g = 'det' dim_arr = MTge.dimensionality(z_object=z_obj) st_arr = -1 * MTge.strike_angle(z_object=z_obj)[:, 0] dis = np.zeros_like(z_obj.z, dtype=np.float) dis_err = np.ones_like(z_obj.z, dtype=np.float) #dictionary of values that should be no distortion in case distortion #cannot be calculated for that component rot_mat = np.matrix([[0, -1], [1, 0]]) for idx, dim in enumerate(dim_arr): if np.any(z_obj.z[idx] == 0.0 + 0.0j) == True: dis[idx] = np.identity(2) print('Found a zero in z at {0}, skipping'.format(idx)) continue if dim == 1: if g in ['01', '10']: gr = np.abs(z_obj.z.real[idx, int(g[0]), int(g[1])]) gi = np.abs(z_obj.z.imag[idx, int(g[0]), int(g[1])]) else: gr = np.sqrt(np.linalg.det(z_obj.z.real[idx])) gi = np.sqrt(np.linalg.det(z_obj.z.imag[idx])) dis[idx] = np.mean(np.array([ (1. / gr * np.dot(z_obj.z.real[idx], rot_mat)), (1. / gi * np.dot(z_obj.z.imag[idx], rot_mat)) ]), axis=0) if z_obj.z_err is not None: # find errors of entries for calculating weights gr_err = 1. / gr * np.abs(z_obj.z_err[idx]) gr_err[np.where(gr_err == 0.0)] = 1.0 gi_err = 1. / gi * np.abs(z_obj.z_err[idx]) gi_err[np.where(gi_err == 0.0)] = 1.0 dis_err[idx] = np.mean(np.array([gi_err, gr_err]), axis=0) elif dim == 2: P = 1 strike_ang = st_arr[idx] if np.isnan(strike_ang): strike_ang = 0.0 if z_obj.z_err is not None: err_arr = z_obj.z_err[idx] err_arr[np.where(err_arr == 0.0)] = 1.0 else: err_arr = None tetm_arr, tetm_err = MTcc.rotatematrix_incl_errors( z_obj.z[idx], strike_ang, inmatrix_err=err_arr) tetm_r = tetm_arr.real tetm_i = tetm_arr.imag t_arr_r = -4 * P * tetm_r[0, 1] * tetm_r[1, 0] / np.linalg.det(tetm_r) t_arr_i = -4 * P * tetm_i[0, 1] * tetm_i[1, 0] / np.linalg.det(tetm_i) try: T = np.sqrt(max([t_arr_r, t_arr_i])) + .001 except ValueError: T = 2 sr = np.sqrt(T**2 + 4 * P * tetm_r[0, 1] * tetm_r[1, 0] / np.linalg.det(tetm_r)) si = np.sqrt(T**2 + 4 * P * tetm_i[0, 1] * tetm_i[1, 0] / np.linalg.det(tetm_i)) par_r = 2 * tetm_r[0, 1] / (T - sr) orth_r = 2 * tetm_r[1, 0] / (T + sr) par_i = 2 * tetm_i[0, 1] / (T - si) orth_i = 2 * tetm_i[1, 0] / (T + si) mat2_r = np.matrix([[0, 1. / orth_r], [1. / par_r, 0]]) mat2_i = np.matrix([[0, 1. / orth_i], [1. / par_i, 0]]) avg_mat = np.mean(np.array( [np.dot(tetm_r, mat2_r), np.dot(tetm_i, mat2_i)]), axis=0) dis[idx] = avg_mat if err_arr is not None: # find errors of entries for calculating weights sigma_sr = np.sqrt((-(2 * P * tetm_r[0, 1] * tetm_r[1, 0] * \ tetm_r[1, 1] * err_arr[0, 0]) / \ (np.linalg.det(tetm_r) ** 2 * sr)) ** 2 + \ ((2 * P * tetm_r[0, 0] * tetm_r[1, 0] * tetm_r[1, 1] * err_arr[0, 1]) / (np.linalg.det(tetm_r) ** 2 * sr)) ** 2 + \ ((2 * P * tetm_r[0, 0] * tetm_r[0, 1] * tetm_r[1, 1] * err_arr[1, 0]) / \ (np.linalg.det(tetm_r) ** 2 * sr)) ** 2 + \ (-(2 * P * tetm_r[0, 1] * tetm_r[1, 0] * \ tetm_r[0, 0] * err_arr[1, 1]) / \ (np.linalg.det(tetm_r) ** 2 * sr)) ** 2) sigma_dr_11 = 0.5 * sigma_sr sigma_dr_22 = 0.5 * sigma_sr sigma_dr_12 = np.sqrt((mat2_r[0, 1] / tetm_r[0, 0] * err_arr[0, 0]) ** 2 + \ (mat2_r[0, 1] / tetm_r[1, 0] * err_arr[1, 0]) ** 2 + \ (0.5 * tetm_r[0, 0] / tetm_r[1, 0] * sigma_sr) ** 2) sigma_dr_21 = np.sqrt((mat2_r[1, 0] / tetm_r[1, 1] * err_arr[1, 1]) ** 2 + \ (mat2_r[1, 0] / tetm_r[0, 1] * err_arr[0, 1]) ** 2 + \ (0.5 * tetm_r[1, 1] / tetm_r[0, 1] * sigma_sr) ** 2) dis_err_r = np.array([[sigma_dr_11, sigma_dr_12], [sigma_dr_21, sigma_dr_22]]) sigma_si = np.sqrt((-(2 * P * tetm_i[0, 1] * tetm_i[1, 0] * \ tetm_i[1, 1] * err_arr[0, 0]) / \ (np.linalg.det(tetm_i) ** 2 * sr)) ** 2 + \ ((2 * P * tetm_i[0, 0] * tetm_i[1, 0] * \ tetm_i[1, 1] * err_arr[0, 1]) / \ (np.linalg.det(tetm_i) ** 2 * sr)) ** 2 + \ ((2 * P * tetm_i[0, 0] * tetm_i[0, 1] * \ tetm_i[1, 1] * err_arr[1, 0]) / \ (np.linalg.det(tetm_i) ** 2 * sr)) ** 2 + \ (-(2 * P * tetm_i[0, 1] * tetm_i[1, 0] * \ tetm_i[0, 0] * err_arr[1, 1]) / \ (np.linalg.det(tetm_i) ** 2 * sr)) ** 2) sigma_di_11 = 0.5 * sigma_si sigma_di_22 = 0.5 * sigma_si sigma_di_12 = np.sqrt((mat2_i[0, 1] / tetm_i[0, 0] * err_arr[0, 0]) ** 2 + \ (mat2_i[0, 1] / tetm_i[1, 0] * err_arr[1, 0]) ** 2 + \ (0.5 * tetm_i[0, 0] / tetm_i[1, 0] * sigma_si) ** 2) sigma_di_21 = np.sqrt((mat2_i[1, 0] / tetm_i[1, 1] * err_arr[1, 1]) ** 2 + \ (mat2_i[1, 0] / tetm_i[0, 1] * err_arr[0, 1]) ** 2 + \ (0.5 * tetm_i[1, 1] / tetm_i[0, 1] * sigma_si) ** 2) dis_err_i = np.array([[sigma_di_11, sigma_di_12], [sigma_di_21, sigma_di_22]]) dis_err[idx] = np.mean(np.array([dis_err_r, dis_err_i])) else: dis[idx] = np.identity(2) nonzero_idx = np.array(list(set(np.nonzero(dis)[0]))) dis_avg, weights_sum = np.average(dis[nonzero_idx], axis=0, weights=(1. / dis_err[nonzero_idx])**2, returned=True) dis_avg_err = np.sqrt(1. / weights_sum) return dis_avg, dis_avg_err
def find_distortion(z_object, g ='det', num_freq=None, lo_dims=None): """ find optimal distortion tensor from z object automatically determine the dimensionality over all frequencies, then find the appropriate distortion tensor D Arguments ------------- **z_object** : mtpy.core.z object **g** : [ 'det' | '01' | '10 ] type of distortion correction *default* is 'det' **num_freq** : int number of frequencies to look for distortion from the index 0 *default* is None, meaning all frequencies are used **lo_dims** : list list of dimensions for each frequency *default* is None, meaning calculated from data Returns --------- **distortion** : np.ndarray(2, 2) distortion array all real values **distortion_err** : np.ndarray(2, 2) distortion error array Example: --------- :Estimate Distortion: :: >>> import mtpy.analysis.distortion as distortion >>> dis, dis_err = distortion.find_distortion(z_obj, num_freq=12) """ z_obj = copy.deepcopy(z_object) if num_freq is not None: if num_freq > z_obj.freq.size: num_freq = z_obj.freq.size print 'Number of frequencies to sweep over is too high for z' print 'setting num_freq to {0}'.format(num_freq) else: num_freq = z_obj.freq.size z_obj.z = z_obj.z[0:num_freq] z_obj.z_err = z_obj.z_err[0:num_freq] z_obj.freq = z_obj.freq[0:num_freq] g = 'det' dim_arr = MTge.dimensionality(z_object=z_obj) st_arr = -1*MTge.strike_angle(z_object=z_obj)[:, 0] dis = np.zeros_like(z_obj.z, dtype=np.float) dis_err = np.ones_like(z_obj.z, dtype=np.float) #dictionary of values that should be no distortion in case distortion #cannot be calculated for that component rot_mat = np.matrix([[0, -1], [1, 0]]) for idx, dim in enumerate(dim_arr): if np.any(z_obj.z[idx] == 0.0+0.0j) == True: dis[idx] = np.identity(2) print 'Found a zero in z at {0}, skipping'.format(idx) continue if dim == 1: if g in ['01', '10']: gr = np.abs(z_obj.z.real[idx, int(g[0]), int(g[1])]) gi = np.abs(z_obj.z.imag[idx, int(g[0]), int(g[1])]) else: gr = np.sqrt(np.linalg.det(z_obj.z.real[idx])) gi = np.sqrt(np.linalg.det(z_obj.z.imag[idx])) dis[idx] = np.mean(np.array([(1./gr*np.dot(z_obj.z.real[idx], rot_mat)), (1./gi*np.dot(z_obj.z.imag[idx], rot_mat))]), axis=0) if z_obj.z_err is not None: #find errors of entries for calculating weights gr_err = 1./gr*np.abs(z_obj.z_err[idx]) gr_err[np.where(gr_err == 0.0)] = 1.0 gi_err = 1./gi*np.abs(z_obj.z_err[idx]) gi_err[np.where(gi_err == 0.0)] = 1.0 dis_err[idx] = np.mean(np.array([gi_err, gr_err]), axis=0) elif dim == 2: P = 1 strike_ang = st_arr[idx] if np.isnan(strike_ang): strike_ang = 0.0 if z_obj.z_err is not None: err_arr = z_obj.z_err[idx] err_arr[np.where(err_arr == 0.0)] = 1.0 else: err_arr = None tetm_arr, tetm_err = MTcc.rotatematrix_incl_errors(z_obj.z[idx], strike_ang, inmatrix_err=err_arr) tetm_r = tetm_arr.real tetm_i = tetm_arr.imag t_arr_r = -4*P*tetm_r[0, 1]*tetm_r[1, 0]/np.linalg.det(tetm_r) t_arr_i = -4*P*tetm_i[0, 1]*tetm_i[1, 0]/np.linalg.det(tetm_i) try: T = np.sqrt(max([t_arr_r, t_arr_i]))+.001 except ValueError: T = 2 sr = np.sqrt(T**2+4*P*tetm_r[0, 1]*tetm_r[1, 0]/np.linalg.det(tetm_r)) si = np.sqrt(T**2+4*P*tetm_i[0, 1]*tetm_i[1, 0]/np.linalg.det(tetm_i)) par_r = 2*tetm_r[0, 1]/(T-sr) orth_r = 2*tetm_r[1, 0]/(T+sr) par_i = 2*tetm_i[0, 1]/(T-si) orth_i = 2*tetm_i[1, 0]/(T+si) mat2_r = np.matrix([[0, 1./orth_r], [1./par_r, 0]]) mat2_i = np.matrix([[0, 1./orth_i], [1./par_i ,0]]) avg_mat = np.mean(np.array([np.dot(tetm_r, mat2_r), np.dot(tetm_i, mat2_i)]), axis=0) dis[idx] = avg_mat if err_arr is not None: #find errors of entries for calculating weights sigma_sr = np.sqrt((-(2*P*tetm_r[0,1]*tetm_r[1,0]*\ tetm_r[1,1]*err_arr[0,0])/\ (np.linalg.det(tetm_r)**2*sr))**2+\ ((2*P*tetm_r[0,0]*tetm_r[1,0]*\ tetm_r[1,1]*err_arr[0,1])/\ (np.linalg.det(tetm_r)**2*sr))**2+\ ((2*P*tetm_r[0,0]* tetm_r[0,1]*\ tetm_r[1,1]*err_arr[1,0])/\ (np.linalg.det(tetm_r)**2*sr))**2 +\ (-(2*P*tetm_r[0,1]* tetm_r[1,0]*\ tetm_r[0,0]*err_arr[1,1])/\ (np.linalg.det(tetm_r)**2*sr))**2) sigma_dr_11 = 0.5*sigma_sr sigma_dr_22 = 0.5*sigma_sr sigma_dr_12 = np.sqrt((mat2_r[0,1]/tetm_r[0,0]*err_arr[0,0])**2+\ (mat2_r[0,1]/tetm_r[1,0]*err_arr[1,0])**2+\ (0.5*tetm_r[0,0]/tetm_r[1,0]*sigma_sr)**2) sigma_dr_21 = np.sqrt((mat2_r[1,0]/tetm_r[1,1]*err_arr[1,1])**2+\ (mat2_r[1,0]/tetm_r[0,1]*err_arr[0,1])**2+\ (0.5*tetm_r[1,1]/tetm_r[0,1]*sigma_sr)**2) dis_err_r = np.array([[sigma_dr_11, sigma_dr_12], [sigma_dr_21, sigma_dr_22]]) sigma_si = np.sqrt((-(2*P*tetm_i[0,1]*tetm_i[1,0]*\ tetm_i[1,1]*err_arr[0,0])/\ (np.linalg.det(tetm_i)**2*sr))**2+\ ((2*P*tetm_i[0,0]*tetm_i[1,0]*\ tetm_i[1,1]*err_arr[0,1])/\ (np.linalg.det(tetm_i)**2*sr))**2+\ ((2*P*tetm_i[0,0]*tetm_i[0,1]*\ tetm_i[1,1]*err_arr[1,0])/\ (np.linalg.det(tetm_i)**2*sr))**2+\ (-(2*P*tetm_i[0,1]*tetm_i[1,0]*\ tetm_i[0,0]*err_arr[1,1])/\ (np.linalg.det(tetm_i)**2*sr))**2) sigma_di_11 = 0.5*sigma_si sigma_di_22 = 0.5*sigma_si sigma_di_12 = np.sqrt((mat2_i[0,1]/tetm_i[0,0]*err_arr[0,0])**2+\ (mat2_i[0,1]/tetm_i[1,0]*err_arr[1,0])**2+\ (0.5*tetm_i[0,0]/tetm_i[1,0]*sigma_si)**2) sigma_di_21 = np.sqrt((mat2_i[1,0]/tetm_i[1,1]*err_arr[1,1])**2+\ (mat2_i[1,0]/tetm_i[0,1]*err_arr[0,1])**2+\ (0.5*tetm_i[1,1]/tetm_i[0,1]*sigma_si)**2) dis_err_i = np.array([[sigma_di_11, sigma_di_12], [sigma_di_21, sigma_di_22]]) dis_err[idx] = np.mean(np.array([dis_err_r, dis_err_i])) else: dis[idx] = np.identity(2) nonzero_idx = np.array(list(set(np.nonzero(dis)[0]))) dis_avg, weights_sum = np.average(dis[nonzero_idx], axis=0, weights=(1./dis_err[nonzero_idx])**2, returned=True) dis_avg_err = np.sqrt(1./weights_sum) return dis_avg, dis_avg_err
def rotate(self, alpha): """ Rotate PT array. Change the rotation angles attribute respectively. Rotation angle must be given in degrees. All angles are referenced to geographic North, positive in clockwise direction. (Mathematically negative!) In non-rotated state, X refs to North and Y to East direction. """ if self._pt is None : print 'pt-array is "None" - I cannot rotate that' return if np.iterable(self.rotation_angle) == 0: self.rotation_angle = np.array([self.rotation_angle for ii in self.pt]) #check for iterable list/set of angles - if so, it must have length 1 #or same as len(pt): if np.iterable(alpha) == 0: try: degreeangle = float(alpha%360) except: print '"Angle" must be a valid number (in degrees)' return #make an n long list of identical angles lo_angles = [degreeangle for i in self.pt] else: if len(alpha) == 1: try: degreeangle = float(alpha%360) except: print '"Angle" must be a valid number (in degrees)' return #make an n long list of identical angles lo_angles = [degreeangle for i in self.pt] else: try: lo_angles = [ float(i%360) for i in alpha] except: print '"Angles" must be valid numbers (in degrees)' return self.rotation_angle = list((np.array(lo_angles) + \ np.array(self.rotation_angle))%360) if len(lo_angles) != len(self._pt): print 'Wrong number Number of "angles" - need %i '%(len(self._pt)) self.rotation_angle = 0. return pt_rot = copy.copy(self._pt) pt_err_rot = copy.copy(self._pt_err) for idx_freq in range(len(self._pt)): angle = lo_angles[idx_freq] if np.isnan(angle): angle = 0. if self.pt_err is not None: pt_rot[idx_freq], pt_err_rot[idx_freq] = MTcc.rotatematrix_incl_errors(self.pt[idx_freq,:,:], angle, self.pt_err[idx_freq,:,:]) else: pt_rot[idx_freq], pt_err_rot = MTcc.rotatematrix_incl_errors(self.pt[idx_freq,:,:], angle) #--> set the rotated tensors as the current attributes self._pt = pt_rot self._pt_err = pt_err_rot
def rotate(self,alpha): """ Rotate PT array. Change the rotation angles attribute respectively. Rotation angle must be given in degrees. All angles are referenced to geographic North, positive in clockwise direction. (Mathematically negative!) In non-rotated state, X refs to North and Y to East direction. """ if self._pt is None : print 'pt-array is "None" - I cannot rotate that' return if np.iterable(self.rotation_angle) == 0: self.rotation_angle = np.array([self.rotation_angle for ii in self.pt]) #check for iterable list/set of angles - if so, it must have length 1 #or same as len(pt): if np.iterable(alpha) == 0: try: degreeangle = float(alpha%360) except: print '"Angle" must be a valid number (in degrees)' return #make an n long list of identical angles lo_angles = [degreeangle for i in self.pt] else: if len(alpha) == 1: try: degreeangle = float(alpha%360) except: print '"Angle" must be a valid number (in degrees)' return #make an n long list of identical angles lo_angles = [degreeangle for i in self.pt] else: try: lo_angles = [ float(i%360) for i in alpha] except: print '"Angles" must be valid numbers (in degrees)' return self.rotation_angle = list((np.array(lo_angles) + \ np.array(self.rotation_angle))%360) if len(lo_angles) != len(self._pt): print 'Wrong number Number of "angles" - need %i '%(len(self._pt)) self.rotation_angle = 0. return pt_rot = copy.copy(self._pt) pterr_rot = copy.copy(self._pt_err) for idx_freq in range(len(self._pt)): angle = lo_angles[idx_freq] if np.isnan(angle): angle = 0. if self.pt_err is not None: pt_rot[idx_freq], pterr_rot[idx_freq] = MTcc.rotatematrix_incl_errors(self.pt[idx_freq,:,:], angle, self.pt_err[idx_freq,:,:]) else: pt_rot[idx_freq], pterr_rot = MTcc.rotatematrix_incl_errors(self.pt[idx_freq,:,:], angle) #--> set the rotated tensors as the current attributes self._pt = pt_rot self._pt_err = pterr_rot